Pattern grading is determined based on measurement feedback from the printed substrate.

Abstract

Methods for training a process model and determining a classification of simulated patterns (e.g., corresponding to hot spots) are described herein. The method for training a machine learning model of a patterning process involves obtaining a training data set, the training data set comprising: i ) a simulated pattern associated with a mask pattern to be printed on a substrate, ( ii ) inspection data of a printed pattern imaged on a substrate using a mask pattern, and ( iii ) measured values ​​of parameters of a patterning process applied during imaging of a mask pattern on a substrate; training a machine learning model based on the training data set to predict differences in characteristics of simulated and printed patterns. The trained machine learning model is also used to determine the classification of hot spots. In another approach, a model is trained based on the measured data to predict the classification of hot spots.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Application No. 62 / 785,977, filed December 28, 2018, which is incorporated herein by reference in its entirety. Technical Field

[0003] The present disclosure relates to a technique for improving the performance of a device manufacturing process. The technique can be used in conjunction with a lithography apparatus. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. For example, a lithographic apparatus may be used to manufacture integrated circuits (ICs). In this case, a patterning device (alternatively referred to as a mask or reticle) may be used to generate a circuit pattern corresponding to a single layer of the IC, and the pattern may be imaged onto a target portion (e.g., including a portion of 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 contain 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 onto the target portion at once, and so-called scanners, in which each target portion is irradiated by synchronously scanning the substrate in a given direction (the "scanning" direction) through a beam scanning pattern while being parallel or antiparallel to that direction.

[0005] Before the circuit pattern is transferred from the pattern forming device to the substrate, the substrate may be subjected to various processes such as primer coating, resist coating, and soft baking. After exposure, the substrate may be subjected to other processes such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. This series 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 intended to complete a single layer of the device. If several layers are required in the device, the entire process or a variation thereof is repeated for each layer. Eventually, a device will appear in each target portion on the substrate. These devices are then separated from each other by techniques such as cutting or sawing, so that the individual devices can be mounted on a carrier, connected to pins, and so on.

[0006] Therefore, manufacturing devices such as semiconductor devices typically involves processing a substrate (e.g., a semiconductor wafer) using a variety of manufacturing processes to form various features and multiple layers of the device. Such layers and features are typically manufactured and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be manufactured on multiple dies on a substrate and then separated into individual devices. The device manufacturing process can be considered a patterning process. The patterning process involves a patterning step for transferring a pattern on a pattern forming device to a substrate, such as optical and / or nanoimprint lithography using a pattern forming device in a lithographic apparatus, and typically but optionally involves one or more related pattern processing steps, such as resist development by a developing apparatus, baking the substrate using a baking tool, etching using a pattern using an etching apparatus, and the like. Summary of the invention

[0007] In one embodiment, a method for training a machine learning model of a patterning process is provided. The method includes: obtaining a training data set, the training data set including: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on a substrate using the mask pattern, and (iii) measured values ​​of parameters of a patterning process applied during imaging of the mask pattern on the substrate; training a machine learning model based on the training data set via a processor to predict differences in characteristics of the simulated pattern and the printed pattern.

[0008] In addition, in one embodiment, a method for correcting a characteristic of a simulated pattern of a patterning process is provided. The method involves: determining a simulated pattern and a characteristic of the simulated pattern via a simulated patterning process model; determining a characteristic adjustment value of the characteristic of the simulated pattern via a trained machine learning model; and correcting the characteristic of the simulated pattern based on the characteristic adjustment value via a processor.

[0009] In addition, in one embodiment, a method of training a machine learning model is provided, the machine learning model being configured to predict a grade of a set of simulated patterns for a patterning process. The method involves: obtaining (i) a set of simulated patterns corresponding to a set of mask patterns, (ii) defect data of a set of printed patterns imaged on a substrate using the set of mask patterns, and (iii) a sampling plan associated with the substrate imaged using the set of mask patterns; and training the machine learning model based on the defect data and the sampling plan via a processor, such that the machine learning model is configured to predict a grade of the set of simulated patterns that matches a reference grade based on the defect data.

[0010] In addition, in one embodiment, a method for determining a ranking of a set of simulated patterns of a patterning process is provided. The method involves: adjusting a characteristic of at least one simulated pattern in the set of simulated patterns via a first machine learning model; determining a subset of simulated patterns based on the adjusted characteristic of at least one simulated pattern via a processor; and determining a ranking of at least one simulated pattern in the subset of simulated patterns via a second machine learning model.

[0011] Furthermore, in one embodiment, a computer program product is provided, the computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the above method when executed by a computer system. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 schematically depicts a lithographic apparatus according to an embodiment;

[0013] Figure 2 schematically depicts an embodiment of a lithography cell or cluster according to one embodiment;

[0014] Figure 3 A flow chart showing a method of determining the presence of defects in a lithography process according to one embodiment;

[0015] Figure 4A shows an example ranking of hot spots assuming an ideal or perfect patterning process model according to one embodiment;

[0016] Figure 4B shows an example ranking of hot spots based on a simulated pattern produced by an existing patterning process model according to one embodiment;

[0017] Figure 5 shows values ​​of simulated CD of a simulated pattern as a function of focus compared to measured CD for FEM conditions according to one embodiment;

[0018] Figure 6 is a flow chart of a method for training a machine learning model of a patterning process according to one embodiment;

[0019] Figure 7 According to one embodiment, a method for Figure 6 A flow chart of a method for correcting the characteristics of a simulated pattern of a patterning process using a trained machine learning model;

[0020] Fig. 8A , 8B and 8C illustrate an example simulation pattern generated during simulation of a patterning process model according to one embodiment;

[0021] Fig. 9A method for using the Figure 6 An example of a machine learning model: Convolutional Neural Network (CNN);

[0022] Fig. 10A An example of grading hot spots based on simulated patterns generated by an existing patterning process model according to one embodiment is shown;

[0023] Fig. 10B According to one embodiment, a Figure 6 An example of hotspot grading using a corrected simulated pattern of a trained machine learning model;

[0024] Fig.11 is a flow chart of a method according to one embodiment for training another machine learning model configured to predict a ranking of a set of simulated patterns of a patterning process;

[0025] Fig.12 is a flowchart of a method according to an embodiment, the method is used based on Figure 6 First train a machine learning model and Fig.11 a second training a machine learning model to determine a ranking of a set of simulated patterns of a patterning process;

[0026] Fig.13 According to one embodiment, a Fig.11 Example grading obtained using a machine learning model and associated defect counts;

[0027] Fig.14A and 14B An example of a ranking algorithm for determining hotspot rankings according to one embodiment is shown;

[0028] Fig.15 schematically depicts an example inspection apparatus and metrology technique according to one embodiment;

[0029] Fig.16 schematically depicts an example inspection device according to one embodiment;

[0030] Fig.17 shows the relationship between the illumination point of an inspection device and a measurement target according to one embodiment;

[0031] Fig.18 schematically depicts a process of deriving a plurality of variables of interest based on measurement data according to one embodiment;

[0032] Fig.19 schematically depicts an embodiment of a scanning electron microscope (SEM) according to one embodiment;

[0033] Fig. 20schematically depicts an embodiment of an electron beam inspection apparatus according to one embodiment;

[0034] Fig.21 shows an example defect on a printed substrate according to one embodiment;

[0035] Fig. 22 depicts an example flow chart for modeling and / or simulating at least a portion of a patterning process according to one embodiment;

[0036] Fig.23 is a block diagram of an example computer system according to one embodiment;

[0037] Fig.24 is a schematic diagram of an extreme ultraviolet (EUV) lithography projection apparatus according to one embodiment;

[0038] Fig.25 According to an embodiment Fig.24 A more detailed view of the devices in the

[0039] Fig.26 According to an embodiment Fig.24 and Fig.25 A more detailed view of the source collector module of a device. DETAILED DESCRIPTION

[0040] Before describing the embodiments in detail, it is helpful to present an example environment in which the embodiments may be implemented.

[0041] Figure 1 An embodiment of a lithographic apparatus LA is schematically depicted. The apparatus comprises: - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV radiation or DUV radiation); - a support structure (e.g. mask table) MT configured to support a patterning device (e.g. mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to certain parameters; - a substrate table (e.g. wafer stage) WT (e.g. WTa, WTb or both) configured to hold a substrate (e.g. a wafer coated with resist) W and connected to a second positioner PW configured to accurately position the substrate according to certain parameters; and - a projection system (e.g. refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g. comprising one or more dies and commonly referred to as a field) of the substrate W, the projection system being supported on a reference frame (RF).

[0042] As depicted here, the device is transmissive (eg, employing a transmissive mask). Alternatively, the device may be reflective (eg, employing a programmable mirror array of the type described above, or employing a reflective mask).

[0043] 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 this case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL with the help of a beam delivery system BD comprising, for example, suitable directional mirrors and / or a beam expander. In other cases, the source may be an integral part of the apparatus, for example when the source is a mercury lamp. If desired, the source SO and the illuminator IL together with the beam delivery system BD may be referred to as a radiation system.

[0044] The illuminator IL may vary the intensity distribution of the beam. The illuminator may be arranged to limit the radial extent of the radiation beam so that the intensity distribution is non-zero within an annular region in a pupil plane of the illuminator IL. Additionally or alternatively, the illuminator IL may be operable to limit the distribution of the beam in the pupil plane so that the intensity distribution is non-zero in a plurality of equally spaced sectors in the pupil plane. The intensity distribution of the radiation beam in the pupil plane of the illuminator IL may be referred to as an illumination pattern.

[0045] Therefore, the illuminator IL may include an adjuster AM configured to adjust the (angular / spatial) intensity distribution of the beam. Typically, at least the outer and / or inner radial extent (typically referred to as outer σ and inner σ, respectively) of the intensity distribution in the pupil plane of the illuminator can be adjusted. The illuminator IL may be operable to change the angular distribution of the beam. For example, the illuminator may be operable to change the number and angular extent of sectors in the pupil plane in which the intensity distribution is not zero. By adjusting the intensity distribution of the beam in the pupil plane of the illuminator, different illumination modes may be achieved. For example, by limiting the radial and angular extent of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution may have a multipole distribution, such as, for example, a dipole, quadrupole or hexapole distribution. The desired illumination mode may be obtained, for example, by inserting an optical device providing the illumination mode into the illuminator IL or by using a spatial light modulator to obtain the desired illumination mode.

[0046] The illuminator IL may be operable to change the polarization of the beam and may be operable to adjust the polarization using the adjuster AM. The polarization state of the radiation beam over the entire pupil plane of the illuminator IL may be referred to as a polarization mode. The use of different polarization modes may allow greater contrast to be achieved in the image formed on the substrate W. The radiation beam may be unpolarized. Alternatively, the illuminator may be arranged to linearly polarize the radiation beam. The polarization direction of the radiation beam may vary over the entire pupil plane of the illuminator IL. In different regions in the pupil plane of the illuminator IL, the polarization direction of the radiation may be different. The polarization state of the radiation may be selected according to the illumination mode. For a multipolar illumination mode, the polarization of each pole of the radiation beam may be generally perpendicular to the position vector of the pole in the pupil plane of the illuminator IL. For example, for a dipole illumination mode, the radiation may be linearly polarized in a direction substantially perpendicular to a line of two opposing sectors bisecting the dipole. The radiation beam may be polarized in one of two different orthogonal directions, which may be referred to as X polarization and Y polarization states. For a quadrupole illumination mode, the radiation in the sector of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the sector. This polarization mode may be referred to as XY polarization. Similarly, for a hexapole illumination mode, the radiation in the sector of each pole may be linearly polarized in a direction substantially perpendicular to a line bisecting the sector. This polarization mode may be referred to as TE polarization.

[0047] Furthermore, the illuminator IL typically includes various other components, such as an integrator IN and a condenser CO. The illumination system may include various types of optical components for directing, shaping or controlling radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof.

[0048] The illuminator thus provides a conditioned radiation beam B having a desired uniformity and intensity distribution in its cross-section.

[0049] The support structure MT supports the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions (such as, for example, whether the patterning device is held in a vacuum environment). The support structure may use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be, for example, a frame or a stage, which may be fixed or movable as required. The support structure may ensure that the patterning device is in a desired position, for example relative to a projection system. Any use of the term "reticle" or "mask" herein may be considered synonymous with the more general term "patterning device".

[0050] The term "patterning device" as used herein should be broadly interpreted as referring to any device that can be used to apply a pattern in a target portion of a substrate. In one embodiment, the patterning device is any device that can be used to impart a pattern to a cross-section of a 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 produced in the target portion, such as an integrated circuit.

[0051] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary, alternating phase shift, and attenuated phase shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam, which is reflected by the matrix of mirrors.

[0052] The term "projection system" as used herein should be broadly interpreted to cover any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, depending on 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".

[0053] The projection system PS has an optical transfer function that may be inhomogeneous, which affects the pattern imaged onto the substrate W. For non-polarized radiation, this effect can be well described by two scalar diagrams that describe the transmission (apodization) and relative phase (aberration) of the radiation exiting the projection system PS as a function of its position in the pupil plane. These scalar diagrams (which may be referred to as transmission diagrams and relative phase diagrams) can be expressed as linear combinations of a complete set of basis functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials defined on the unit circle. The determination of each scalar diagram may involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients may be determined by computing the inner product of the measured scalar diagrams of each Zernike polynomial in turn and dividing it by the square of the norm of that Zernike polynomial.

[0054] The transmission diagram and the relative phase diagram are field and system dependent. That is, in general, each projection system PS will have a different Zernike expansion for each field point (i.e. for each spatial position in its image plane). The relative phase of the projection system PS in its pupil plane can be determined, for example, by projecting radiation from a point source in the object plane of the projection system PS (i.e. the plane of the patterning device MA) through the projection system PS and measuring the wavefront (i.e. the locus of points with the same phase) using a shearing interferometer. One type of shearing interferometer is a common path interferometer and therefore, advantageously, no auxiliary reference beam is required to measure the wavefront. The shearing interferometer may comprise a diffraction grating (e.g. a two-dimensional grid) in the image plane of the projection system (i.e. the substrate table WT) and a detector arranged to detect an interference pattern in a plane conjugate to the pupil plane of the projection system PS. The interference pattern is related to the derivative of the phase of the radiation relative to a coordinate in the pupil plane in the shear direction. The detector may comprise an array of sensing elements such as, for example, a charge coupled device (CCD).

[0055] The projection system PS of the lithographic apparatus may not produce visible fringes, and therefore the accuracy of the wavefront determination may be enhanced using phase stepping techniques such as, for example, moving a diffraction grating. Stepping may be performed in the plane of the diffraction grating and in a direction perpendicular to the scanning direction of the measurement. The stepping range may be one grating period, and at least three (evenly distributed) phase steps may be used. Thus, for example, three scanning measurements may be performed in the y-direction, each for a different position in the x-direction. Such stepping of the diffraction grating effectively converts phase changes into intensity changes, so that phase information can be determined. The grating may be stepped in a direction perpendicular to the diffraction grating (z-direction) to calibrate the detector.

[0056] The diffraction grating may be scanned sequentially in two perpendicular directions, which may coincide with the axes (x and y) of the coordinate system of the projection system PS or may be at an angle such as 45 degrees to these axes. The scan may be performed over an integer number of grating periods (e.g. one grating period). The scan averages the phase variations in one direction to allow reconstruction of the phase variations in the other direction. This allows the wavefront to be determined as a function of the two directions.

[0057] The transmission (apodization) of the projection system PS in its pupil plane can be determined, for example, by projecting radiation through the projection system PS from a point source in the object plane of the projection system PS (i.e. the plane of the patterning device MA) and measuring the intensity of the radiation in a plane conjugate to the pupil plane of the projection system PS using a detector. The same detectors as used for measuring the wavefront to determine aberrations can be used.

[0058] The projection system PS may include multiple optical (e.g., lens) elements and may also include an adjustment mechanism AM configured to adjust one or more optical elements to correct aberrations (phase changes in the entire pupil plane throughout the field). To achieve this, the adjustment mechanism may be operable to manipulate one or more optical (e.g., lens) elements within the projection system PS in one or more different ways. The projection system may have a coordinate system in which its optical axis extends in the z direction. The adjustment mechanism may be operable to perform any combination of the following: displacing one or more optical elements; tilting one or more optical elements; and / or deforming one or more optical elements. The displacement of the optical element may be in any direction (x, y, z, or a combination thereof). The tilting of the optical element is typically performed outside the plane perpendicular to the optical axis by rotating about an axis in the x and / or y direction, but for non-rotationally symmetric aspheric optical elements, rotation about the z axis may be possible. The deformation of the optical element may include low-frequency shapes (e.g., astigmatism) and / or high-frequency shapes (e.g., free-form aspheric surfaces). The deformation of the optical element may be performed, for example, by applying a force on one or more sides of the optical element using one or more actuators and / or by heating selected one or more regions of the optical element using one or more heating elements. In general, it may not be possible to adjust the projection system PS to correct for apodization (variation of transmission across the pupil plane). When designing a patterning device (e.g., mask) MA for the lithographic apparatus LA, a transmission map of the projection system PS may be used. Using computational lithography techniques, the patterning device MA may be designed to at least partially correct for apodization.

[0059] The lithographic apparatus may be of a type having two (dual stage) or more work tables (e.g. two or more substrate tables WTa, WTb, two or more patterning device tables, a substrate table WTa and a table WTb below the projection system without a dedicated substrate table for example to facilitate measurement and / or cleaning etc.). 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 exposures are being carried out using one or more other tables. For example, alignment measurements using an alignment sensor AS and / or level (height, tilt etc.) measurements using a level sensor LS may be performed.

[0060] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g., water) 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 between the patterning device and the projection system. Immersion techniques are well known in the art and are used to increase the numerical aperture of the projection system. The term "immersion" as used herein does not imply that structures such as the substrate must be submerged in the liquid, but only that the liquid is located between the projection system and the substrate during exposure.

[0061] Thus, in operation of the lithographic apparatus, a radiation beam is conditioned and provided by the illumination system IL. The radiation beam B is incident on a patterning device (e.g. a mask) MA held on a support structure (e.g. a mask table) MT and is patterned by the patterning device. After passing through the patterning device MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g. an interferometric device, a linear encoder, a 2D encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example in order to position a different target portion C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor (in Figure 1 The support structure MT may be used to accurately position the patterning device MA relative to the path of the radiation beam B, for example after mechanical retrieval from a mask library, or during scanning. In general, movement of the support structure 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 positioner PM. Similarly, movement of the substrate table WT 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 support structure MT may be connected to the short-stroke actuator only, or may be fixed. The patterning device MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as shown occupy dedicated target portions, they may be located in the spaces between target portions (these are referred to as scribe alignment marks). Similarly, where more than one die is provided on the patterning device MA, the patterning device alignment marks may be located between the dies.

[0062] The depicted device can be used in at least one of the following modes:

[0063] 1. In step mode, the support structure MT and substrate table WT remain essentially stationary while the entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then moved in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

[0064] 2. In scan mode, the support structure MT and 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 speed and direction of the substrate table WT relative to the support structure 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 a single dynamic exposure (in the non-scanning direction), while the length of the scanning movement determines the height of the target portion (in the scanning direction).

[0065] 3. In another mode, the support structure MT is held substantially stationary to hold the programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is 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 can be readily applied to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type described above.

[0066] Combinations and / or variations of the above-described modes of use or entirely different modes of use may also be employed.

[0067] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, it should be understood that the lithographic apparatus described herein may have other applications, such as manufacturing integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, etc. The skilled person will understand that in the context of such alternative applications, any use of the term "wafer" or "die" herein may be considered synonymous with the more general term "substrate" or "target portion", respectively. Before or after exposure, the substrate referred to herein may be processed in, for example, a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist) or a measurement or inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, a substrate may be processed more than once, for example to create a multi-layer IC, so the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0068] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of 365, 248, 193, 157 or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams.

[0069] Various patterns on or provided by a pattern forming device may have different process windows, i.e., the space of process variables under which the pattern will be formed within specifications. Examples of pattern specifications related to potential system defects include checking for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut, and / or bridging. This is a non-exhaustive list of defects, and additional defect types and corresponding defect detectors may be defined. The process windows of all patterns on a pattern forming device or a region thereof may be obtained by merging (e.g., overlapping) the process windows of each individual pattern. The boundaries of the process windows of all patterns contain the boundaries of the process windows of some individual patterns. In other words, these individual patterns limit the process windows of all patterns. These patterns may be referred to as "hot spots" or "process window limiting patterns (PWLPs)", which are used interchangeably herein. It is possible and economical to focus on hot spots when controlling a portion of a patterning process. When a hot spot is defect-free, it is likely that all patterns are defect-free.

[0070] like Figure 2 As shown, the lithography apparatus LA may form part of a lithography cell LC, sometimes also referred to as a lithography cell or cluster, which also includes equipment for performing pre-exposure and post-exposure processes on a substrate. Typically, these include one or more spin coaters SC for depositing one or more resist layers, one or more developers DE for developing the exposed resist, one or more chill plates CH and / or one or more bake plates BK. A substrate handler or robot RO picks up one or more substrates from input / output ports I / O1, I / O2, moves them between different processing devices, and transfers them to a feed station LB of the lithography apparatus. These devices, often collectively referred to as tracks, are under the control of a track control unit TCU, which itself is controlled by a supervisory control system SCS, which also controls the lithography apparatus via a lithography control unit LACU. Thus, the different devices may be operated to maximize throughput and processing efficiency.

[0071] In order to correctly and consistently expose a substrate exposed by a lithographic apparatus and / or to monitor a part of a patterning process (e.g. a device manufacturing process) comprising at least one pattern transfer step (e.g. a lithography step), it is necessary to inspect the substrate or other object to measure or determine one or more properties, such as alignment, overlay (e.g. between structures in an overlying layer or between structures in the same layer provided separately from the layer by, for example, a double patterning process), line thickness, critical dimension (CD), focus offset, material properties, etc. Therefore, the manufacturing facility in which the lithography cell LC is located also typically includes a metrology system MET, which measures some or all substrates W that have been processed in the lithography cell or other objects in the lithography cell. The metrology system MET may be part of the lithography cell LC, for example it may be part of the lithography apparatus LA (such as an alignment sensor AS).

[0072] The one or more measured parameters may include, for example, the overlap between successive layers formed in or on the patterned substrate, for example, the critical dimension (CD) of features formed in or on the patterned substrate (e.g., critical line width), the focus or focus error of a lithography step, the dose or dose error of a lithography step, the optical aberration of a lithography step, etc. The measurement may be performed on a target on the product substrate itself and / or on a dedicated metrology target provided on the substrate. The measurement may be performed after resist development but before etching, or may be performed after etching.

[0073] There are a variety of techniques for measuring structures formed during patterning, including the use of scanning electron microscopes, image-based measurement tools, and / or various specialized tools. As described above, a fast and non-invasive form of specialized measurement tools is a tool that directs a radiation beam onto a target on a substrate surface and measures the properties of the scattered (diffraction / reflection) beam. By evaluating one or more properties of the radiation scattered by the substrate, one or more properties of the substrate can be determined. This can be referred to as diffraction-based measurement. One such application of such diffraction-based measurement is to measure the asymmetry of features within a target. For example, this can be used as a measure of overlap, but other applications are also known. For example, asymmetry can be measured by comparing relative portions of the diffraction spectrum (e.g., comparing the -1 order and +1 order in the diffraction spectrum of a periodic grating). This can be performed as described above and, for example, in U.S. Patent Application Publication US 2006-066855, which is incorporated herein by reference in its entirety. Another application of diffraction-based measurement is to measure the width of features (CD) within a target. Such a technique can use the apparatus and method described below.

[0074] Thus, in a device manufacturing process (e.g., a patterning process or a lithography process), a substrate or other object may be subjected to various types of measurements during or after the process. The measurement may determine whether a particular substrate is defective, may adjust the process and equipment used in the process (e.g., aligning two layers on a substrate or aligning a pattern forming device with a substrate), may measure the performance of the process and equipment, or may be used for other purposes. Examples of measurements include optical imaging (e.g., optical microscopy), non-imaging optical measurements (e.g., measurements based on diffraction such as ASML YieldStar metrology tools, ASML SMASH metrology systems), mechanical measurements (e.g., analysis using a stylus, atomic force microscopy (AFM)), and / or non-optical imaging (e.g., scanning electron microscopy (SEM)). The SMASH (Smart Alignment Sensor Hybrid) system, as described in U.S. Pat. No. 6,961,116 (which is incorporated herein by reference in its entirety), employs a self-referencing interferometer that produces two overlapping and relatively rotated images of an alignment mark, detects the intensity in a pupil plane where Fourier transforms of the images interfere, and extracts position information from the phase difference between the diffraction orders of the two images, which manifests itself as intensity variations of the interference orders.

[0075] The measurement results may be provided directly or indirectly to the supervisory control system SCS. If an error is detected, the exposure of subsequent substrates may be adjusted (particularly if the inspection can be performed as soon as possible and quickly enough so that one or more other substrates in the batch will still be exposed), and / or the subsequent exposure of the exposed substrate may be adjusted. Furthermore, already exposed substrates may be stripped and reprocessed to improve yield, or discarded to avoid further processing of substrates known to be defective. In the case where only some target portions of the substrate are defective, further exposures may be performed only on the good target portions.

[0076] In a measurement system MET, a measurement device is used to determine one or more properties of a substrate, in particular to determine how one or more properties vary from one substrate to another or how different layers of the same substrate vary from layer to layer. As described above, the metrology device may be integrated into the lithographic apparatus LA or the lithography cell LC or may be a stand-alone device.

[0077] To enable measurement, one or more targets may be provided on the substrate. In one embodiment, the target is specially designed and may include a periodic structure. In one embodiment, the target is a portion of a device pattern, such as a periodic structure of the device pattern. In one embodiment, the device pattern is a periodic structure of a memory device (e.g., a bipolar transistor (BPT), a bit line contact (BLC), etc. structure).

[0078] In one embodiment, the target on the substrate may include one or more one-dimensional periodic structures (e.g., gratings) that are printed such that after development, the periodic structural features are formed by solid resist lines. In one embodiment, the target may include one or more two-dimensional periodic structures (e.g., gratings) that are printed such that after development, the one or more periodic structures are formed by solid resist posts or vias in the resist. The bars, posts, or vias may alternatively be etched into the substrate (e.g., etched into one or more layers on the substrate).

[0079] In one embodiment, one of the parameters of interest in the patterning process is overlap. Overlap can be measured using a dark field scattering method, in which the zero-order diffraction (corresponding to specular reflection) is blocked and only the high order is processed. Examples of dark field measurements can be found in PCT patent application publications No. WO 2009 / 078708 and WO 2009 / 106279 (the entire contents of which are incorporated herein by reference). Further developments of the technology are described in U.S. patent application publications US2011-0027704, US2011-0043791, and US2012-0242970 (the entire contents of which are incorporated herein by reference). Diffraction-based overlap using dark field detection of diffraction orders can be used to measure overlap on smaller targets. These targets can be smaller than the irradiation spot and can be surrounded by device product structures on the substrate. In one embodiment, multiple targets can be measured in one radiation capture.

[0080] Figure 3A flow chart of a method for determining the presence of a hot spot (or a defect resulting therefrom) in a lithography process according to one embodiment is shown. In process P311, a hot spot or its location is identified from a pattern (e.g., a pattern on a pattern forming device) using any suitable method. For example, the hot spot can be identified by analyzing the pattern on the pattern forming device using an empirical model or a computational model. In an empirical model, an image of the pattern (e.g., a resist image, an optical image, an etching image) is not simulated; instead, the empirical model predicts the hot spot based on correlations between processing parameters, parameters of the pattern, and hot spots. For example, the empirical model can be a classification model or a database of patterns prone to defects. In a computational model, a portion or characteristic of the image is calculated or simulated, and the hot spot is identified based on the portion or characteristic. For example, a line pullback defect / hot spot can be identified by finding a line end that is too far from its expected position; a bridging defect / hot spot can be identified by finding a location where two lines undesirably join; an overlapping defect / hot spot can be identified by finding two features that undesirably overlap or undesirably do not overlap on a separate layer. The computational cost of an empirical model is generally lower than that of a computational model. The process window of the hotspot can be determined and / or compiled into a map based on the hotspot location and the process window of the single hotspot, that is, the process window as a function of the location is determined. The process window map can characterize the layout-specific sensitivity and processing margin of the pattern. In another example, the hotspots, their locations and / or their process windows can be determined experimentally, such as by FEM wafer inspection or suitable measurement tools. The collection of defects / hotspots can include those defects / hotspots that cannot be detected in post-development inspection (ADI) (usually optical inspection), such as resist top loss, resist undercut, etc. Conventional inspection only reveals such defects / hotspots after the substrate is irreversibly processed (e.g., etched), at which time the wafer cannot be reworked. Therefore, when this document was drafted, such resist top loss defects could not be detected using current optical technology. However, simulations can be used to determine where and how severe resist top loss may occur. Based on this information, a decision can be made to inspect specific hot spots / possible defects using more accurate inspection methods (usually more time consuming) to determine if the defect / wafer requires rework, or a decision can be made to rework the imaging of a specific resist layer (remove the resist layer with the resist top loss defect and re-coat the wafer to re-image the specific layer) before performing irreversible processing (e.g., etching).

[0081] In process P312, processing parameters for processing hot spots (e.g., imaging or etching onto a substrate) are determined. Processing parameters may be local—depending on the location of the hot spot, the die, or both. Processing parameters may be global—independent of the location of the hot spot and the die. One exemplary method for determining processing parameters is to determine the state of the lithographic apparatus. For example, laser bandwidth, focus, dose, source parameters, projection optical parameters, and spatial or temporal variations of these parameters may be measured from the lithographic apparatus. Another exemplary method is to infer processing parameters from data obtained from measurements performed on the substrate or from an operator of the processing apparatus. For example, the measurements may include inspecting the substrate using a diffraction tool (e.g., ASML YieldStar), an electron microscope, or other suitable inspection tool. Processing parameters may be obtained for any location on the processed substrate, including the identified hot spots. Processing parameters may be compiled into a map—lithographic parameters or processing conditions, as a function of location. Of course, other processing parameters may be expressed as a function of location, i.e., a map. In one embodiment, processing parameters may be determined before processing each hot spot and preferably immediately before processing each hot spot.

[0082] In process P313, the presence, probability of presence, characteristics, or a combination thereof of a defect at the hotspot are determined using the processing parameters of the processing hotspot. The determination can simply compare the processing parameters to the process window of the hotspot—if the processing parameters fall within the process window, no defects exist; if the process parameters fall outside the process window, at least one defect is expected to exist. The determination can also be made using a suitable empirical model (including a statistical model). For example, a classification model can be used to provide the probability of the presence of a defect. Another way to make such a determination is to simulate an image or expected pattern profile of the hotspot under the processing parameters using a computational model and measure the image or profile parameters. In one embodiment, the processing parameters can be determined immediately after processing a pattern or substrate (i.e., before processing a pattern or the next substrate). The presence and / or characteristics of the determined defects can serve as the basis for a disposal decision: rework or acceptance. In one embodiment, the processing parameters can be used to calculate a moving average of the lithography parameters. The moving average can be used to capture long-term drifts in the lithography parameters without being shifted by short-term fluctuations.

[0083] In one embodiment, hot spots are detected based on simulated images of patterns on a substrate. Once a simulation of a patterning process (e.g., including process models such as OPC and manufacturability checks) is complete, potential weaknesses in the design as a function of process conditions, i.e., hot spots, can be calculated based on one or more definitions (e.g., certain rules, thresholds, or metrics). Hot spots can be determined based on absolute CD values, the rate of change of CD with one or more parameters that are varied in the simulation ("CD sensitivity"), the slope of the spatial image intensity, or NILS (i.e., "edge slope" or "normalized image logarithmic slope" (commonly abbreviated as "NILS") indicating lack of clarity or image blur) where the edges of resist features are expected (calculated from a simple threshold / bias model or a more complete resist model). Alternatively, hot spots can be determined based on a set of predetermined rules, such as those used in a design rule checking system, including but not limited to line pullback, rounded corners, proximity of adjacent features, pattern necking or shrinkage, and other metrics of pattern deformation relative to the desired pattern. The sensitivity of CD to small variations in mask CD is a particularly important lithography parameter, referred to as MEF (Mask Error Factor) or MEEF (Mask Error Enhancement Factor). Calculation of the MEF as a function of focus and exposure provides a key measure of the probability that mask process variations combined with wafer process variations will result in unacceptable pattern degradation for a particular pattern element. Hotspots can also be identified based on variations in overlay error relative to underlying or subsequent process layers and CD variations or by sensitivity to overlay and / or CD variations between exposures in a multi-exposure process.

[0084] In one embodiment, pattern fidelity metrology can be performed as a guided defect inspection, where simulation tools are used to identify patterns that may fail, which guides the inspection system to the location of the identified pattern in the wafer to improve the efficiency of the inspection system. The inspection system acquires and analyzes the pattern / hotspot / defect image on the wafer. For example, the wafer image can be acquired from a reflection image of an optical system (dark field or bright field inspection system) or an electron beam (e-beam) system.

[0085] E-beam systems have the advantage of much higher resolution than optical systems, but it is also very slow and it is impractical to scan the entire wafer image. To speed up e-beam inspection (or even optical systems), simulations are configured to guide the inspection system to look at areas on the wafer where the probability of defects occurring within the wafer is relatively high. By doing so, the inspection process can be sped up by several orders of magnitude without losing accuracy in defect capture.

[0086] Each chip design contains a large number of patterns, and only a small fraction of the patterns may cause defects. For example, such patterns are called hot spots or hot spot patterns. Defects occur due to process variations (e.g., variations in process parameters such as focus and dose), and hot spots refer to patterns that may fail first or have a higher probability of failure due to such process variations. Process simulations can be performed to identify hot spots without the need for actual wafers and inspection tools.

[0087] Thus, guided inspection uses simulation to identify a very small number of hot spots relative to the entire design layout of a chip or wafer, and then drives the inspection system to focus on inspecting the areas on the wafer that correspond to the hot spot pattern and not inspect the rest, thereby achieving several orders of magnitude of yield gains.

[0088] Various aspects of methods for pattern fidelity measurement and hotspot determination or verification are discussed in detail in various patents / patent applications, which are incorporated herein by reference in their entirety. For example, U.S. patent application 15 / 546,592 describes a process variability-aware adaptive inspection and measurement that discusses, for example, a defect prediction method based on process parameter changes for defect discovery. U.S. patent application 15 / 821,051 describes hotspot identification of process windows or overlapping process windows based on regions of interest (e.g., process window limit patterns or hotspot patterns) of a design layout. U.S. patent application 15 / 580,515 describes a method for defect verification that aligns a measurement image with a first image of a wafer (e.g., a simulated image) and employs a verification process and threshold feedback related to image alignment / misalignment. PCT patent application publication WO2017080729A1 describes a method for identifying process window boundaries for improved hotspot discovery.

[0089] Existing computational lithography-related solutions (e.g., pattern fidelity metrology / monitoring for wafer defect inspection, as described above) employ modules (e.g., software), such as hotspot detection based on lithography manufacturability check (LMC), which uses computational lithography models to identify hotspots throughout the chip to guide inspection equipment (e.g., electron beam). Computational lithography software that employs such hotspot detection based on lithography manufacturability check is also configured to perform beyond OPC verification (e.g., OPC-related defects) and discover process window defects, and may also generate hundreds of thousands of hotspots for full-chip designs. Due to the fast turnaround time requirements and the relatively low speed at which measurements are implemented using inspection tools, only a small fraction (e.g., parts per million) of full-wafer hotspots may be detected. To address this computational model, a grading indicator (also referred to as grading) is used to indicate the severity of each hotspot. The severity of a hotspot is a measure of the likelihood that a hotspot pattern will transform into a real wafer defect. A hotspot with a higher severity indicates that it may transform into a defect, and the actual count of such defects associated with the hotspot may be relatively high compared to other patterns. Therefore, such a hotspot will also be graded high. A low severity hotspot indicates that it is unlikely to transform into a defect and the actual defect count on the wafer may be small or non-existent. Such a hotspot will be graded lower.

[0090] Based on the classification, the inspection system can select a small number of hot spots (e.g., hot spots with relatively high classification) for defect inspection. Therefore, accurate identification of hot spots and their severity / classification is very important to ensure high capture rate (i.e., more true positives or more data revealing defects associated with patterns) and low interference rate (i.e., fewer false positives or less data associated with defect-free patterns).

[0091] As previously described, due to the amount of time and resources required to implement the measurements, measurements are performed via a metrology tool at a limited number of selected locations (e.g., hotspot locations) on the printed wafer. In one embodiment, incorrect hotspot grading may direct the inspection equipment to less critical locations (e.g., non-hotspot locations) on the printed substrate, thereby spending (or wasting) tool time to inspect patterns that are unlikely to be true defects. For example, a non-representative measurement sample may include some measurements that may not reveal defects, and some defects may be omitted or missed. For example, a critical hotspot pattern that is considered unlikely to be a true defect based on an incorrect low grading of the hotspot is skipped, resulting in missing true defects, which may result in missing information related to frequently occurring defects. In one embodiment, defects missed by the guided inspection can be discovered by other means, i.e., optical inspection systems, intensive (with guided) electron beam inspection. When (such measurements) are used to improve the patterning process, the simulation inaccuracies revealed from the measurements (also referred to as inaccurate measurements) may not be able to observe the expected results (e.g., expected yield or process improvements).

[0092] In one embodiment, after a mask design including OPCs such as assist features (e.g., SRAF and SERIF), the next step is mask verification such as OPC verification. Mask verification is a standard step in the mask data preparation (MDP) flow, which is used for reticle tapeout before sending the mask design to a production or manufacturing facility. The purpose of such mask verification is to identify errors or weaknesses in the post-OPC design that may result in pattern defects on the printed substrate. In one embodiment, such mask verification may be performed using software that employs lithography manufacturability checking (LMC), such as Tachyon software that employs lithography manufacturability checking rules. The accuracy of mask verification depends on the accuracy of the patterning process model including the OPC model. Any inaccuracy in the process model will result in missing real defects on the substrate or false nuisance defects. In one embodiment, a defect refers to a feature or a portion of a feature that is out of specification when imaged on the substrate. For example, a defect may be necking, hole closure, merged holes, etc.

[0093] Some defects identified via lithography manufacturability inspection are also sent for substrate inspection or monitoring. In one embodiment, locations on the mask corresponding to defects identified by lithography manufacturability inspection are referred to as hot spots. In one embodiment, hot spots can be defined as locations on the mask that have a higher probability of being true defects when the pattern associated with the hot spot is imaged on the substrate.

[0094] For example, ASML's pattern fidelity metrology (PFM) product relies on certain patterns or their locations (e.g., hot spots) identified by lithography manufacturability inspection to guide the electron beam inspection equipment only to specific locations on the printed substrate to improve the efficiency of the inspection equipment. Due to the turnaround time requirements of PFM and the speed of the inspection tool, PFM can only detect a small number of these locations (e.g., hot spots) of the complete printed substrate, usually thousands. In order to solve such inspection problems, the mask patterns (e.g., related to hot spots) identified by lithography manufacturability inspection need to be graded based on the possibility of being a real defect when imaged on the substrate, and PFM relies on such hot spot grading to select a small number of hot spots for inspection. Therefore, accurately identifying hot spots and their severity is one of the key steps to ensure high capture rate and low interference rate of PFM. In the present disclosure, the mask pattern corresponds to, for example, a hot spot to explain the concept, but such use of hot spots does not limit the present disclosure. In the present disclosure, the term "defect" refers to a lithography manufacturability inspection defect (interchangeably referred to as a hot spot) when it comes to a mask defect or refers to a wafer defect when it comes to a substrate. Those skilled in the art may apply the method of the present disclosure to other mask patterns to be inspected.

[0095] Process models, including OPC models, may not provide accurate results due to several approximations, such as those used to simplify or increase the speed of the simulation process. In other words, the model alone does not capture the physical characteristics of the process or the defects resulting therefrom. Therefore, a more conservative approach is used where strict specifications are applied to the pattern or features therein so that potential defects are not missed. However, the result is a large number of annoying defects, i.e., hot spots that may not appear on a real printed substrate. Therefore, the number of hot spots identified based on lithography manufacturability inspection should be reduced to fit the inspection cycle time budget.

[0096] In one embodiment, a lithography manufacturability check may be run for each layer of each substrate, thereby checking and processing millions of such defects, which is currently done by humans and can be very time consuming. Therefore, the lithography manufacturability check needs to reduce the number of nuisance defects while identifying most or all of the real defects. In addition, the severity of the defect can be assessed based on the simulated defect size. In one embodiment, the defect size is defined as the number of defect counts on the printed wafer. In one embodiment, the defect size may refer to the CD value of the pattern printed on the substrate. However, since the process model involves approximations that lead to inaccurate results, there may also be errors in the defect size.

[0097] Errors in hotspot identification via lithography manufacturability inspection will also affect the grading of hotspots. When the grading is inaccurate, guided inspection is performed using an inaccurately graded hotspot list, resulting in missing true defects on the printed substrate because they may not be in the sampled hotspot list, or a large number of annoying defects may be used, thereby wasting inspection time.

[0098] Figure 4A An example ranking of hotspots 410 assuming an ideal or perfect patterning process model (e.g., including an OPC model) is shown, which provides an accurate correlation between the measured occurrence of defects 410 from a printed substrate and the ranking of hotspots 405 based on the ideal patterning model. However, such a correlation will never be perfect because several process variations can cause defects to appear on a substrate that are essentially random. For example, as shown, lithography manufacturability inspection hotspots ranked at 350 and above do not appear to have defects on the printed substrate, so hotspots ranked above 350 are troublesome. Therefore, in this case, the lithography manufacturability inspection should ideally only report the top 350 hotspots.

[0099] However, even for hotspots with very low classification (e.g., hotspots with classification of 350 or higher), using the same lithography manufacturability check with a less accurate process model can result in defects, such as Figure 4B As shown. Figure 4B , the grading of hotspot 420 is inconsistent with the measured defect counts. For example, hotspots with a lower grading (e.g., about 600) have a higher defect incidence on printed substrates, while hotspots with a higher grading (e.g., about 400) have a lower defect incidence on printed wafers. In other words, the grading of hotspot 420 is reversed or inaccurate. Therefore, Figure 4B The curve in shows that the correlation between the defect data and the classification of the hotspot 420 is poor. Poor correlation or inaccurate classification results in loss of measurement time, low capture rate and high nuisance rate, which are all undesirable results. In other words, a large number of hotspots can be sampled to capture most of the real wafer defects. Sampling a large number of hotspots may result in a high nuisance rate because many of the sampled hotspots will have few or no real defect occurrences.

[0100] Therefore, feedback from the printed substrate must be obtained and fed to the lithography manufacturability check based on the hotspot grading so that the grading 420 is corrected and the next substrate will be sampled more accurately, thereby increasing the measurement capture rate and reducing the disturb rate. In other words, more defects will be captured due to the improved grading of the hotspot.

[0101] In one embodiment, the model inaccuracy results in inaccurate values ​​of the characteristics (e.g., CD or contour) of the simulated pattern, such as corresponding to hot spots. Figure 5 The values ​​of simulated CD (i.e., simulated characteristics) of the simulated pattern as a function of focus are shown compared to the true characteristics (i.e., measured values). In one embodiment, simulated CD 510 is obtained by simulating a Bossung curve using a dose-focus relationship or simulating one or more patterning process models (e.g., Fig. 22 The simulated CD 510 is obtained by using a simulated CD 510 (as discussed in ). This simulated CD 510 is very different from the measured CD 520 (i.e., the real CD). The difference between the simulated CD 510 and the measured CD 520 is due to the inaccuracy of the model. According to this embodiment, a method is provided (e.g., in Figure 6 5 (in the example of FIG. 5 ) to obtain a trained machine learning model configured to determine a correction to a characteristic (e.g., CD) of a simulated pattern. Thus, the simulated CD 510 can be corrected by the trained machine learning model to obtain a corrected CD 530, or generally a corrected pattern. Such a corrected pattern or corrected characteristic of a simulated pattern can be used for various purposes, such as hotspot grading, sampling planning, optimization of process parameters, or other patterning related applications.

[0102] In one embodiment, a model (e.g., a machine learning model) is configured to correct for features of a pattern obtained by simulation that corresponds to a mask pattern (e.g., corresponding to a hotspot). In one embodiment, such a machine learning model is trained based on measured data (e.g., Figure 6 As discussed in ), this measurement data allows accurate correction of the characteristics of the simulated pattern and further more accurate grading of hot spots corresponding to the corrected simulated pattern. Figure 5 As shown, the characteristics 510 of the simulated pattern can be corrected via a machine learning model to produce a corrected simulated pattern or a corrected characteristic 530 thereof.

[0103] Figure 6 6 is a flow chart of a method 600 for training a machine learning model 604 for a patterning process. The training of the machine learning model 604 is based on measurement data, such as inspection data and measured values ​​of parameters (e.g., dose focus, level control, etc.) used during imaging of a mask pattern (e.g., corresponding to a hot spot) on a substrate. In the present disclosure, a mask pattern refers to a post-OPC pattern, i.e., an optimized mask pattern obtained after the OPC process. Using such data from a real printed substrate allows the machine learning model to correct inaccuracies in simulation results. In one embodiment, the machine learning model 604 is a convolutional neural network (CNN), a deep learning model, or other model. Although all IC manufacturing in HVM today uses photomasks, the present disclosure is not limited to a specific patterning process, and the method 600 is also applicable to other patterning techniques, such as a direct write process that does not use a photomask.

[0104] In process P602, method 600 involves obtaining a training data set that includes (i) a simulated pattern 601 associated with a mask pattern to be printed on a substrate, (ii) inspection data 603 of a printed pattern imaged on a substrate using the mask pattern, and (iii) measured values ​​of parameters 605 of a patterning process applied during imaging of the mask pattern on the substrate. In one embodiment, the training data set includes a plurality of simulated patterns (e.g., obtained based on measured values ​​of parameters 605) and measurement data (e.g., inspection data and measured values ​​of parameters) associated with a corresponding plurality of printed patterns imaged on the substrate.

[0105] In one embodiment, the simulated pattern 601 is a simulated image, such as an aerial image, a mask image, a resist image, and / or an etching image. Therefore, in one embodiment, obtaining the simulated pattern 601 involves simulating a patterning process model (e.g., a mask model, an optical model, a resist model, etc.) using a mask pattern (e.g., a portion of a design layout corresponding to a hot spot) as an input and manipulating patterning process parameters such as dose, focus, etc. Figures 8A-8C An example simulation pattern generated during a simulation of a patterning process model is shown (e.g., Fig. 22 For example, the simulated pattern 601 may be a mask image 801, an aerial image 803, and / or a resist image 805. Each such image 801, 803, 805 includes a plurality of patterns where one or more features may fail or generate defects on the printed substrate.

[0106] In one embodiment, the simulated pattern 601 includes hot spots that may fail when imaged on a substrate. In one embodiment, the simulated pattern 601 includes a pattern that does not meet lithography manufacturability checks when the simulated pattern 601 is imaged on a substrate. For example, certain portions of a curved mask may result in a pattern with characteristics that exceed CD specifications.

[0107] In one embodiment, the inspection data is an image of the printed substrate. In one embodiment, the image is a scanning electron beam image and / or an optical metrology image. The inspection data may be obtained from, for example, an optical inspection system (e.g., Figure 15-18 ), scatterometers, or electron beam tools (e.g., as discussed in Figure 19-20 In one embodiment, such inspection data corresponding to the simulated pattern 601 provides a basis for modifying model parameters (e.g., weights and biases) of the machine learning model 604 (e.g., CNN) during training.

[0108] In one embodiment, the measured values ​​of the parameters of the patterning process can be any variable that affects the pattern printed on the substrate. In one embodiment, the measured values ​​of the parameters include one or more of the measured values ​​of dose, focus, MSDx, y, optical parameters, or other measured values ​​of the parameters of the patterning process applied during the imaging of the mask pattern on the substrate. In one embodiment, the printed wafer pattern or printed pattern image 603 is obtained from an inspection tool (e.g., SEM) together with the values ​​of the corresponding patterning process conditions (e.g., measurements of dose and focus). Then, the measured values ​​605 of the process parameters (or process conditions) are used to simulate the patterning process using the patterning process model to obtain simulated images 601 (e.g., MI / AI / RI). Using these simulated images 601 (e.g., MI / AI / RI) as input and using the printed pattern image 603 as ground truth, the machine learning model is trained by modifying the model parameters (e.g., hyperparameters, weights, and biases) of the machine learning model 604 (e.g., CNN).

[0109] In one embodiment, the measured values ​​of the parameters of the patterning process are obtained via a metrology tool.In one embodiment, one or more metrology tools may be integrated in a lithographic apparatus.

[0110] In process P604, method 600 involves training a machine learning model 604 based on a training data set via a processor (e.g., processor 104) to predict differences in characteristics of simulated pattern 601 and printed pattern. At the end of the training process, a trained machine learning model 640 is obtained, which is configured to determine corrections to simulated pattern 601 (e.g., such as regarding Figure 5 discussed).

[0111] In one embodiment, the characteristic of the simulated pattern 601 or the printed pattern is a critical dimension of a feature of the simulated pattern 601 or a profile of a feature of the simulated pattern 601. Therefore, the trained machine learning model 640 is configured to predict, for example, a CD difference (ΔCD) between a simulated CD value of the simulated pattern 601 and a measured CD value of the printed pattern. ΔCD can also be used to correct the CD of the simulated pattern 601, thereby producing a more accurate value of the CD of the simulated pattern 601. For example, as previously described with reference to Figure 5 As discussed, simulated CD 510 is calibrated to CD 530, which is closer to real CD 520 printed on the substrate.

[0112] In one embodiment, the training step (i.e., process P604) is an iterative process. Training involves receiving inspection data including a printed pattern and / or a printed pattern image thereof, and measured values ​​of parameters of a patterning process; predicting an image corresponding to the simulated pattern 601 based on the inspection data via a machine learning model; determining the difference between the predicted pattern image and the printed pattern image; and adjusting the model parameter values ​​of the machine learning model so that the difference between the predicted pattern image and the printed pattern image is reduced. In one embodiment, the output of the machine learning model is not limited to an image. The machine learning model can be configured to predict not only a wafer image, but also a CD of a feature within a predicted wafer image, an image difference (e.g., a difference in pixel values) or a CD difference between a printed image and a predicted image, or other relevant process parameters.

[0113] In one embodiment, adjusting model parameter values ​​of a machine learning model involves: determining a gradient map of the difference between a predicted pattern image and a printed pattern image as a function of model parameters; identifying model parameter values ​​based on the gradient map such that the predicted pattern image and the printed pattern image are reduced; and adjusting the model parameter values ​​based on the identified values.

[0114] In one embodiment, the adjustment of the model parameter values ​​includes adjusting the values ​​of: one or more weights of a layer of a convolutional neural network, one or more biases of a layer of a convolutional neural network, a hyperparameter of the CNN, and / or the number of layers of the CNN. In one embodiment, the number of layers is a hyperparameter of the CNN that can be pre-selected and cannot be changed during the training process. In one embodiment, a series of training processes can be performed in which the number of layers can be modified. An example of a CNN such as Fig. 9 shown.

[0115] In one embodiment, training (e.g., Fig. 9 A CNN (e.g., a CNN) involves determining the value of a cost function and gradually adjusting the weights of one or more layers of the CNN so that the cost function is reduced (in one embodiment, minimized). In one embodiment, the cost function is the difference between a predicted pattern obtained from a convolutional neural network (e.g., the output of the CNN) and a mask pattern (e.g., a pattern from inspection data, a design layout, etc.). In one embodiment, the cost function can be defined based on a contour-based metric, CD, or other suitable geometric or process parameter. Improvements in the cost function are achieved by modifying the values ​​of CNN model parameters (e.g., weights, biases, strides, etc.).

[0116] For example, the cost function may be an edge placement error (EPE). In this case, contours may be extracted from the printed pattern image 603 and the predicted pattern image to further determine the EPE (e.g., the difference between the printed pattern contour and the predicted pattern contour). The cost function may then be expressed as: cost = f(printed pattern image - CNN(input, cnn_parameters), where the cost may be EPE (or EPE2 or other suitable EPE-based metric), and the function f performs contour extraction from the predicted pattern (e.g., by CNN) and the printed pattern to further determine the difference between the predicted pattern image and the printed pattern image. In one embodiment, the input to the CNN includes a simulated image (e.g., MI / AI / RI). For example, the function f may first derive contours from the predicted image and then calculate the EPE for the printed pattern. cnn_parameters is a gradient-based method in Optimization parameters determined during CNN training. In one embodiment, cnn_parameters may be the weights and biases of the CNN. Further, the gradient corresponding to the cost function may be dcost / dparameter, where the parameter may be updated based on the equation (e.g., parameter=parameter-learning_rate*gradient). In one embodiment, the parameter may be the weights and / or biases of a machine learning model (e.g., a CNN), and learning_rate may be a hyperparameter for tuning the training process and may be selected by a user or computer to improve the convergence of the training process (e.g., faster convergence).

[0117] Trained machine learning model 640 (e.g., Fig. 9 A trained CNN) can also be used to correct the simulated pattern or any of its characteristics.

[0118] Figure 7 is a flow chart of a method 700 for correcting a characteristic of a simulated pattern of a patterning process based on a trained machine learning model (e.g., 640). In process P702, method 700 includes determining a simulated pattern and a characteristic of the simulated pattern via a simulated patterning process model. In one embodiment, for example, Fig. 22 As discussed in , simulation involves executing a patterning process model (e.g., a mask model, an optical model, a resist model, etc.) using a mask pattern (e.g., a portion of a design layout corresponding to a hotspot) as input. Thus, the simulated pattern 702 is an aerial image, a mask image, a resist image, and / or an etch image.

[0119] In process P704, method 700 involves determining, via the trained machine learning model (e.g., 640), a characteristic adjustment value 704 for a characteristic of simulated pattern 702. In one embodiment, the characteristic adjustment value is a value by which the simulated characteristic will be modified to account for process model inaccuracies. In one embodiment, the trained machine learning model is trained based on simulated patterns and measurement data from printed substrates, and thus the trained machine learning model is configured to predict such adjustment values ​​for any simulated pattern received as input.

[0120] As previously described, a characteristic of a pattern (e.g., simulated pattern 701 or a printed pattern) can be a critical dimension of a feature or a profile of a feature. Thus, the trained machine learning model 640 predicts, for example, a CD difference (ΔCD) to be applied to the simulated CD value of the simulated pattern 702 to adjust for any model inaccuracies.

[0121] In process P706, the characteristic adjustment value of the simulated pattern 702 is further used to correct the simulated pattern. Process P706 involves correcting the characteristics of the simulated pattern 702 based on the characteristic adjustment value 704 via a processor (e.g., processor 104). The corrected characteristics or the associated corrected simulated pattern can be used for various purposes, such as grading of hot spots, optimization of process parameters, controlling parameters of a patterning process, or other applications related to improving a pattern printed on a substrate that has undergone a patterning process.

[0122] In one embodiment, multiple design patterns can be used to generate multiple simulated patterns. For example, the patterning process model (e.g., Fig. 22 Thousands to millions of simulated patterns are generated (as discussed in ). Not every one of these patterns may be a mask pattern, because the probability of failure of having several patterns when printed on a substrate is very low. Therefore, multiple simulated patterns may correspond only to hot spots (e.g., typically in the thousands).

[0123] Therefore, in one embodiment, method 700 further includes: in process P708, obtaining multiple simulation patterns and multiple adjustment characteristic values ​​corresponding to the multiple simulation patterns via the trained machine learning model. In one embodiment, the multiple simulation patterns include patterns corresponding to multiple hot spots.

[0124] Additionally, process P710 involves adjusting, via a processor, a characteristic of each of the plurality of simulation patterns based on a plurality of adjusted characteristic values.

[0125] In process P712, a ranking 712 of the plurality of simulated patterns is determined based on the adjusted characteristics of the simulated patterns. For example, when the characteristics of the plurality of hot spots are adjusted based on the trained machine learning model 640 to account for inaccuracies in the process model based on the simulation, one or more of the plurality of hot spots may no longer be critical (i.e., highly likely to cause a printed substrate to fail). In this way, the ranking 712 based on the adjusted characteristics will be more accurate, and only a subset of hot spots with a relatively high probability of failure will be analyzed first, thereby improving the results of the patterning process. For example, a better sampling plan can be determined based on the ranking 712, thereby improving not only the measurement time and resource allocation, but also the defect capture rate.

[0126] In one embodiment, the rating 712 may be an integer scale from 1 to n, where n is the number of total hot spots. A rating of 1 represents the highest rating, for example, indicating the highest probability of failure of the associated hot spot, and as the integer value increases, the rating is considered lower, for example, n is the lowest rating. For example, in a rating of 1 to 10, a rating of 1 is the highest and a rating of 10 is the lowest.

[0127] In one embodiment, the determination of the rating 712 may be based on, for example, Fig.14A and 14B In the classification algorithm. Fig.14A and 14B In one embodiment, the ranking may be determined based on a defect metric (e.g., defect size). For example, based on defect size, a high ranking (e.g., 1) may be assigned to a hotspot (or hotspot pattern) with a larger defect size, and as the defect size decreases, the ranking algorithm may gradually assign lower rankings to other hotspots. In one embodiment, the ranking may be based on the total number of defects or the probability of occurrence of a defect corresponding to the ranked hotspot. In one embodiment, the ranking algorithm (e.g., Fig.14A and 14B ) can be part of a process model or a simulation of a patterning process, so that the simulation result can be a hotspot pattern and its classification.

[0128] In one embodiment, the rating 712 may be determined based on another machine learning model 1140 configured to predict the rating based on simulated patterns, such as the following with respect to Fig.11 discussed.

[0129] In one embodiment, method 700 may also include: in process P714, determining a sampling plan 714 for measurement of printed substrate 713 based on the ranking of multiple simulated patterns. The determination of sampling plan 714 identifies the location and / or number of measurements that should be performed at a particular hotspot. In one embodiment, the sampling plan is based on the ranking of hotspots. For example, the hotspot with the highest ranking (e.g., ranking 1) can be sampled first with a relatively high number of measurements so that defects are not missed because the measurements can represent defects that can be found at such locations. Similarly, hotspots with relatively lower rankings than the hotspots with the highest rankings can be sampled later in the sequence of hotspots to be sampled.

[0130] Method 700 may also include, in process P716, directing, via the processor, the inspection device to collect measurement data on the printed substrate based on the hotspot classification 712. For example, the inspection device (e.g., Figure 19-20 The electron beam tool in the apparatus) can be guided in an order starting from the hot spot with the highest ranking to the hot spot with the lowest ranking. In one embodiment, in addition to the ranking 712 of the hot spots, the guidance (or the related sampling plan) can be based on different parameters (e.g., the number of measurements to be performed at a specific location, the distance between different hot spots, etc.) to optimize the measurement data and propagation time between different hot spots. The present disclosure is not limited to a specific sampling scheme determination algorithm or guidance method, and any algorithm can be configured to receive the ranking 712 to determine the sampling scheme or guidance of the inspection equipment.

[0131] In addition, in process P718, based on the measurement data from the inspection, defects on the printed substrate can be determined. In one embodiment, any existing defect detection algorithm can be used to determine the defects. For example, defect detection can involve image processing and inspection related to the specification of feature size (e.g., specification related to CD value).

[0132] Fig. 10A and 10B Example improvements in ranking resulting from feedback (eg, adjusted features 704 ) from a trained machine learning model 640 are shown. Fig. 10A A ranking 1003 of hot spots (x-axis) based on existing results such as computational lithography simulations using a patterning process model is shown. As shown, the ranking 1003 is inaccurate because higher ranked hot spots capture a lower number of defects, while lower ranked hot spots show a higher number of defects. Furthermore, in order to capture more than 90% of the defects, as shown in the capture rate curve 1010, approximately 300 hot spots must be measured.

[0133] On the other hand, Fig. 10BAs shown, the ranking 1004 of the hot spots is more accurate. Such ranking can be based on adjusted characteristics of the simulated pattern, as described above. The ranking 1004 of the hot spots (x-axis) is such that hot spots with a relatively high ranking (e.g., between 1-50) capture the majority of defects that may occur on the printed substrate (left y-axis). As shown, curve 1020 indicates the capture rate (right y-axis). The capture rate curve 1020 indicates that approximately 90% of the total number of defects are captured by the top 50 ranked hot spots. Therefore, the ranking based on method 700 is an improved ranking compared to an inaccurate ranking, such as Fig. 10A As shown, approximately 300 hot spots must be evaluated to capture approximately 90% of the defects. For example, the measurement time for 50 hot spots will be significantly less than the time to measure 300 hot spots to capture a similar number of defects.

[0134] In one embodiment, reference Fig.11 , a flowchart of a method for training another machine learning model 1110 is provided, the machine learning model 1110 being configured to predict a grade for a set of simulated patterns for a patterning process. The machine learning model 1110 is configured to receive a simulated pattern (e.g., MI / AI / RI) or a characteristic (e.g., CD) as an input under patterning process conditions (e.g., Bossung curve, FEM, etc.), and predict a grade or defect count associated with the simulated pattern as an output. In one embodiment, the machine learning model 1110 may be a CNN, a regression model, or a classification model with a relatively small number of parameters compared to a CNN. After the training process, a trained machine learning model 1140 is generated, and the trained machine learning model 1140 is configured to predict a grade or defect count associated with the simulated pattern for at least one simulated pattern in the set of simulated patterns (e.g., obtained via a simulation process model) or a corrected simulated pattern (e.g., from Figure 7 obtained by the method) for classification.

[0135] In process P1102, method 1100 involves obtaining (i) a set of simulated patterns 1101 corresponding to a set of mask patterns (e.g., instances of 601 or 702), (ii) defect data 1103 for a set of printed patterns imaged on a substrate using the set of mask patterns, and (iii) a sampling plan 1105 associated with the substrate imaged using the set of mask patterns.

[0136] In one embodiment, obtaining a set of simulated patterns 1101 involves simulating a patterning process model (e.g., Fig. 22), and a set 1101 of simulated patterns that may fail when imaged on a substrate is identified from the simulation results. Thus, the set 1101 of simulated patterns corresponds to a set of hotspot patterns. In one embodiment, the set 1101 of simulated patterns includes simulated patterns that do not satisfy the lithography manufacturability check.

[0137] In one embodiment, the defect data (e.g., via an inspection device (e.g., Figure 15-20 ) includes features that failed (e.g., did not meet specifications) on the printed substrate. In one embodiment, defects can be identified by analyzing SEM images of the printed substrate. Therefore, in one embodiment, the total number of defects (i.e., defect count) associated with a particular pattern (e.g., hot spot) can be determined, and the defect count can further be used to correlate with the grading of the particular pattern (e.g., hot spot).

[0138] In one embodiment, the defect data 1103 is a defect count associated with one or more patterns on a printed substrate. In one embodiment, the defect data 1103 is a value or range of values ​​of a critical dimension associated with one or more patterns on a printed substrate. In one embodiment, the defect data 1103 is extracted from an image of the printed substrate, wherein the image is a scanning electron beam image and / or an optical metrology image.

[0139] In one embodiment, defect data 1103 from a printed substrate is collected via a metrology tool (e.g., Figure 15-20 ). In one embodiment, the printed substrate can be measured using a metrology tool (e.g., SEM) and the parameters of the patterning process can be extracted from the measurement. For example, the outline of the pattern can be extracted from an SEM image from the SEM, and the outline can be checked against the expected outline or design specifications. When the outline does not meet the design specifications, the outline is marked as a defect. In one embodiment, defect-based defect metrics can be defined to quantify the characteristics of the hotspot (e.g., severity or criticality) and / or for grading the hotspots. In one embodiment, the defect metric is any metric related to a defect feature. In one embodiment, the defect feature is a feature that violates (e.g., exceeds) an expected threshold value (e.g., CD<30nm or CD>30) for a parameter of the patterning process.

[0140] In one embodiment, the defect metric may be defect size, defect occurrence probability, defect count associated with a particular hotspot, or other defect related metrics. The defect size may be defined as the value of a process parameter (e.g., CD) associated with the defect signature, or the difference between the value of a process parameter relative to a threshold. For example, the CD threshold for a bar may be 30 nanometers, and the CD for a bar on an exposed wafer may be 25 nanometers, then the defect size may be 25 nanometers or the CD difference, i.e., 5 nanometers. Thus, in one embodiment, the defect size associated with a hotspot pattern may be used to determine the severity or criticality of the hotspot. In one embodiment, the greater the difference between the defect size and the threshold, the higher the severity of the hotspot, and vice versa.

[0141] In one embodiment, the defect metric may be a defect count defined as the total number of defects of a particular defect type (eg, wire pullback, hole closure, missing hole, etc.) For example, the total number of defects may be an integer obtained by counting defects of a particular type.

[0142] In one embodiment, the sampling plan 1105 includes a set of locations on the printed substrate at which measurements are performed, wherein the set of locations is based on an initial ranking of the set of simulated patterns 1101; and / or a number of measurements to be performed at one or more locations in the set of locations based on the initial ranking of the set of simulated patterns 1101.

[0143] In process P1104, method 1100 involves training a machine learning model 1110 based on defect data 1103 and a sampling plan 1105 via a processor (e.g., processor 104), such that the machine learning model 1110 is configured to predict a grade for a set 1101 of simulated patterns that matches a reference grade based on the defect data 1103. The reference grade is considered to be a true grade because the grade is based on actual measured defect data from a printed substrate. After the training process, a trained machine learning model 1140 is obtained that can predict a grade 1142 for any set 1101 of simulated patterns (e.g., an instance of 601 or 702). Since the trained machine learning model includes model parameters adjusted based on real data obtained from a printed substrate, such a grade will be more accurate.

[0144] In one embodiment, the training step is an iterative process. The training process involves predicting the grading of the set 1101 of simulated patterns using the sampling plan 1105 and the defect data 1103 as input via the machine learning model 1110; determining 1103 the difference between the predicted grading and the reference grading based on the defect data; and adjusting the model parameter values ​​of the machine learning model so that the difference between the gradings is reduced.

[0145] Method 1100 includes: in process P1106, receiving a set 1101 of simulation patterns and an initial ranking of the set 1101 of simulation patterns; predicting a ranking 1142 of the set 1101 of simulation patterns via a trained machine learning model 1140; and adjusting a sampling plan 1105 based on the predicted ranking 1142 of the set 1101 of simulation patterns via a processor.

[0146] In one embodiment, adjustment of sampling plan 1105 involves adjusting the positions to be measured in the set of positions, and / or the number of measurements to be performed at one or more positions to be measured in the set of positions. In one embodiment, adjusting the positions in the set of positions involves omitting positions in the set of positions that correspond to relatively lower ranked simulation patterns; and / or adding new positions to the set of positions that correspond to relatively higher ranked simulation patterns. In one embodiment, adjusting the positions in the set of positions includes increasing and / or decreasing the number of measurements to be performed at the positions in the subset of positions.

[0147] In process P1108 (similar to Figure 7 In process P716 of the method 1100 , the method 1100 involves directing, via a processor, an inspection device to collect measurement data on a printed substrate based on a predicted grade 1042 of a set of simulated patterns, and determining, via the processor, defects on the printed substrate based on the measurement data.

[0148] In one embodiment, reference Fig.12 , another method 1200 is provided for determining a ranking of a set of simulated patterns of a patterning process based on a first trained machine learning model 640 and a second trained machine learning model 1140. In one embodiment, when both trained models 640 and 1140 are combined, the ranking of a set of patterns, such as those including hot spots, can also be improved so that the characteristics of the simulated patterns are improved and further ranked based on the improved characteristics.

[0149] In process P1202, method 1200 involves adjusting a characteristic of at least one simulated pattern in a set of simulated patterns via a first machine learning model (e.g., 640). In one embodiment, the characteristic of at least one simulated pattern or printed pattern is a critical dimension of a feature of at least one simulated pattern in the set of simulated patterns. In one embodiment, the adjustment of the characteristic involves determining a characteristic adjustment value (e.g., ΔCD) for a simulated characteristic of at least one simulated pattern in the set of simulated patterns. In one embodiment, first trained machine learning model 640 is trained based on simulated patterns and measurement data from printed substrates, so that first trained machine learning model 640 is configured to predict such an adjustment value for any simulated pattern received as input.

[0150] In process P1204, method 1200 involves determining, via a processor, a subset of simulated patterns 1204 based on an adjusted characteristic of at least one simulated pattern. In one embodiment, determining the subset of simulated patterns involves determining whether the adjusted characteristic of at least one simulated pattern satisfies a lithography manufacturability check; and in response to not satisfying the lithography manufacturability check, including at least one simulated pattern in the subset of simulated patterns. For example, a set of initial simulated patterns may include 200,000 hot spots, and after adjusting the characteristics of the simulated patterns, one or more simulated patterns may satisfy the lithography manufacturability check, thereby possibly no longer meeting the hot spots. Therefore, such one or more simulated patterns that satisfy the lithography manufacturability check may be removed from the 200,000 hot spots, and a subset of, for example, 2000 hot spots may be obtained. Typically, several of the 200,000 hot spots are annoying, resulting in a waste of inspection tool time. Therefore, grading based on such a reduced number of hot spots is desirable because it requires less time and results in improved measurement time and improved yield due to better capture rate.

[0151] In process P1206 , method 1200 involves determining 1206 a ranking of at least one simulated pattern in a subset of simulated patterns 1204 via a second machine learning model 1140 .

[0152] Fig.13 An example ranking obtained based on the machine learning model 1140 and the associated defect counts is shown. For example, as shown, the ranking 1304 of hot spots (x-axis) is such that hot spots with relatively high rankings (e.g., between 1-50) capture the majority of defects that may occur on a printed substrate (left y-axis). In one embodiment, curve 1310 indicates the capture rate (right y-axis). The capture rate curve 1310 indicates that approximately 90% of the total number of defects are captured by the top 50 ranked hot spots. Thus, the ranking based on method 1200 demonstrates better ranking than an inaccurate ranking, such as Fig. 10A As shown, approximately 300 hot spots must be evaluated to capture approximately 90% of the defects. For example, the time to measure 50 hot spots will be significantly less than the time to measure 300 hot spots to capture a similar number of defects.

[0153] Return to reference Fig.12 In process P1208, method 1200 also includes guiding the inspection device via the processor to collect measurement data on the printed substrate based on the grading of at least one simulated pattern in the simulated pattern subset; and determining defects on the printed substrate based on the measurement data via the processor.

[0154] The above method provides several advantages. For example, a machine learning model or a trained machine learning model (e.g., 640, 1140) can be used to calculate lithography products (e.g., Tachyon using lithography manufacturability inspection) without changing the production OPC model. The use of such a machine learning model does not cause baseline drift and significantly improves tool availability time. For example, a baseline involves a qualified baseline (e.g., a model, a recipe, etc.) that will be used for a patterning process, and changes to such a baseline typically involve redefining such models and recipes, which is not preferred because the redefinition process requires a lot of work and is very time-consuming. For example, an existing patterning process model can be used to establish a baseline OPC. Although existing process models are not perfect, using such an OPC to determine OPC and related patterning process verification (e.g., patterning process recipes) involves a lot of work.

[0155] The machine learning model 1140 more accurately grades the severity of hot spots and the likelihood of being a true defect. This does not require specific prior knowledge of all the factors that cause defects, as the model "learns" these factors over time. Machine learning models (e.g., 640 and 1140) are adaptive, and over time, as more designs go through production and more measurement feedback is provided from printed substrates, the lithography manufacturability checks become more accurate.

[0156] On the other hand, the classic approach is to recalibrate the process model for lithography manufacturability checking capabilities (e.g., OPC). However, this approach has several disadvantages: Model calibration is a time-consuming exercise with specific skill requirements and is not practical for PFM users. Feedback from printed wafers can occur regularly, but it is impractical to recalibrate the model regularly. Recalibrating the process model would require a baseline shift, which may be undesirable.

[0157] Fig.14A and 14BAn example of a grading algorithm for determining the grading of hotspots is shown. In one embodiment, the example grading algorithm is based on a Bossung graph 1050 that defines the relationship between defect size and patterning process parameters. For example, the grading is based on the relationship between defect size (e.g., CD value or CD difference relative to a threshold) and focus value. The defect relationship depends on the type of pattern (e.g., different hotspots). Therefore, different hotspots may exhibit different defect behaviors relative to changes in focus value. In one embodiment, as focus increases (e.g., from left to right along the x-axis of the graph 1050), the defect size decreases (e.g., see 1052 or 1053). For example, for a first hotspot, the first relationship 1052 may indicate the inverse of the defect occurrence probability as the focus value changes. Similarly, for a second hotspot, the second relationship 1053 may indicate the inverse of the defect occurrence probability as the focus value changes. In one embodiment, the second relationship 1053 may correspond to the maximum limiting condition of the process window. In other words, the second hotspot applies constraints to, for example, the CD value and the outer limits of the corresponding dose / focus value. Such a second hotspot may result in the highest defect probability and therefore the highest grading.

[0158] Typically, during substrate manufacturing, focus value variations result in variations in the CD printed on the substrate. Therefore, in one embodiment, a probability distribution 1051 of focus values ​​may be used to define a range in which defect sizes may be calculated for a particular hotspot. In one embodiment, the probability distribution 1051 may be a Gaussian distribution, i.e., a normalized distribution, within a selected range. In one embodiment, the selected range may correspond to a positive focus range defined by boundary values ​​f+ and f++Δf; where f+ is a lower limit and f++Δf is an upper limit. The grading algorithm may then determine defect sizes within the selected positive focus range (e.g., 1055). For example, based on the relationship (e.g., 1052 or 1053), defect sizes within the focus range 1055 may be calculated.

[0159] As previously described, in one embodiment, the classification may be calculated based on the defect size relative to a defect threshold (e.g., a minimum allowable CD limit). In one embodiment, the defect threshold may be based on a desired yield (e.g., 99.9%). For example, the defect size may be calculated relative to the defect threshold 1060, such as Fig. 14B shown.

[0160] In one embodiment, the defect size of the hotspot may be defined as the sum of the product of the focus value probability and the difference between the defect occurrence of the hotspot and the defect threshold. For example, the defect size may be calculated based on the following equation:

[0161] ΔDFSZi=Σj(focus value probability)j(DFSZij-Dth)

[0162] =A1×W1+A2×W2+ … + A10×W10

[0163] Where ΔDFSZi is the expected defect size of the i-th hotspot Hi that is most likely to be printed within the focus uncertainty range; DFSZij is the defect size of the i-th hotspot at the j-th focus value, and Dth is the defect threshold. Fig. 14B As shown, values ​​A1-A10 may be the difference between the defect relationship (e.g., 1052) and the defect threshold, and W1-W10 may be the probability of focus values ​​calculated from, for example, normalized focus values ​​within a selected focus range. In one example, A1-A7>0, A8-A10<0, and W1>W2>W3 ... >W10.

[0164] Based on the above equation, the defect size of one or more hot spots in the set of hot spots (e.g., 4001 or 5001) can be determined. In addition, the hot spot with the highest defect size can be assigned the highest grade (e.g., grade 1). For example, the second hot spot (corresponding to 1053) can be assigned grade 1, the first hot spot can be assigned grade 2, the third hot spot can be assigned grade 3, and so on. According to one embodiment, the grading depends on the accuracy of the defect relationship (e.g., 1052 and 1053) and the focus value. Therefore, if the relationship changes, the grading will also change. In one embodiment, the adjusted value of the focus and / or defect relationship (e.g., from method 4000 or 5000) based on the measurement feedback (e.g., 4008 or 5004) can result in accurate grading of the hot spots. For example, in one embodiment, the Bossung curve can be adjusted based on the deviation function, which can effectively affect the grading of the hot spots.

[0165] Fig.15 An example inspection device (e.g., a scatterometer) is depicted. It comprises a broadband (white light) radiation projector 2 that projects radiation onto a substrate W. The redirected radiation is passed to a spectrometer detector 4, which measures a spectrum 10 (intensity, as a function of wavelength) of the specularly reflected radiation, as shown, for example, at the bottom left in the figure. From this data, the processor PU may generate a signal, for example, by rigorous coupled wave analysis and nonlinear regression, or by comparing the signal with the signal, e.g., Fig.19 The simulated spectral library shown in the lower right is compared to reconstruct the structure or profile that produced the detected spectrum. Typically, for the reconstruction, the general form of the structure is known and some variables are assumed from knowledge of the process by which the structure was made, leaving only some structural variables to be determined from the measured data. This inspection device can be configured as a normal incidence inspection device or an oblique incidence inspection device.

[0166] Fig.16Another inspection device that may be used is shown in . In this arrangement, radiation emitted by a radiation source 2 is collimated using a lens system 12 and transmitted through an interference filter 13 and a polarizer 17, reflected by a partially reflective surface 16 and focused to a spot S on a substrate W via an objective lens 15, which has a high numerical aperture (NA), ideally at least 0.9 or at least 0.95. Immersion inspection devices (using a fluid with a relatively high refractive index, such as water) may even have a numerical aperture of more than 1.

[0167] As in the lithographic apparatus LA, one or more substrate tables may be provided to hold a substrate W during measurement operations. The substrate table may be similar in form to Figure 1 The substrate table WT of the inspection apparatus may be similar or identical to that of the lithographic apparatus. In examples where the inspection apparatus is integrated with the lithographic apparatus, they may even be the same substrate table. A coarse positioner and a fine positioner may be provided to a second positioner PW which is configured to accurately position the substrate relative to the measuring optical system. For example, various sensors and actuators are provided to obtain the position of an object of interest and to bring it into position below the objective lens 15. Typically, many measurements will be made on targets at different positions across the substrate W. The substrate support may be moved in the X and Y directions to obtain different targets, and in the Z direction to obtain the desired position of the target relative to the focus of the optical system. For example, when in practice the optical system may be kept essentially stationary (usually in the X and Y directions, but possibly also in the Z direction) and only the substrate moves, it is convenient to think about and describe the operation by bringing the objective lens to different positions relative to the substrate. As long as the relative position of substrate and optical system is correct, it does not matter in principle which one is moving in the real world, or whether both are moving, or a combination of a part of the optical system is moving (e.g. in Z and / or tilt direction) while the rest of the optical system is stationary and the substrate is moving (e.g. in X and Y direction, but optionally also in Z and / or tilt direction).

[0168] The radiation redirected by the substrate W then passes through the partially reflective surface 16 into the detector 18 for detection of the spectrum. The detector 18 may be located at the back-projected focal plane 15 (i.e., at the focal length of the lens system 15), or the plane 15 may be re-imaged onto the detector 18 with auxiliary optics (not shown). The detector may be a two-dimensional detector, so that a two-dimensional angular scattering spectrum of the substrate target 30 may be measured. The detector 18 may be, for example, a CCD or CMOS sensor array, and may use, for example, an integration time of 40 milliseconds per frame.

[0169] The reference beam can be used, for example, to measure the intensity of the incident radiation. To this end, when the radiation beam is incident on the partially reflecting surface 16, a portion of it is projected through the partially reflecting surface 16 as a reference beam towards the reference reflector 14. The reference beam is then projected onto a different portion of the same detector 18 or alternatively onto a different detector (not shown).

[0170] One or more interference filters 13 may be used to select a wavelength of interest in the range of, for example, 405-790 nm or even lower, such as 200-300 nm. The interference filter may be tunable, rather than comprising a collection of different filters. A grating may be used instead of an interference filter. An aperture stop or spatial light modulator (not shown) may be provided in the illumination path to control the range of angles of incidence of the radiation on the target.

[0171] The detector 18 can measure the intensity of the redirected radiation at a single wavelength (or a narrow wavelength range), the intensity separated at multiple wavelengths, or the intensity integrated over a wavelength range. In addition, the detector can measure the intensity of the transverse magnetic polarized radiation and the transverse electric polarized radiation separately and / or the phase difference between the transverse magnetic polarized radiation and the transverse electric polarized radiation.

[0172] The target 30 on the substrate W may be a one-dimensional grating that is printed so that after development, the bars are formed by solid resist lines. The target 30 may be a two-dimensional grating that is printed so that after development, the grating is formed by solid resist columns or vias in the resist. The bars, columns or vias may be etched into or onto the substrate (e.g., into one or more layers on the substrate). The pattern (e.g., the pattern of bars, columns or vias) is sensitive to process variations during the patterning process (e.g., optical aberrations in the lithographic projection apparatus (particularly the projection system PS), focus variations, dose variations, etc.) and will be reflected in variations in the printed grating. Therefore, measurement data of the printed grating is used to reconstruct the grating. One or more parameters of the one-dimensional grating (such as line width and / or shape) or one or more parameters of the two-dimensional grating (such as column or via width or length or shape) may be input into a reconstruction process performed by the processor PU based on knowledge of the printing step and / or other inspection processes.

[0173] In addition to measuring parameters by reconstruction, angle-resolved scatterometry can also be used to measure the asymmetry of features in the product and / or resist pattern. A special application of asymmetry measurement is for overlay measurements, where the target 30 includes a set of periodic features superimposed on another set of periodic features. Fig.15 or Fig.16The concept of asymmetry measurement of an instrument is described, for example, in U.S. Patent Application Publication US2006-066855 (the entire contents of which are incorporated herein). In brief, while the positions of the diffraction orders in the diffraction spectrum of a target are determined solely by the period of the target, the asymmetry in the diffraction spectrum represents the asymmetry of the individual features that make up the target. Fig.16 In an instrument in which the detector 18 may be an image sensor, such asymmetry in the diffraction orders manifests itself directly as an asymmetry in the pupil image recorded by the detector 18. Such asymmetry may be measured by digital image processing in the unit PU and calibrated against a known overlap value.

[0174] Fig.17 A plan view of a typical target 30 is shown, and Fig.16 In order to obtain a diffraction spectrum that is not disturbed by surrounding structures, in one embodiment, the target 30 is a periodic structure (e.g., a grating) that is larger than the width (e.g., diameter) of the illumination spot S. The width of the spot S may be smaller than the width and length of the target. In other words, the target is "underfilled" by the illumination, and the diffraction signal is substantially free of any signal from product features, etc., external to the target itself. The illumination device 2, 12, 13, 17 may be configured to provide illumination of uniform intensity across the back focal plane of the objective 15. Alternatively, the illumination may be limited to an on-axis or off-axis direction, for example by including an aperture in the illumination path.

[0175] Fig.18 An example process of determining values ​​of one or more variables of interest for a target pattern 30' based on measurement data obtained using metrology is schematically depicted.The radiation detected by the detector 18 provides a measured radiation distribution 108 for the target 30'.

[0176] For a given target 30', a radiation distribution 208 may be calculated / simulated from a parameterized model 206 using, for example, a numerical Maxwell solver 210. The parameterized model 206 shows example layers of various materials that make up the target and are associated with the target. The parameterized model 206 may include one or more variables of features and layers of a portion of the target under consideration that may be varied and derived. Fig.18As shown, the one or more variables may include the thickness t of one or more layers, the width w (e.g., CD) of one or more features, the height h of one or more features, and / or the sidewall angle α of one or more features. Although not shown, the one or more variables may also include, but are not limited to, the refractive index (e.g., real or complex refractive index, refractive index tensor, etc.) of one or more layers, the extinction coefficient of one or more layers, the absorptivity of one or more layers, the resist loss during development, the footing of one or more features, and / or the line edge roughness of one or more features. The initial values ​​of the variables may be the expected values ​​of the target being measured. Then, at 212, the measured radiation distribution 108 is compared to the calculated radiation distribution 208 to determine the difference between the two. If there is a difference, the values ​​of one or more variables of the parameterized model 206 may be changed, a new calculated radiation distribution 208 is obtained, and it is compared with the measured radiation distribution 108 until there is a sufficient match between the measured radiation distribution 108 and the calculated radiation distribution 208. At this point, the values ​​of the variables of the parameterized model 206 provide a good or best match to the geometry of the actual target 30'. In one embodiment, a sufficient match exists when the difference between the measured radiation distribution 108 and the calculated radiation distribution 208 is within a tolerance threshold.

[0177] Fig.19 Schematically depicting an embodiment of an electron beam inspection apparatus 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 focus.

[0178] When the substrate 100 is irradiated by 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. By synchronously detecting the electrons generated from the sample with, for example, two-dimensional scanning of the electron beam by the beam deflector 204 or repeated scanning of the electron beam 202 in the X or Y direction by the beam deflector 204, together with continuous movement of the substrate 100 in the other of the X or Y directions by the substrate stage 101, a two-dimensional electron beam image can be obtained. Therefore, in one embodiment, the electron beam inspection device has a field of view of the electron beam defined by the angular range of the electron beam that can be provided by the electron beam inspection device (for example, the angular range of the electron beam 202 that the deflector 204 can provide). Therefore, the spatial range of the field of view is the spatial range of the angular range of the electron beam that can impinge on a surface (where the surface can be stationary or can move relative to the field).

[0179] 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 one embodiment, the image processing system 300 may have a memory 303 to store all or part of the digital image for processing by a processing unit 304. The processing unit 304 (e.g., specially designed hardware or a combination of hardware and software or a computer-readable medium including software) is configured to convert or process the digital image into a data set representing the digital image. In one embodiment, the processing unit 304 is configured or programmed to cause the execution of the method described herein. 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 the reference database. The display device 302 may be connected to the image processing system 300 so that the operator can perform necessary operations on the device with the help of a graphical user interface.

[0180] Fig. 20 Another embodiment of the inspection device is schematically shown. The system is used to inspect a sample 90 (such as a substrate) on a sample stage 88, and includes a charged particle beam generator 81, a focusing 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.

[0181] The charged particle beam generator 81 generates a primary charged particle beam 91. The focusing lens module 82 converges 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 region of interest on the sample 90 fixed on the sample stage 88. In one embodiment, the charged particle beam generator 81, the focusing lens module 82 and the probe forming objective lens module 83 or their equivalent designs, substitutes or any combination thereof together form a charged particle beam probe generator, which generates a scanning charged particle beam probe 92.

[0182] The secondary charged particle detector module 85 detects secondary charged particles 93 emitted from the sample surface when bombarded by the charged particle beam probe 92 (possibly also 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 thereby form at least one scanning image. In one embodiment, the secondary charged particle detector module 85 and the image forming module 86 or their equivalent designs, substitutes, or any combination thereof together form an image forming device that forms a scanning image from the detected secondary charged particles emitted from the sample 90 bombarded by the charged particle beam probe 92.

[0183] In one embodiment, the monitoring module 87 is coupled to the image forming module 86 of the image forming device to monitor, control, etc. the patterning process, and / or uses the scanned image of the sample 90 received from the image forming module 86 to derive parameters for patterning process design, control, monitoring, etc. Thus, in one embodiment, the monitoring module 87 is configured or programmed to cause the execution of the methods described herein. In one embodiment, the monitoring module 87 includes a computing device. In one embodiment, the monitoring module 87 includes a computer program for providing the functionality described herein and encoded on a computer readable medium formed or disposed within the monitoring module 87.

[0184] In one embodiment, similar to Fig.19 An electron beam inspection tool that uses a probe to inspect the substrate, Fig. 20 The electron current in a system is related to, for example Fig.19 The CD SEM shown is significantly larger than that shown, so that the detection spot is large enough for fast detection. However, due to the larger probe spot, the resolution may not be as high as the CD SEM. In one embodiment, the inspection device discussed above (in Figure 7 and 8) can be single-beam or multi-beam devices without limiting the scope of the present disclosure.

[0185] From e.g. Fig.19 and / or Fig. 20 SEM images of the system can be processed to extract contours describing the edges of objects representing device structures in the image. These contours are then typically quantified via a metric (such as CD) at a user-defined cut line. Thus, typically, images of device structures are compared and quantified via a metric such as edge-to-edge distance (CD) measured on the extracted contours or a simple pixel difference between images.

[0186] Fig.21Example defects such as footing 2402 and necking 2412 type failures that may be observed for certain settings of process variables such as dose / focus are shown. In the case of footing, descum may be performed to remove footing 2404 at the substrate. In the case of necking 2412, the resist thickness may be reduced by removing the top layer 2414. In one embodiment, another grading criterion may be whether defects generated by some hot spots can be fixed by post-patterning processes. For example, hot spots that cause defects that can be fixed in post-patterning processes and occur less frequently than other defects may be graded much lower.

[0187] Fig. 22 An exemplary flow chart for modeling and / or simulating portions of a patterning process is shown in . It will be appreciated that the model may represent different patterning processes and need not include all of the models described below. Source model 1200 represents the optical characteristics of the illumination of the patterning device (including the radiation intensity distribution, bandwidth, and / or phase distribution). Source model 1200 may represent the optical characteristics of the illumination, including but not limited to numerical aperture settings, illumination sigma (σ) settings, and any specific illumination shape (e.g., off-axis radiation shapes such as toroidal, quadrupole, dipole, etc.), where σ (or sigma) is the outer radial extent of the illuminator.

[0188] The projection optics model 1210 represents the optical properties of the projection optics (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics). The projection optics model 1210 can represent the optical properties of the projection optics, including aberrations, distortions or distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0189] The patterning device / design layout model module 1220 captures how design features are arranged in a pattern of a patterning device, and may include a representation of detailed physical properties of the patterning device, as described, for example, in U.S. Pat. No. 7,587,704 (the entire contents of which are incorporated herein by reference). In one embodiment, the patterning device / design layout model module 1220 represents the optical properties (including changes in radiation intensity distribution and / or phase distribution caused by a given design layout) of a design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.), which is a representation of the arrangement of features on or formed by the patterning device. Since the patterning device used in a lithographic projection apparatus can vary, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the illumination and projection optics. The goal of the simulation is typically to accurately predict, for example, edge location and CD, which can then be compared to the device design. The device design is typically defined as a pre-OPC patterning device layout and will be provided in a standardized digital file format such as GDSII or OASIS.

[0190] An aerial image 1230 can be simulated from a source model 1200, a projection optics model 1210, and a patterning device / design layout model 1220. The aerial image (AI) is the radiation intensity distribution at the substrate level. The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, patterning device, and projection optics) determine the aerial image.

[0191] A resist layer on a substrate is exposed by an aerial image, and the aerial image is transferred to the resist layer as a potential "resist image" (RI) therein. The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. A resist image 1250 can be simulated from the aerial image 1230 using a resist model 1240. A resist model can be used to calculate a resist image from an aerial image, an example of which can be found in U.S. Patent Application Publication No. US 2009-0157360 (the disclosure of which is incorporated herein by reference in its entirety). The resist model typically describes the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development to predict, for example, the profile of a resist feature formed on a substrate, and therefore it is typically only related to such properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking, and development). In one embodiment, the optical properties of the resist layer (e.g., refractive index, film thickness, propagation, and polarization effects) can be captured as part of the projection optical model 1210.

[0192] Thus, in general, the connection between the optical model and the resist model is the simulated spatial image intensity within the resist layer, which results from the projection of radiation onto the substrate, refraction at the resist interface and multiple reflections in the resist film stack. By absorbing the incident energy, the radiation intensity distribution (spatial image intensity) becomes a latent "resist image", which is further modified by diffusion processes and various loading effects. Efficient simulation methods that are fast enough for full-chip applications approximate the true three-dimensional intensity distribution in the resist stack by a two-dimensional spatial (and resist) image.

[0193] In one embodiment, the resist image may be used as input to the post-pattern transfer process model module 1260. The post-pattern transfer process model 1260 defines one or more post-resist development processes (eg, etching, developing, etc.).

[0194] The simulation of the patterning process can, for example, predict the profile, CD, edge position (e.g., edge position error), etc. in the resist and / or etch image. Thus, the purpose of the simulation is to accurately predict, for example, edge position and / or spatial image intensity slope and / or CD, etc. of the printed pattern. These values ​​can be compared to the expected design, for example, to correct the patterning process, identify locations where defects are expected to occur, etc. The expected design is typically defined as a pre-OPC design layout, which can be provided in a standardized digital format file format such as GDSII or OASIS or other file formats.

[0195] Thus, the model formula describes most, if not all, of the known physical and chemical properties of the overall process, and each model parameter ideally corresponds to a different physical or chemical effect. The model formula therefore sets an upper limit on the extent to which the model can be used to simulate the overall manufacturing process.

[0196] In one embodiment, a method for training a machine learning model of a patterning process is provided. The method includes: obtaining a training data set, the training data set including: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on a substrate using the mask pattern, and (iii) measured values ​​of parameters of a patterning process applied during imaging of the mask pattern on the substrate; training a machine learning model based on the training data set via a processor to predict differences in characteristics of the simulated pattern and the printed pattern.

[0197] In one embodiment, the training step is an iterative process, which involves: receiving inspection data including measurement values ​​of a printed pattern image and parameters of a patterning process; obtaining a simulated pattern via a simulated patterning process model based on the measurement values ​​of the parameters of the patterning process; predicting an image corresponding to the simulated pattern via a machine learning model; determining the difference between the predicted pattern image and the printed pattern image; and adjusting model parameter values ​​of the machine learning model so that the difference between the predicted pattern image and the printed pattern image is reduced.

[0198] In one embodiment, adjustment of model parameter values ​​of a machine learning model involves: determining a gradient map of the difference between a predicted pattern image and a printed pattern image as a function of the model parameters; identifying model parameter values ​​based on the gradient map so that the predicted pattern image and the printed pattern image are reduced; and adjusting the model parameter values ​​based on the identified values.

[0199] In one embodiment, the simulated pattern is an aerial image, a mask image, a resist image, and / or an etch image.

[0200] In one embodiment, obtaining the simulated pattern includes simulating a patterning process model using the mask pattern as input.

[0201] In one embodiment, the simulated pattern includes hot spots that may fail when imaged on the substrate.

[0202] In one embodiment, the simulated pattern includes a pattern that does not satisfy a lithography manufacturability check.

[0203] In one embodiment, the characteristic of the simulated pattern or the printed pattern is a critical dimension of a feature of the simulated pattern or a profile of a feature of the simulated pattern.

[0204] In one embodiment, the inspection data includes defect data of the imaged substrate obtained via an inspection device.

[0205] In one embodiment, the inspection data is an image of the printed substrate, wherein the image is a scanning electron beam image and / or an optical metrology image.

[0206] In one embodiment, the parameters of the patterning process are dose and / or focus.

[0207] In one embodiment, measurements of parameters of the patterning process are obtained via a metrology tool.

[0208] In one embodiment, the machine learning model is a convolutional neural network.

[0209] In one embodiment, adjusting the model parameter values ​​includes adjusting the values ​​of: one or more weights of a layer of a convolutional neural network, one or more biases of a layer of a convolutional neural network, hyperparameters associated with the convolutional neural network, and / or the number of layers of the convolutional neural network.

[0210] In one embodiment, a method for correcting a characteristic of a simulated pattern of a patterning process is provided. The method involves: determining a simulated pattern and a characteristic of the simulated pattern via a simulated patterning process model; determining a characteristic adjustment value of the characteristic of the simulated pattern via a trained machine learning model; and correcting the characteristic of the simulated pattern based on the characteristic adjustment value via a processor.

[0211] In one embodiment, the method also involves: obtaining multiple simulation patterns and multiple adjustment characteristic values ​​corresponding to the multiple simulation patterns via a trained machine learning model; adjusting the characteristics of each simulation pattern in the multiple simulation patterns based on the multiple adjustment characteristic values ​​via a processor; and determining the ranking of the multiple simulation patterns based on the adjusted characteristics of the simulation patterns via the processor.

[0212] In one embodiment, the method further involves determining a sampling plan for metrology of the printed substrate based on the ranking of the plurality of simulated patterns.

[0213] In one embodiment, the plurality of simulated patterns include patterns corresponding to a plurality of hot spots.

[0214] In one embodiment, the sampling plan is based on a hierarchy of hot spots.

[0215] In one embodiment, the method further involves: directing, via the processor, the inspection device to collect measurement data on the printed substrate based on the ranking of hot spots; and determining, via the processor, defects on the printed substrate based on the measurement data.

[0216] In addition, in one embodiment, a method of training a machine learning model is provided, the machine learning model being configured to predict a grade of a set of simulated patterns for a patterning process. The method involves: obtaining (i) a set of simulated patterns corresponding to a set of mask patterns, (ii) defect data of a set of printed patterns imaged on a substrate using the set of mask patterns, and (iii) a sampling plan associated with the substrate imaged using the set of mask patterns; and training the machine learning model based on the defect data and the sampling plan via a processor so that the machine learning model is configured to predict a grade of the set of simulated patterns that matches a reference grade based on the defect data.

[0217] In one embodiment, the training step is an iterative process, the iterations involving: predicting the grading of a set of simulated patterns via a machine learning model using a sampling plan and defect data as input; determining the difference between the predicted grading and a reference grading based on the defect data; and adjusting the model parameter values ​​of the machine learning model so that the difference between the gradings is reduced.

[0218] In one embodiment, obtaining the set of simulated patterns involves simulating a patterning process model using each mask pattern in the set of mask patterns, and identifying from the simulation results the set of simulated patterns that are likely to fail when imaged on the substrate.

[0219] In one embodiment, the set of simulated patterns corresponds to a set of hot spots.

[0220] In one embodiment, the set of simulated patterns includes simulated patterns that do not satisfy a lithography manufacturability check.

[0221] In one embodiment, the defect data is a defect count associated with one or more patterns on a printed substrate.

[0222] In one embodiment, the defect data is a value or range of values ​​of a critical dimension associated with one or more patterns on a printed substrate.

[0223] In one embodiment, the defect data is extracted from an image of the printed substrate, wherein the image is a scanning electron beam image and / or an optical metrology image.

[0224] In one embodiment, the sampling plan involves: a set of locations on a printed substrate at which measurements are performed, wherein the set of locations is based on an initial ranking of a set of simulated patterns; and / or a number of measurements to be performed at one or more locations in the set of locations based on the initial ranking of the set of simulated patterns.

[0225] In one embodiment, the method further involves: receiving a set of simulated patterns; predicting a ranking of the set of simulated patterns via a trained machine learning model; and adjusting a sampling plan based on the predicted ranking of the set of simulated patterns via a processor.

[0226] In one embodiment, adjustment of the sampling plan involves adjusting: the locations in the set of locations to be measured; and / or the number of measurements to be made at one or more locations in the set of locations.

[0227] In one embodiment, adjusting positions in the set of positions involves: omitting positions in the set of positions corresponding to relatively lower ranked simulated patterns; and / or adding new positions to the set of positions corresponding to relatively higher ranked simulated patterns.

[0228] In one embodiment, adjusting a position in the set of positions includes increasing and / or decreasing the number of measurements to be performed at the positions in the subset of positions.

[0229] In one embodiment, the method further involves: directing, via the processor, the inspection device to collect measurement data on the printed substrate based on the predicted grading of the set of simulated patterns; and determining, via the processor, defects on the printed substrate based on the measurement data.

[0230] In addition, in one embodiment, a method for determining a ranking of a set of simulated patterns of a patterning process is provided. The method involves: adjusting a characteristic of at least one simulated pattern in the set of simulated patterns via a first machine learning model; determining a subset of simulated patterns based on the adjusted characteristic of at least one simulated pattern via a processor; and determining a ranking of at least one simulated pattern in the subset of simulated patterns via a second machine learning model.

[0231] In one embodiment, determining the subset of simulated patterns involves: determining whether an adjusted characteristic of at least one simulated pattern satisfies a lithographic manufacturability check; and in response to not satisfying the lithographic manufacturability check, including the at least one simulated pattern in the subset of simulated patterns.

[0232] In one embodiment, the method further involves: directing, via the processor, the inspection device to collect measurement data on the printed substrate based on the grading of at least one simulated pattern in the subset of simulated patterns; and determining, via the processor, defects on the printed substrate based on the measurement data.

[0233] In one embodiment, the characteristic of at least one simulated pattern or printed pattern is a critical dimension of a feature of at least one simulated pattern in the set of simulated patterns.

[0234] In one embodiment, a computer program product is provided. The computer program product includes a non-transitory computer-readable medium having instructions recorded thereon. The instructions implement the above method when executed by a computer system.

[0235] Fig.231 is a block diagram illustrating a computer system 100 that may help implement the methods and processes 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 to store information and instructions to be executed by the processor 104. The main memory 106 may also be used to store temporary variables or other intermediate information during the execution of instructions to be 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 to store 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 to store information and instructions.

[0236] The computer system 100 may be coupled via the bus 102 to a display 112, such as a cathode ray tube (CRT) or a flat panel or touch panel display, for displaying information to a computer user. An input device 114 including alphanumeric and other keys is coupled to the bus 102 to communicate information and command selections to the processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selections to the processor 104 and for controlling cursor movement on the display 112. The input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), to allow the device to specify a position in a plane. A touch panel (screen) display may also be used as an input device.

[0237] According to one embodiment, according to one example, portions of the process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the processing steps described herein. One or more processors of a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuitry and software.

[0238] 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 the wires that make up 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 storage chips or boxes, carrier waves described below, or any other media from which a computer can read.

[0239] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and then send the instructions over a telephone line using a modem. A modem local to computer system 100 may receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0240] The computer system 100 also desirably includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides bidirectional data communications to couple to a network link 120 connected to a local area network 122. For example, the communication interface 118 may be an integrated services digital network (ISDN) card or a modem for providing a data communication connection to a corresponding type of telephone line. As another example, the communication interface 118 may be a local area network (LAN) card for providing a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, the communication interface 118 sends and receives electrical, electromagnetic or optical signals carrying digital data streams representing various types of information.

[0241] The network link 120 typically provides data communications through one or more networks to other data devices. For example, the network link 120 may provide a connection through a local network 122 to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126. The ISP 126, in turn, provides data communication services through a global packet data communications network, now commonly referred to as the "Internet" 128. Both the local network 122 and the Internet 128 use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 120 and through the communication interface 118, which carry the digital data to and from the computer system 100, are example forms of carrier waves that transport the information.

[0242] The computer system 100 can send messages and receive data, including program code, through the network, network link 120, and communication interface 118. In the Internet example, server 130 can send the requested code for an application through Internet 128, ISP 126, local network 122, and communication interface 118. For example, one such downloaded application can provide illumination optimization of an embodiment. The received code can be executed by processor 104 as it is received, and / or stored in storage device 110 or other non-volatile storage for later execution. In this manner, computer system 100 can obtain application code in the form of a carrier wave.

[0243] Fig.24 Another exemplary lithographic projection apparatus 1000 is schematically depicted, the lithographic projection apparatus 1000 comprising:

[0244] - a source collector module SO providing radiation;

[0245] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. EUV radiation) coming from the source collector module SO;

[0246] a support structure (eg, mask table) MT configured to support a patterning device (eg, mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0247] a substrate table (eg, wafer stage) WT configured to hold a substrate (eg, a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

[0248] - 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).

[0249] As depicted here, the device LA is reflective (e.g., employing a reflective mask). It should be noted that because most materials are absorptive in the EUV wavelength range, the patterning device can have a multilayer reflector comprising, for example, a multilayer stack of molybdenum and silicon. In one example, the multilayer stack reflector has 40 pairs of molybdenum and silicon layers, each with a thickness of a quarter wavelength. X-ray lithography can produce even smaller wavelengths. Since most materials are absorptive at both EUV and X-ray wavelengths, a thin piece of patterned absorbing material (e.g., a TaN absorber on the multilayer reflector) on the topography of the patterning device defines where features are printed (positive resist) or where they are not printed (negative resist).

[0250] refer to Fig.24 , the illuminator IL receives the extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not limited to, converting a material into a plasma state of at least one element having one or more emission lines in the EUV range (e.g., xenon, lithium, or tin). In one such method, the plasma can be generated by irradiating a fuel (such as a droplet, stream, or cluster of material having a line emitting element) with a laser beam, commonly referred to as laser produced plasma ("LPP"). The source collector module SO can be part of an EUV radiation system, which includes Fig.24 A laser not shown in the figure is used to provide a laser beam for exciting the fuel. The resulting plasma emits output radiation, such as EUV radiation, which is collected using a radiation collector disposed in a source collector module. 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.

[0251] 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 with the aid of a beam delivery system including, for example, suitable guide mirrors and / or a beam expander. In other cases, the radiation source may be an integral part of the source collector module, for example when the radiation source is a discharge produced plasma EUV generator (commonly referred to as a DPP source).

[0252] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as outer σ and inner σ, respectively) may be adjusted. In addition, the illuminator IL may include various other components, such as faceted field and pupil mirror devices. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0253] The radiation beam B is incident on a patterning device (e.g. a mask) MA, which is held on a support structure (e.g. a mask table) MT, and is patterned by the patterning device. After reflection from the patterning device (e.g. a mask) MA, the radiation beam B passes through a projection system PL, which focuses the beam onto a target portion C of a substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g. an interferometric device, a linear encoder or a 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, a first positioner PM and a further position sensor PS1 can be used to precisely position the patterning device (e.g. a mask) MA relative to the path of the radiation beam B. The patterning device (e.g. a mask) MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0254] The depicted device LA can be used in at least one of the following modes:

[0255] 1. In step mode, the support structure (e.g. mask table) MT and the substrate table WT are kept substantially stationary while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

[0256] 2. 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 speed 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.

[0257] 3. In another mode, the support structure (e.g. mask table) MT is kept substantially stationary so as to hold the programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, typically a pulsed radiation source is employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or between consecutive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type described above.

[0258] Fig.25The 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 can be maintained in an enclosed structure 220 of the source collector module SO. An EUV radiation emitting plasma 210 can be formed by a discharge-generated plasma radiation source. EUV radiation can be generated by a gas or vapor (e.g., xenon, lithium vapor, or tin vapor), wherein a very hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is generated, for example, by a discharge that causes an at least partially ionized plasma. In order to effectively generate radiation, a partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required. In one embodiment, a plasma that excites tin (Sn) is provided to generate EUV radiation.

[0259] The radiation emitted by the hot plasma 210 enters the collector chamber 212 from the source chamber 211 via an optional gas barrier or contaminant collector 230 (also referred to as a contaminant barrier or foil collector in some cases) located in or below an opening in the source chamber 211. The contaminant collector 230 may include a channel structure. The contaminant collector 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. As known in the art, the contaminant collector or contaminant barrier 230 further referred to herein includes at least a channel structure.

[0260] The collector chamber 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 from the grating spectral filter 240 to be focused in a virtual source point IF along the optical axis indicated by the dash-dot line "O". The virtual source point IF is often referred to as an intermediate focus, and the source collector module is arranged so that the intermediate focus IF is located at or near an opening 221 in the enclosure 220. The virtual source point IF is an image of the radiation emitting plasma 210.

[0261] The radiation then passes through an illumination system IL which may include a polygonal field mirror arrangement 22 and a polygonal pupil mirror arrangement 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA and to provide a desired uniformity of radiation intensity at the patterning device MA. When the radiation beam 21 held by the support structure MT is reflected at the patterning device MA, 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.

[0262] There may typically be more elements than shown in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, a grating spectral filter 240 may optionally be present. Furthermore, there may be more mirrors than shown in the figures, for example with Fig.25 Compared to the ones shown, there may be 1-6 more reflective elements in the projection system PS.

[0263] like Fig.25 As shown, the collector optics CO is depicted as a nested collector with grazing incidence reflectors 253, 254 and 255, merely as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254 and 255 are arranged axially symmetrically around the optical axis O, and this type of collector optics CO is expected to be used in conjunction with a discharge produced plasma radiation source.

[0264] Alternatively, the source collector module SO may be as follows Fig.26 Part of the LPP radiation system shown. The laser LAS is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li) to produce a highly ionized plasma 210 with an electron temperature of tens of eV. The high-energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by the collector optics CO at near normal incidence and focused onto an opening 221 in the enclosed structure 220.

[0265] The embodiments may be further described using the following terms:

[0266] 1. A method for training a machine learning model of a patterning process, the method comprising:

[0267] obtaining a training data set comprising: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on the substrate using the mask pattern, and (iii) measured values ​​of parameters of the patterning process applied during imaging of the mask pattern on the substrate;

[0268] The machine learning model is trained, via a processor, based on the training data set to predict differences in characteristics of the simulated pattern and the printed pattern.

[0269] 2. A method according to clause 1, wherein the training step is an iterative process, the iterative process comprising:

[0270] receiving said inspection data including a printed pattern image and said measured values ​​of said parameters of said patterning process;

[0271] obtaining the simulated pattern via a simulated patterning process model based on the measured values ​​of the parameters of the patterning process;

[0272] predicting, via the machine learning model, an image corresponding to the simulated pattern;

[0273] determining the difference between the predicted pattern image and the printed pattern image; and

[0274] The model parameter values ​​of the machine learning model are adjusted so that the difference between the predicted pattern image and the printed pattern image is reduced.

[0275] 3. The method of clause 2, wherein the adjusting of the model parameter values ​​of the machine learning model comprises:

[0276] determining a gradient map of the difference between the predicted pattern image and the printed pattern image as a function of model parameters;

[0277] identifying the model parameter values ​​based on the gradient map such that the predicted pattern image and the printed pattern image are reduced; and

[0278] The model parameter value is adjusted based on the identified value.

[0279] 4. A method according to any one of clauses 1 to 3, wherein the simulated pattern is an aerial image, a mask image, a resist image and / or an etching image.

[0280] 5. A method according to any one of clauses 1 to 4, wherein obtaining the simulated pattern comprises: simulating the patterning process model using the mask pattern as input.

[0281] 6. A method according to any one of clauses 1 to 5, wherein the simulated pattern includes hot spots that may fail when imaged onto the substrate.

[0282] 7. A method according to any one of clauses 1 to 6, wherein the simulated pattern comprises a pattern that does not satisfy a lithographic manufacturability check.

[0283] 8. A method according to any one of clauses 1 to 7, wherein the characteristic of the simulated pattern or the printed pattern is a critical dimension of a feature of the simulated pattern or a profile of the feature of the simulated pattern.

[0284] 9. A method according to any one of clauses 1 to 8, wherein the inspection data comprises defect data of the imaged substrate obtained via an inspection device.

[0285] 10. A method according to any of clauses 1 to 9, wherein the inspection data is an image of the printed substrate, wherein the image is a scanning electron beam image and / or an optical metrology image.

[0286] 11. A method according to any one of clauses 1 to 10, wherein the parameters of the patterning process are dose and / or focus.

[0287] 12. A method according to any one of clauses 1 to 11, wherein the measured value of the parameter of the patterning process is obtained via a metrology tool.

[0288] 13. A method according to any one of clauses 1 to 12, wherein the machine learning model is a convolutional neural network.

[0289] 14. A method according to any one of clauses 2 to 13, wherein said adjusting the model parameter value comprises adjusting the value of:

[0290] one or more weights of a layer of the convolutional neural network,

[0291] one or more biases of a layer of the convolutional neural network,

[0292] Hyperparameters associated with the convolutional neural network, and / or

[0293] The number of layers of the convolutional neural network.

[0294] 15. A method of correcting a characteristic of a simulated pattern of a patterning process, the method comprising:

[0295] determining the simulated pattern and the characteristics of the simulated pattern via a simulated patterning process model;

[0296] determining, via the trained machine learning model, a characteristic adjustment value for the characteristic of the simulated pattern; and

[0297] The characteristic of the simulation pattern is corrected based on the characteristic adjustment value via a processor.

[0298] 16. The method of clause 15, further comprising:

[0299] obtaining, via the trained machine learning model, a plurality of simulation patterns and a plurality of adjustment characteristic values ​​corresponding to the plurality of simulation patterns;

[0300] adjusting, via the processor, the characteristic of each of the plurality of simulated patterns based on the plurality of adjusted characteristic values; and

[0301] A ranking of the plurality of simulated patterns is determined, via the processor, based on the adjusted characteristics of the simulated patterns.

[0302] 17. The method of any one of clauses 15 to 16, further comprising:

[0303] A sampling plan for metrology of a printed substrate is determined based on the ranking of the plurality of simulated patterns.

[0304] 18. A method according to any one of clauses 15 to 17, wherein the plurality of simulated patterns comprises patterns corresponding to a plurality of hot spots.

[0305] 19. A method according to any one of clauses 15 to 18, wherein the sampling plan is based on the classification of the hot spots.

[0306] 20. The method of any one of clauses 15 to 19, further comprising:

[0307] directing, via the processor, an inspection device to collect measurement data on the printed substrate based on the ranking of the hot spots; and

[0308] Defects on the printed substrate are determined, via the processor, based on the measurement data.

[0309] 21. A method of training a machine learning model, the machine learning model configured to predict a ranking of a collection of simulated patterns of a patterning process, the method comprising:

[0310] obtaining (i) the set of simulated patterns corresponding to the set of mask patterns, (ii) defect data for a set of printed patterns imaged on a substrate using the set of mask patterns, and (iii) a sampling plan associated with the substrate imaged using the set of mask patterns; and

[0311] The machine learning model is trained, via a processor, based on the defect data and the sampling plan such that the machine learning model is configured to predict a grade for the set of simulated patterns that matches a reference grade based on the defect data.

[0312] 22. The method of clause 21, wherein the training step is an iterative process, the iterations comprising:

[0313] predicting the ranking of the set of simulated patterns via the machine learning model using the sampling plan and the defect data as input;

[0314] determining a difference between the predicted grade and the reference grade based on the defect data; and

[0315] The model parameter values ​​of the machine learning model are adjusted so that the differences between the classifications are reduced.

[0316] 23. The method of clauses 21 to 22, wherein obtaining the set of simulated patterns comprises:

[0317] simulating a patterning process model using each mask pattern in the set of mask patterns, and

[0318] A set of the simulated patterns that are likely to fail when imaged onto the substrate are identified from the simulation results.

[0319] 24. A method according to any one of clauses 21 to 23, wherein the set of simulated patterns corresponds to a set of hotspots.

[0320] 25. A method according to any of clauses 21 to 24, wherein the set of simulated patterns includes simulated patterns that do not satisfy a lithographic manufacturability check.

[0321] 26. A method according to any of clauses 21 to 25, wherein the defect data is a defect count associated with one or more patterns on the printed substrate.

[0322] 27. A method according to any of clauses 21 to 26, wherein the defect data is a value or range of values ​​of a critical dimension associated with the one or more patterns on the printed substrate.

[0323] 28. A method according to any of clauses 21 to 27, wherein the defect data is extracted from an image of the printed substrate, wherein the image is a scanning electron beam image and / or an optical metrology image.

[0324] 29. The method of any one of clauses 21 to 28, wherein the sampling plan comprises:

[0325] a set of locations on the printed substrate where measurements are performed, wherein the set of locations is based on an initial ranking of the set of simulated patterns; and / or

[0326] A number of measurements to be performed at one or more locations in the set of locations based on the initial ranking of the set of simulated patterns.

[0327] 30. The method of clause 29, further comprising:

[0328] receiving the set of simulation patterns;

[0329] predicting, via the trained machine learning model, the ranking for the set of simulated patterns; and

[0330] The sampling plan is adjusted, via the processor, based on the predicted hierarchy of the set of simulation patterns.

[0331] 31. The method of clause 30, wherein said adjusting said sampling plan comprises:

[0332] adjusting a position in the set of positions to be measured; and / or

[0333] The number of measurements to be performed at one or more locations in the set of locations.

[0334] 32. The method of clause 31, wherein said adjusting said position in said set of positions comprises:

[0335] omitting positions in the set of positions corresponding to relatively lower ranked simulated patterns; and / or

[0336] New positions corresponding to relatively higher ranked simulated patterns are added to the set of positions.

[0337] 33. A method according to clause 31, wherein said adjusting the positions in the set of positions comprises increasing and / or decreasing the number of measurements to be made at the positions in the subset of positions.

[0338] 34. A method according to any one of clauses 21 to 33, further comprising:

[0339] directing, via the processor, an inspection device to collect measurement data on the printed substrate based on the predicted grading of the set of simulated patterns; and

[0340] Defects on the printed substrate are determined, via the processor, based on the measurement data.

[0341] 35. A method of determining a ranking of a collection of simulated patterns of a patterning process, the method comprising:

[0342] adjusting a characteristic of at least one simulated pattern in the set of simulated patterns via a first machine learning model;

[0343] determining, via a processor, a subset of the simulated patterns based on the adjusted characteristic of the at least one simulated pattern; and

[0344] A ranking of the at least one simulated pattern within the subset of simulated patterns is determined via a second machine learning model.

[0345] 36. The method of clause 35, wherein determining the subset of simulated patterns comprises:

[0346] determining whether the adjusted characteristic of the at least one simulated pattern satisfies a lithography manufacturability check; and

[0347] In response to failing to satisfy the lithographic manufacturability check, including the at least one simulated pattern in the subset of simulated patterns.

[0348] 37. A method according to any one of clauses 35 to 36, further comprising:

[0349] directing, via the processor, an inspection device to collect measurement data on the printed substrate based on the ranking of the at least one simulated pattern in the subset of simulated patterns; and

[0350] Defects on the printed substrate are determined, via a processor, based on the measurement data.

[0351] 38. A method according to any one of clauses 35 to 37, wherein the characteristic of the at least one simulated pattern or the printed pattern is a critical dimension of a feature of the at least one simulated pattern in the set of simulated patterns.

[0352] 39. A computer program product comprising a non-transitory computer-readable medium having recorded thereon instructions which, when executed by a computer system, implement the method of any one of clauses 1 to 38.

[0353] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features and are particularly useful for emerging imaging technologies that are capable of producing wavelengths of increasingly smaller sizes. Emerging technologies already in use include EUV (extreme ultraviolet) lithography, which is capable of producing 193nm wavelengths using ArF lasers and even 157nm wavelengths using fluorine lasers. In addition, EUV lithography is capable of producing wavelengths in the 20-5nm range by using synchrotrons or by bombarding materials (solid or plasma) with high-energy electrons to produce photons in this range.

[0354] 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 (e.g., those used for imaging on substrates other than silicon wafers).

[0355] Although specific reference may be made herein to the use of embodiments in IC manufacturing, it should be understood that the embodiments herein may have many other possible applications. For example, it may be used to manufacture integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, micromechanical systems (MEMs), etc. The skilled person will understand that in the context of such alternative applications, any use of the terms "reticle", "wafer" or "die" herein may be considered synonymous or interchangeable with the more general terms "patterning device", "substrate" or "target portion", respectively. Before or after exposure, the substrate referred to herein may be processed in, for example, a track (a tool that typically applies a resist layer to a substrate and develops the exposed resist) or a measurement or inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, the substrate may be processed more than once, for example to create, for example, a multi-layer IC, so the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0356] In this document, the terms "radiation" and "beam" as used herein encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of about 365, about 248, about 193, about 157, or about 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams.

[0357] As used herein, the terms "optimizing" and "optimization" refer to or mean adjusting a pattern forming device (e.g., a lithographic apparatus), a patterning process, etc., so that the result and / or process has more desirable characteristics, such as higher projection accuracy of the design pattern on the substrate, a larger process window, etc. Therefore, the terms "optimizing" and "optimization" as used herein refer to or mean a process of identifying one or more values ​​of one or more parameters that provide an improvement, such as a local optimum in at least one relevant metric compared to an initial set of one or more values ​​of those one or more parameters. "Optimal" and other related terms should be interpreted accordingly. In one embodiment, the optimization steps can be iteratively applied to provide further improvements in one or more metrics.

[0358] Aspects of the present invention may be implemented in any convenient form. For example, an embodiment may be implemented by one or more appropriate computer programs, which may be carried on an appropriate carrier medium, which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Embodiments of the present invention may be implemented using a suitable device, which may specifically take the form of a programmable computer running a computer program, which is arranged to implement the method as described herein. Therefore, embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include a read-only memory (ROM); a random access memory (RAM); a disk storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), etc. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are merely for convenience and that such actions are actually caused by the computing device, processor, controller or other device executing firmware, software, routines, instructions, etc.

[0359] In the block diagrams, the illustrated components are depicted as discrete functional blocks, but the embodiments are not limited to systems in which the functionality described herein is organized as shown. The functionality provided by each component may be provided by software or hardware modules organized differently than currently described, such as such software or hardware may be mixed, combined, replicated, decomposed, distributed (e.g., in a data center or geographically), or otherwise organized. The functionality described herein may be provided by one or more processors of one or more computers that execute code stored on a tangible, non-transitory machine-readable medium. In some cases, a third-party content delivery network may host some or all of the information transmitted over the network, in which case, to the extent that information (e.g., content) is referred to as provided or otherwise provided, the information may be provided by sending instructions for retrieving the information from the content delivery network.

[0360] Unless otherwise specifically stated, as will be clear from the discussion, it should be understood that throughout the discussion of this specification, terms such as "processing," "computing," "calculating," "determining," etc. are used to refer to the actions or processes of a specific apparatus such as a special purpose computer or similar special purpose electronic processing / computing device.

[0361] The reader should understand that this application describes several inventions. Rather than dividing these inventions into multiple independent patent applications, it is better to combine these inventions into one file because their related subject matter helps save the application process. However, the unique advantages and aspects of such inventions should not be lumped together. In some cases, the embodiments solve all the defects pointed out in this article, but it should be understood that the present invention is independently useful, and some embodiments only solve a subset of such problems or provide other unmentioned benefits, which are clear to those skilled in the art who review this disclosure. Due to cost constraints, some inventions disclosed in this article may not be claimed for protection at present, and may be claimed in later applications, such as continued applications or by amending current claims. Similarly, due to space limitations, the abstract and summary sections of this document should not be regarded as a comprehensive list containing all such inventions or all aspects of such inventions.

[0362] It should be understood that the specification and drawings are not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

[0363] In view of this description, modifications and alternative embodiments of various aspects of the present invention will be clear to those skilled in the art. Therefore, this specification and the drawings are to be interpreted as illustrative only, and are intended to teach those skilled in the art the general manner of implementing the present invention. It should be understood that the forms of the present invention shown and described herein will be considered as examples of embodiments. Elements and materials may replace those shown and described herein, parts and processes may be reversed or omitted, certain features may be used independently, and embodiments or features of embodiments may be combined, all of which are clear to those skilled in the art who benefit from this specification. Changes may be made to the elements described herein without departing from the spirit and scope of the present invention as described in the following claims. The headings used herein are for organizational purposes only and are not intended to limit the scope of the specification.

[0364] As used throughout this application, the word "may" is used in a permissive sense (i.e., indicating a potential) rather than a mandatory sense (i.e., indicating a must). The words "include", "including", and "includes" and the like mean, but are not limited to. The singular forms "a", "an", and "the" used throughout this application include plural referents unless the content clearly indicates otherwise. Thus, for example, reference to "an" element or "a" element includes a combination of two or more elements, although other terms and phrases, such as "one or more", are used for one or more elements. Unless otherwise indicated, the term "or" is non-exclusive, i.e., includes both "and" and "or". Terms describing conditional relationships such as "in response to X, Y", "at X, Y", "if X, Y", "when X, Y", etc. include causal relationships in which the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributing causal condition of the consequent, for example, "the statement X occurs when condition Y holds" is a general form of "X only occurs when Y" and "X occurs when Y and Z". Such conditional relationships are not limited to consequences occurring immediately after the antecedent is obtained, as some consequences may be delayed, and in conditional statements, the antecedent is related to its consequences, for example, the antecedent is related to the likelihood of the consequence occurring. Statements in which multiple attributes or functions are mapped to multiple objects (e.g., one or more processors perform steps A, B, C, and D) include all of these attributes or functions mapped to all of these objects, as well as subsets of attributes or functions mapped to subsets of these attributes or functions (e.g., all processors perform steps AD, and the case in which processor 1 performs step A, processor 2 performs step B and part of step C, and processor 3 performs part of step C and step D), unless otherwise specified. Furthermore, unless otherwise stated, a statement that a value or action is "based on" another condition or value includes both the case where the condition or value is the only factor and the case where the condition or value is one of multiple factors. Unless otherwise stated, a statement that "each" instance of some set has some property should not be understood to exclude the case where some other identical or similar member of the larger set does not have that property, i.e., each does not necessarily mean every. References to selections from a range include the endpoints of the range.

[0365] In the above description, any process, description or block in the flowchart should be understood to represent a module, segment or code portion, which includes one or more executable instructions for implementing specific logical functions or steps in the process, and alternative implementations are included in the scope of the exemplary embodiments of this advancement, in which the functions may be performed in a different order than shown or discussed, including substantially simultaneously or in reverse order, depending on the functions involved, as will be understood by those skilled in the art.

[0366] To the extent that certain U.S. patents, U.S. patent applications, or other materials (e.g., articles) are incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is incorporated by reference only to the extent that there is no conflict between such materials and the statements and drawings set forth herein. In the event of such a conflict, any such conflicting text in such incorporated by reference U.S. patents, U.S. patent applications, and other materials is not expressly incorporated by reference herein.

[0367] Although certain embodiments have been described, these embodiments are presented by way of example only and are not intended to limit the scope of the present disclosure. In fact, the new methods, devices, and systems described herein may be embodied in a variety of other forms; moreover, various omissions, substitutions, and changes in the form of the methods, devices, and systems described herein may be made without departing from the spirit of the present disclosure. The attached claims and their equivalents are intended to overlap such forms or modifications that fall within the scope and spirit of the present disclosure.

Claims

1. A method for training a machine learning model of a patterning process, the method comprising: obtaining a training data set comprising: (i) a simulated pattern associated with a mask pattern to be printed on a substrate, (ii) inspection data of a printed pattern imaged on the substrate using the mask pattern, and (iii) measured values ​​of parameters of the patterning process applied during imaging of the mask pattern on the substrate; The machine learning model is trained, via a processor, based on the training data set to predict differences in characteristics of the simulated pattern and the printed pattern.

2. The method according to claim 1, wherein the training step is an iterative process, the iterative process comprising: receiving said inspection data including a printed pattern image and said measured values ​​of said parameters of said patterning process; obtaining the simulated pattern via a simulated patterning process model based on the measured values ​​of the parameters of the patterning process; predicting, via the machine learning model, an image corresponding to the simulated pattern; determining the difference between the predicted image corresponding to the simulated pattern and the printed pattern image; as well as The model parameter values ​​of the machine learning model are adjusted so that the difference between the predicted image corresponding to the simulated pattern and the printed pattern image is reduced.

3. The method of claim 2, wherein said adjusting the model parameter value of the machine learning model comprises: determining a gradient map of the difference between the predicted image corresponding to the simulated pattern and the printed pattern image as a function of model parameters; identifying the model parameter values ​​based on the gradient map such that the predicted image corresponding to the simulated pattern and the printed pattern image are reduced; as well as The model parameter value is adjusted based on the identified value. 4 . The method according to claim 1 , wherein the simulation pattern is an aerial image, a mask image, a resist image and / or an etching image.

5. The method according to claim 1, wherein obtaining the simulated pattern comprises: The patterning process model is simulated using the mask pattern as input.

6. The method of claim 1, wherein the simulated pattern includes hot spots that may fail when imaged onto the substrate. The method of claim 1 , wherein the simulated pattern comprises a pattern that does not satisfy a lithography manufacturability check.

8. The method of claim 1, wherein the characteristic of the simulated pattern or the printed pattern is a critical dimension of a feature of the simulated pattern or a profile of the feature of the simulated pattern.

9. The method of claim 1, wherein the inspection data comprises defect data of the imaged substrate obtained via an inspection device.

10. The method of claim 1, wherein the inspection data is a printed pattern image, wherein the image is a scanning electron beam image and / or an optical metrology image. The method according to claim 1 , wherein the parameters of the patterning process are dose and / or focus.

12. The method of claim 1, wherein the measured values ​​of the parameters of the patterning process are obtained via a metrology tool.

13. The method of claim 1, wherein the machine learning model is a convolutional neural network.

14. The method of claim 2, wherein the machine learning model is a convolutional neural network, and wherein adjusting the model parameter values ​​of the machine learning model comprises adjusting the values ​​of: one or more weights of a layer of the convolutional neural network, one or more biases of a layer of the convolutional neural network, Hyperparameters associated with the convolutional neural network, and / or The number of layers of the convolutional neural network.

15. A method for correcting a characteristic of a simulated pattern of a patterning process, the method comprising: determining the simulated pattern and the characteristics of the simulated pattern via a simulated patterning process model; determining a characteristic adjustment value for the characteristic of the simulated pattern via a trained machine learning model, wherein the trained machine learning model is trained based on measurement data; as well as The characteristic of the simulation pattern is corrected based on the characteristic adjustment value via a processor.

16. The method according to claim 15, further comprising: obtaining, via the trained machine learning model, a plurality of simulation patterns and a plurality of characteristic adjustment values ​​corresponding to the plurality of simulation patterns; adjusting, via the processor, the characteristic of each of the plurality of simulation patterns based on the plurality of characteristic adjustment values; as well as A ranking of the plurality of simulated patterns is determined, via the processor, based on the adjusted characteristics of the simulated patterns.

17. The method according to claim 16, further comprising: A sampling plan for metrology of a printed substrate is determined based on the ranking of the plurality of simulated patterns. The method of claim 17 , wherein the simulated pattern comprises a pattern corresponding to a plurality of hot spots. The method of claim 18 , wherein the sampling plan is based on the ranking of the hot spots.

20. The method according to claim 19, further comprising: directing, via the processor, an inspection device to collect measurement data on the printed substrate based on the ranking of the hot spots; as well as Defects on the printed substrate are determined, via the processor, based on the measurement data.

21. A method of training a machine learning model, the machine learning model being configured to predict a ranking of a collection of simulated patterns of a patterning process, the method comprising: obtaining (i) a set of simulated patterns corresponding to a set of mask patterns, (ii) defect data for a set of printed patterns imaged on a substrate using the set of mask patterns, and (iii) a sampling plan associated with the substrate imaged using the set of mask patterns; as well as The machine learning model is trained, via a processor, based on the defect data and the sampling plan such that the machine learning model is configured to predict a grade for the set of simulated patterns that matches a reference grade based on the defect data.

22. The method of claim 21, wherein the training step is an iterative process, the iterations comprising: predicting the ranking of the set of simulated patterns via the machine learning model using the sampling plan and the defect data as input; determining a difference between the predicted grade and the reference grade based on the defect data; as well as The model parameter values ​​of the machine learning model are adjusted so that the differences between the classifications are reduced.

23. The method according to claim 21 or 22, wherein obtaining the set of simulation patterns comprises: simulating a patterning process model using each mask pattern in the set of mask patterns, and A set of the simulated patterns that are likely to fail when imaged onto the substrate are identified from the simulation results.

24. The method of claim 21 or 22, wherein the set of simulated patterns corresponds to a set of hot spots.

25. The method of claim 21 or 22, wherein the set of simulated patterns includes simulated patterns that do not satisfy a lithography manufacturability check.

26. The method of claim 25, wherein the defect data is a defect count associated with one or more patterns of printed patterns on the substrate.

27. The method of claim 26, wherein the defect data is a value or range of values ​​of a critical dimension associated with the one or more patterns of printed patterns on the substrate.

28. The method of claim 27, wherein the defect data is extracted from an image of a printed pattern on the substrate, wherein the image is a scanning electron beam image and / or an optical metrology image.

29. The method of claim 28, wherein the sampling plan comprises: a set of locations on a printed pattern on a substrate at which measurements are performed, wherein the set of locations is based on an initial ranking of the set of simulated patterns; and / or A number of measurements to be performed at one or more locations in the set of locations based on the initial ranking of the set of simulated patterns.

30. The method of claim 29, further comprising: receiving the set of simulation patterns; predicting the ranking of the set of simulated patterns via a trained machine learning model; as well as The sampling plan is adjusted, via the processor, based on the predicted hierarchy of the set of simulation patterns.

31. The method of claim 30, wherein said adjusting said sampling plan comprises: adjusting a position in a set of positions to be measured; and / or The number of measurements to be performed at one or more locations in the set of locations.

32. The method of claim 31 , wherein said adjusting said position in said set of positions comprises: omitting positions corresponding to relatively lower ranked simulated patterns from the set of positions; and / or New positions corresponding to relatively higher ranked simulated patterns are added to the set of positions.

33. The method of claim 31 , wherein said adjusting said positions in said set of positions comprises increasing and / or decreasing a number of measurements to be made at positions in said subset of positions.

34. The method according to any one of claims 21 to 33, further comprising: directing, via the processor, an inspection device to collect measurement data of a printed pattern on the substrate based on the predicted grading of the set of simulated patterns; as well as Defects on the printed substrate are determined, via the processor, based on the measurement data.

35. A method of determining a ranking of a set of simulated patterns of a patterning process, the method comprising: training a first machine learning model based on the measurement data to adjust a characteristic of at least one simulated pattern in the set of simulated patterns via the trained first machine learning model; determining, via a processor, a subset of the simulated patterns based on the adjusted characteristic of the at least one simulated pattern; as well as A second machine learning model is trained based on the defect data and the sampling plan to determine, via the trained second machine learning model, a grading of the at least one simulated pattern in the subset of simulated patterns that matches a reference grading based on the defect data.

36. The method of claim 35, wherein determining the subset of simulated patterns comprises: determining whether the adjusted characteristic of the at least one simulated pattern satisfies a lithographic manufacturability check; as well as In response to failing to satisfy the lithographic manufacturability check, including the at least one simulated pattern in the subset of simulated patterns.

37. The method according to claim 35 or 36, further comprising: directing, via the processor, an inspection device to collect measurement data of a printed pattern on a substrate based on the grading of the at least one simulated pattern in the subset of simulated patterns; as well as Defects of a printed pattern on the substrate are determined, via a processor, based on the measurement data.

38. The method of claim 37, wherein the characteristic of the at least one simulated pattern or the printed pattern is a critical dimension of a feature of the at least one simulated pattern in the set of simulated patterns.

39. A computer program product comprising a non-transitory computer readable medium having recorded thereon instructions, the instructions implementing the method of claim 1 when executed by a computer system.

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