Method for improving process-based contour information of structures within an image

Abstract

A method for generating a modified simulated contour and / or a method for generating a metrology gauge based on the modified contour is described herein. A method for generating a metrology gauge for measuring physical properties of a structure on a substrate comprises: (i) obtaining measurement data related to physical properties of a structure printed on a substrate, and (ii) obtaining at least a portion of a simulated contour of the structure (the portion of the simulated contour is related to the measurement data); modifying the portion of the simulated contour of the structure based on the measurement data; and generating a metrology gauge (the metrology gauge is placed to measure physical properties of the simulated contour of the structure) on or adjacent thereto of the modified portion of the simulated contour.

Description

Technology Field

[0001] This application claims priority to U.S. application 62 / 889,248 filed on August 20, 2019 and CN / PCT application PCT / CN2020 / 085643 filed on April 20, 2020, the full text of which is incorporated herein by reference. Background Technology

[0002] The present disclosure relates to a technique for improving the performance of a metrology tool and a device manufacturing process. This technique may be used in connection with lithography device metrology related to device manufacturing or manufacturing processes based on contour information.

[0003] A lithography device is a machine that applies a desired pattern to a target portion of a substrate. A lithography device can be used, for example, in the manufacture of an integrated circuit (IC). In such situations, a patterning device, alternatively called a mask or reticle, can be used to create a circuit pattern corresponding to an individual layer of the IC, and this pattern can be imaged onto a target portion (e.g., a silicon wafer) on a substrate having a layer of radiation-sensitive material (resist) (e.g., a silicon wafer). Generally, a single substrate comprises a network of adjacent target portions that are continuously exposed. A known lithography device includes a so-called stepper that exposes the entire pattern to the target portion at once and irradiates each target portion, and a so-called scanner that scans the pattern in a given direction ("scanning" direction) through a beam to irradiate each target portion while simultaneously scanning the substrate parallel or antiparallel to this direction. means of solving the problem

[0004] In one embodiment, a method for generating a metrology gauge for measuring physical properties of a structure on a substrate is provided. The method comprises: (i) obtaining measurement data related to physical properties of a structure printed on a substrate, and (ii) obtaining at least a portion of a simulated contour of the structure (a portion of the simulated contour is related to the measurement data); modifying a portion of the simulated contour of the structure based on the measurement data; and generating a metrology gauge—the metrology gauge is placed on or adjacent thereto to measure physical properties of the simulated contour of the structure.

[0005] Additionally, in one embodiment, a method for determining a hotspot location associated with a substrate is provided. The method comprises: (i) obtaining a simulated contour associated with one or more patterns—wherein the simulated contour is associated with measurement data of physical properties of one or more patterns printed on a substrate—and (ii) obtaining a metrology gauge associated with the simulated contour; determining a value of a physical property associated with one or more patterns based on the metrology gauge; determining a hotspot location on the substrate based on the physical property value; and determining a hotspot location on the substrate based on the physical property value (the hotspot location is a location on the substrate where the physical property value is smaller than a hotspot threshold value associated with one or more patterns).

[0006] Additionally, in one embodiment, a method for training a model associated with a patterning process is provided. The method comprises the steps of: (i) obtaining measurement data associated with physical properties of a structure printed on a substrate, and (ii) obtaining a metrology gauge associated with a simulated contour of a structure to be printed on a substrate (the simulated contour is a defined location on the substrate where physical properties are measured); and training a model using the measurement data and the metrology gauge so as to improve a performance metric of the patterning process around a defined location on the substrate (the performance metric is a function of the metrology gauge and physical properties).

[0007] Additionally, in one embodiment, a method for generating a metrology gauge for measuring physical properties of a structure on a substrate is provided, the method comprises the steps of: (i) obtaining measurement data related to physical properties of a structure printed on a substrate and (ii) obtaining at least a portion of a simulated contour of the structure—the portion of the simulated contour being associated with the measured data; generating a modified contour of the portion of the simulated contour of the structure based on the measured data; and providing the modified contour to a model of a patterning process to determine parameters of the patterning process.

[0008] In addition, in one embodiment, a computer program product is provided comprising a non-transient computer-readable medium on which instructions for implementing the above-described method are recorded when executed by a computer system.

[0009] Additionally, in one embodiment, a method for training a machine learning model associated with a patterning process is provided. The method comprises: (i) contour data of a post-development image (ADI) pattern on a substrate, (ii) measurement data of a post-etching image (AEI) pattern printed on the substrate, and (iii) a reference bias value based on the contour data of the ADI pattern and the measurement data of the AEI pattern; and a step of determining a bias value to be applied to the ADI contour by training a machine learning model using the measurement data and the contour data as training data.

[0010] Additionally, in one embodiment, a method for determining a bias vector associated with a post-development image (ADI) pattern is provided. The method comprises the steps of: (i) obtaining a probability distribution function (PDF) corresponding to a particle deposited within an ADI pattern on a substrate, and (ii) obtaining a contour function characterizing an ADI contour associated with the ADI pattern; determining a deposition rate of a particle at a specific location of the ADI contour based on a combination of the PDF of the particle and the contour function for a region of the ADI contour; and determining a bias vector associated with the ADI pattern based on the deposition rate, wherein the bias vector, when applied to the ADI contour of the ADI pattern, generates a post-etching image (AEI) contour.

[0011] Additionally, in one embodiment, a method for determining a bias vector for a contour is provided. The method comprises the steps of: (i) obtaining a probability distribution function (PDF) corresponding to a process to be performed on the contour, and (ii) obtaining a contour function that characterizes the shape of the contour; convolving the contour function with the PDF over a region of the contour to determine a processing speed at a specific location of the contour; and determining a bias vector to be applied to the contour based on the process speed to generate a biased contour representing the effect of the process applied to the contour.

[0012] In addition, in one embodiment, a non-transient computer-readable medium is provided that includes instructions that cause the operation of a step of the method described herein when executed by one or more processors. Brief explanation of the drawing

[0013] Now, embodiments will be described merely as examples with reference to the attached drawings: FIG. 1 illustrates a block diagram of various subsystems of a lithography system according to one embodiment. FIG. 2 illustrates an exemplary flowchart for modeling and / or simulating at least a portion of a patterning process according to one embodiment. FIG. 3a is a flowchart of a method for generating a metrology gauge (e.g., edge placement gauge, CD gauge, etc.) for measuring the physical properties of a structure on a substrate according to one embodiment. FIG. 3b is a flowchart of an exemplary implementation of the steps used to modify the simulated contour in the method of FIG. 3a according to one embodiment. FIG. 4a illustrates an example of simulated contour and measurement data at a location (e.g., within the FOV of an SEM tool) according to one embodiment. FIG. 4b illustrates an example of a modified contour associated with the simulated contour of FIG. 4a according to one embodiment. FIG. 5 illustrates an example of a threshold value used to generate a modified contour and a signal associated with a simulated contour according to one embodiment. FIG. 6 is a flowchart of a method for determining a hotspot location associated with a substrate according to one embodiment. FIG. 7 is a flowchart of a method for training a model associated with a patterning process according to one embodiment. FIG. 8 illustrates an exemplary model such as a convolutional neural network (CNN) comprising multiple layers, each layer being associated with model parameters such as weights and biases, according to one embodiment. FIG. 9 is a flowchart of a method for training a model associated with a patterning process according to one embodiment. FIGS. 10a to 10c are examples of etching biasing a resist contour according to an embodiment and problems caused by etching bias. Figure 11 is a flowchart of a method for determining a bias vector associated with a post-development image (ADI) pattern. FIG. 12 is an example of particles in a resist trench according to an embodiment. FIG. 13 is an exemplary biasing in the vertical direction according to one embodiment. FIGS. 14a and FIGS. 14b are exemplary biasing in the direction determined in FIG. 11 according to one embodiment. FIG. 15 is a flowchart of a method for determining a bias vector associated with a process according to one embodiment. FIGS. 16a and 16b illustrate an exemplary application of a biased contour according to one embodiment. FIG. 17 schematically illustrates an example of a scanning electron microscope (SEM) according to an embodiment. FIG. 18 schematically illustrates an embodiment of an electron beam inspection device according to one embodiment. FIG. 19 is a block diagram of an exemplary computer system according to one embodiment. FIG. 20 is a schematic diagram of a lithography projection device according to one embodiment. FIG. 21 is a schematic diagram of an extreme ultraviolet (EUV) lithography projection device according to one embodiment. FIG. 22 is a more detailed drawing of the device of FIG. 21 according to one embodiment. FIG. 23 is a more detailed drawing of the source collector module of the device of FIG. 21 and FIG. 22 according to one embodiment. Specific details for implementing the invention

[0014] FIG. 1 illustrates an exemplary lithography projection device (10A). The main components are a radiation source (12A) which may be a deep-ultraviolet excimer laser source or other types of source including an extreme ultraviolet (EUV) source (as previously mentioned, the lithography projection device itself does not need to have a radiation source); an illumination optical device that defines partial coherence (indicated by sigma), which may include, for example, optical devices (14A, 16Aa and 16Ab) that shape radiation from the source (12A); a patterning device (18A); and a transmission optical device (16Ac) that projects an image of the patterning device pattern onto a substrate plane (22A). An adjustable filter or aperture (20A) in the pupil plane of the projection optical system can limit the range of beam angles that strike the substrate plane (22A), wherein the maximum possible angle is the numerical aperture of the projection optical system NA = n sin(Θ max Define ), where n is the refractive index of the medium between the final element of the projection optical system and the substrate, and Θ max is the maximum angle of the beam coming from the projection optical system that can still collide on the substrate plane (22A).

[0015] In a lithography projection device, a source provides illumination (i.e., radiation) to a patterning device, and a projection optical system directs and shapes the illumination onto a substrate through the patterning device. The projection optical system may include at least some of the components (14A, 16Aa, 16Ab, and 16Ac). An aerial image (AI) is a radiation intensity distribution at the substrate level. A resist layer on the substrate is exposed, and the aerial image is transferred to the resist layer as a potential "resist image" (RI) within it. The resist image (RI) can be defined as a spatial distribution of the solubility of the resist in the resist layer. A resist model may be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent Application Publication US 2009-0157360, the full text of which is cited herein. The resist model is concerned only with the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of the lithography projection device (e.g., properties of the source, patterning device, and projection optical system) determine the aerial image. Since the patterning device used in the lithography projection device can be changed, it may be desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithography projection device, including at least the source and projection optical system.

[0016] In one embodiment, assist features (sub-resolution assist features and / or printable resolution assist features) may be placed in a design layout based on the way the design layout is optimized according to the methods of the present invention. For example, in one embodiment, the methods employ a machine learning-based model to determine a patterning device pattern. The machine learning model may be a neural network, such as a convolutional neural network, which can be trained in a predetermined manner (e.g., as discussed in FIG. 3) to obtain accurate predictions at high speed, thereby enabling full-chip simulation of the patterning process.

[0017] A neural network can be trained using a set of training data (i.e., its parameters are determined). The training data may include or consist of a set of training samples. Each sample may be a pair containing or consisting of an input object [typically a vector referred to as a feature vector] and a desired output value [also referred to as a supervisory signal]. A training algorithm analyzes the training data and adjusts the behavior of the neural network by adjusting the network's parameters (e.g., weights of one or more layers) based on the training data. After training, the neural network can be used to map new samples.

[0018] In the context of determining a patterning device pattern, the feature vector may include one or more characteristics of a design layout configured or formed by the patterning device (e.g., shape, arrangement, size, etc.), one or more characteristics of the patterning device (e.g., one or more physical properties such as dimensions, refractive index, material composition, etc.), and one or more characteristics of the illumination used in the lithography process (e.g., wavelength). The monitoring signal may include one or more characteristics of the patterning device pattern (e.g., CD, contour, etc. of the patterning device pattern).

[0019] x i is the feature vector of the i-th example and y i is that monitoring signal {(x1,y1),(x2,y2),… ,(x N ,y N Given a set of N training samples of the form )}, the training algorithm is a neural network It finds , where X is the input space and Y is the output space. A feature vector is an n-dimensional vector of numerical features representing some objects. The vector space associated with these vectors is commonly called the feature space. Sometimes, a scoring function is defined such that g is defined as returning the y value that provides the highest score It is convenient to represent g using: . F represents the space of scoring functions.

[0020] Neural networks can be probabilistic, in which case g takes the form of a conditional probability model g(x) = P(y|x) or f takes the form of a concurrent probability model f(x,y) = P(x,y).

[0021] There are two basic approaches for selecting f or g: empirical risk minimization and structural risk minimization. Empirical risk minimization finds the neural network that best fits the training data. Structural risk minimization involves a penalty function that controls the bias / variance trade-off. For example, in one embodiment, the penalty function may be based on a cost function, which may be squared error, number of defects, EPE, etc. The functions (or weights within the functions) may be modified so that the variance is reduced or minimized.

[0022] In both cases, the training set consists of independent and identically distributed pairs (x i ,y i It is assumed to include or consist of one or more samples of ). In one embodiment, to measure how well the function fits the training data, the loss function is defined. Training samples (x i ,y i For ), value The loss predicting is L(y i , )am.

[0023] The risk R(g) of the function g is defined as the expected loss of g. This is derived from the training data. It can be estimated as.

[0024] In one embodiment, machine learning models of the patterning process may be trained to predict, for example, contours, patterns, CDs, and / or contours, CDs, edge placement (e.g., edge placement error) within a mask pattern and / or an etched image on a wafer. The purpose of the training is to enable accurate prediction of, for example, contours, aerial image intensity gradients, and / or CDs of a printed pattern on a wafer. A contour refers to the contour of a pattern to be printed on a print or a pattern printed on a print. For example, a contour can be obtained through image processing algorithms such as edge detection or other user-defined algorithms. The intended design (e.g., a wafer target layout to be printed on a wafer) is generally defined as an OPC-pre-design layout, which may be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0025] An exemplary flowchart for modeling and / or simulating part of a patterning process is shown in FIG. 22. As is understood, the model may represent different patterning processes and does not need to include all models described below. The source model (1200) represents the optical properties of the illumination of the patterning device (including radiation intensity distribution, bandwidth and / or phase distribution). The source model (1200) may represent optical properties of the illumination including, but not limited to, aperture number settings, illumination sigma (σ) settings, and any specific illumination shape (e.g., annular, quadrupole, dipole, etc.), where σ (or sigma) is the outer radius range of the illuminator.

[0026] The projection optical system model (1210) represents the optical properties of the projection optical system (including changes in radiation intensity distribution and / or phase distribution caused by the projection optical system). The projection optical system model (1210) may represent the optical properties of the projection optical system including aberrations, distortion, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0027] The patterning device / design layout model module (1220) captures how design features are laid out in the pattern of the patterning device and may include a representation of the detailed physical properties of the patterning device, for example, as described in U.S. Patent 7,587,704 (the full text incorporated herein by reference). In one embodiment, the patterning device / design layout model module (1220) is a representation of a design layout (e.g., features of an integrated circuit, memory, electronic device, etc.) on or by the patterning device. Since the patterning device used in the lithography projection device may change, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithography projection device, including at least the illumination and projection optical systems. The purpose of the simulation is often to accurately predict, for example, edge placement and CD, and then compare them with the device design. The device design is typically defined by a pre-OPC patterning device layout and is provided in a standardized digital file format such as GDSII or OASIS.

[0028] An aerial image (1230) can be simulated from a source model (1200), a projection optical system model (1210), and a patterning device / design layout model (1220). The aerial image (AI) is a radiation intensity distribution at the substrate level. Optical properties of the lithography projection device (e.g., lighting, properties of the patterning device and projection optical system) determine the aerial image.

[0029] 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) within it. The resist image (RI) can be defined as a spatial distribution of the solubility of the resist in the resist layer. A resist image (1250) can be simulated from an aerial image (1230) using a resist model (1240). A resist model can be used to calculate a resist image from an aerial image, and an example of this can be found in U.S. Patent Application Publication US 2009-0157360, the full text of which is cited herein. The resist model typically explains the effects of chemical processes occurring during resist exposure, post-exposure bake (PEB), and development to predict, for example, the contours of resist features formed on a substrate, and thus is typically only related to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure bake, and development). In one embodiment, optical properties of the resist layer, such as refractive index, film thickness, propagation, and polarization effects, may be captured as part of a projection optical system model (1210).

[0030] Therefore, generally, the connection between optical and resist models is the simulated aerial image intensity within the resist layer, which arises from the projection of radiation onto the substrate, refraction at the resist interface, and multiple reflections in the resist film stack. The radiation intensity distribution (aerial image intensity) is transformed into a potential "resist image" by the absorption of incident energy, which is further modified by diffusion processes and various loading effects. Efficient simulation methods sufficiently fast for full-chip applications approximate a realistic 3-dimensional intensity distribution in the resist stack by a 2-dimensional aerial (and resist) image.

[0031] In one embodiment, the resist image may be used as an input to the pattern transfer-post-process model module (1260). The pattern transfer-post-process model (1260) defines the performance of one or more resist development-post-processes (e.g., etching, development, etc.).

[0032] Simulation of the patterning process can predict, for example, contours, CD, edge placement (e.g., edge placement error) within the resist and / or etched image. Therefore, the purpose of the simulation is to accurately predict, for example, the edge placement of the printed pattern and / or aerial image intensity gradient and / or CD. These values ​​can be compared to the intended design to, for example, correct the patterning process and identify where defects are predicted to occur. The intended design is generally defined as an OPC-pre-design layout, which may be provided in a standardized digital file format such as GDSII or OASIS, or in other file formats.

[0033] Therefore, the model formulation explains most, if not all, of the known physical and chemical properties of the entire process, and each model parameter preferably corresponds to a distinct physical or chemical effect. Thus, the model formulation sets an upper limit on how well the model can be used to simulate the entire manufacturing process.

[0034] In one example, computer analysis of a lithography or etching process uses a predictive model (e.g., as discussed in FIG. 2) that, when properly calibrated, can generate accurate predictions of the dimensions output from the lithography and / or etching process. Models of the lithography or etching process are typically calibrated based on empirical measurements. This calibration involves running test wafers with various process parameters, measuring the consequently critical dimensions after the etching process, and correcting the model based on the measured results. In practice, fast and accurate models help improve device performance or yield, enhance the process window, or increase design choices. It will be understood by those skilled in the art that the method described herein is not limited to a specific model of lithography. For the calibration of the desired model, images may be obtained after the semiconductor manufacturing step. These may be, for example, aerial images, resist images, etching images, images after chemical mechanical polishing, or other images related to the process of the patterning process.

[0035] In computer lithography models, the critical dimension (CD) gauge, typically measured by a CD-SEM (scanning electron microscope), is used as input data to calibrate the model. The goal of lithography modeling is to predict the accurate resist contour for every location on the substrate. However, when using intensive model formats or deep convolution-neutral networks, the problem of the model overfitting due to calibration arises. For example, when such an overfitted model is used to predict the resist contour, it may deviate from the printed contour of the substrate, particularly for patterns where the CD gauge cannot be used.

[0036] To mitigate these overfitting problems, the present invention provides a method for extracting metrological gauges, such as edge placement (EP) gauges, based on raw CD SEM images to provide better pattern coverage. EP gauges help cover complex 2D patterns (e.g., holes). Complex 2D patterns are defined by at least two dimensions (e.g., width and length), and it may not be easy to place CD cutting lines or there may be no reliable CD measurement methods. Additionally, existing metrological tools require several days of additional data processing time, making it difficult to meet tight production schedules. A further challenge is that it is very difficult to extract accurate 2D contours from SEM images due to scan orientation, shadow effects, and / or fill effects.

[0037] As such, there are several limitations to generating computer lithography models using only CD gauges from CD SEM metrology. These limitations stem from the fact that lithography and plasma etching processes consist of complex physical and chemical reactions. These reactions are so complex that linear terms can model pattern-dependent etching bias to only a certain extent. However, more complex higher-order terms or deep convolution-neutral networks tend to provide overfitting, failing to predict the contours of physical structures beyond the metrology measurement locations. To prevent overfitting to CD SEM metrology data, a method is needed to extend the CD metrology data to provide better data coverage and prevent overfitting.

[0038] The method of the present invention provides a method for generating a metrology gauge, such as an EP gauge based on a model and a CD gauge, to mitigate the problem of model overfitting. Additionally, a method is provided for modifying a simulated model contour to match, for example, the measured CD data of a printed substrate. Thus, a model calibrated using the metrology gauge of the present invention can provide a better model capable of providing additional accurate contour shape information.

[0039] In one embodiment, a method is provided for using an EP gauge associated with a model simulation and a CD gauge associated with a printed substrate to train a DCNN lithography and / or etching model.

[0040] In one embodiment, CD metrology data and a physical model (e.g., from a CD-SEM) are used to generate a modified simulated contour that matches the metrology data. Additionally, simulated metrology data (e.g., EP gauge) is generated based on the modified contour. The currently simulated metrology provides more metrology information compared to, for example, the CD gauge obtained from the CD-SEM.

[0041] FIG. 3a is a flowchart of a method for generating a metrology gauge (e.g., edge placement gauge, CD gauge, etc.) for measuring the physical properties of a structure on a substrate. The method (300) generates a metrology gauge for use in measuring the physical properties of the structure. In one embodiment, the measurement may be performed using a metrology tool. In one embodiment, the metrology gauge may be exported (e.g., in a GDS file format) to a model (e.g., OPC, etching model, resist model, etc.) used to improve the patterning process. Furthermore, in one embodiment, the method (300) may also be used to generate a modified simulated contour and to export this modified contour (e.g., in a GDS file format) to a model (e.g., etching model) used to improve the patterning process.

[0042] In one embodiment, the term “gauge” or “metrology gauge” refers to a structure used to measure dimensions (e.g., size, shape) associated with physical properties (e.g., memory patterns or other circuit patterns) of a structure on a substrate. In one embodiment, the gauge may be, for example, a visual mark or visual indication of this information. In one embodiment, a gauge used to measure edge placement (e.g., a point on the contour of the structure) is referred to as an edge placement (EP) gauge. Similarly, a gauge used to measure the critical dimension (CD) of a structure may be referred to as a CD gauge. The gauge is also associated with a location on the substrate. The location may be a defined location (e.g., user-defined) or other locations of interest, such as a location with a minimum or maximum dimension associated with the structure. For example, a location may be associated with the minimum CD value of a line or bar-shaped structure. EP and CD gauges are used as examples to illustrate the concepts. However, the present invention is not limited to gauges used to measure physical properties associated with structures on a substrate.

[0043] The procedure (P301) includes the step of (i) obtaining measurement data (301) associated with physical properties of a structure printed on a substrate, and (ii) obtaining at least a portion (302) of a simulated contour of the structure, wherein the portion of the simulated contour is associated with the measurement data (301). In one embodiment, the portion of the simulated contour is a portion of the simulated contour within a defined area around the measurement data (301) associated with the structure. In one embodiment, the portion may be the entire simulated contour.

[0044] In one embodiment, the step of acquiring a portion (302) of a simulated contour includes: defining an area of ​​the substrate around a defined location associated with the measured data (301); and simulating a patterning process to obtain a portion (302) of the simulated contour of the structure within the defined area of ​​the substrate. For example, the defined location may be the field of view (FOV) of a metrology tool or a user-selected area around the portion (302) of the structure. In one embodiment, the FOV is a limited area on the substrate captured for observation or measurement purposes. For example, the FOV is an area around a structure printed on the substrate, a location where the CD value of the structure is measured, or other given location. In one embodiment, the size of the defined location (i.e., local area) may be selected so that the contour shape within the area has the best physical accuracy. The area may be selected so that two CD gauges do not overlap when they are very close to each other.

[0045] In one embodiment, the measured data (301) is obtained through a metrology tool. In one embodiment, the metrology tool is a scanning electron microscope (SEM) and the measured data (301) is obtained from an SEM image. In one embodiment, the SEM tool captures an image of a structure printed on a substrate. The image can be obtained at a given location using a FOV.

[0046] The simulated contour is the contour of the structure to be printed on the substrate. In one embodiment, the simulated contour is obtained through a patterning process simulation (e.g., FIG. 2). In one embodiment, the simulation process may be configured to run the process model (e.g., FIG. 2) only for specific locations instead of simulating the entire substrate. Simulating only a portion of the substrate enables faster execution and reduces computational resources compared to simulating the entire substrate.

[0047] FIG. 4a illustrates an example of data (410) measured at a location (e.g., within the FOV of an SEM tool) and a simulated contour (401a, 401b) (collectively referred to as 401). In one embodiment, the simulated contour (401) is obtained by simulating a patterning process by running one or more process models (e.g., FIG. 2). In one embodiment, the measurement data (410) is a physical property related to the structure (e.g., CD, EPE, etc.). Values ​​related to the physical property can also be obtained from the simulated contour (401). However, the simulated value of the physical property may differ substantially from the actual measured value of the physical property. Therefore, if the measurement is based on the simulated contour, the measurement will eventually become inaccurate and may affect the yield of the patterning process. The present invention provides a method for modifying the simulated contour and further generating a metrology gauge (e.g., EP gauge, CD gauge) based on the modified contour. For example, procedure (P303) is one method of modifying a simulated contour. FIG. 4b illustrates examples of modified contours (e.g., 411a and 411b) of a simulated contour (401).

[0048] In one embodiment, the measured data (410) is a CD value associated with a structure at a given location on the substrate. In one embodiment, the CD value is the distance between two contours at a given location. In one embodiment, the measured CD value is substantially different from the CD value obtained from the simulated contour (401). In one embodiment, the simulated contour (401) is modified so that the measured CD value and the simulated CD value are similar.

[0049] The procedure (P303) includes the step of generating a modified contour (304) of the simulated contour by modifying a portion (302) of the simulated contour of the structure based on measurement data (301). An exemplary implementation of the step used to modify the simulated contour is described in relation to FIG. 3b.

[0050] Procedure (P311) includes the step of determining simulated data (312) associated with the physical properties of the simulated contour of the structure based on a portion (302) of the simulated contour. Procedure (P313) includes the step of determining the difference between the measured data (301) and the simulated data (312) associated with the physical properties of the structure. Procedure (P315) includes modifying the portion (302) of the simulated contour based on the difference (314) so ​​that the difference (314) between the measured data (301) and the simulated data (312) is reduced. The modified contour (304) thus generated can be further used in various applications related to the patterning process (e.g., pattern improvement, process parameter determination, OPC, etc.).

[0051] As previously described, the measured data is the CD value at a defined location associated with the structure. Subsequently, the modification of the portion (302) of the simulated contour is based on the difference (314) between the simulated CD value and the measured CD value associated with the structure.

[0052] FIG. 4b illustrates an example of a simulated contour (401) and a modified contour (411) associated with measurement data (410) at a given location (e.g., within the FOV of an SEM tool). The modified contour (411) may be obtained using procedures P311, P312, and P315 (or P317) as discussed herein. For example, the simulated contour (401) may be modified based on measurement data (410), such as CD values. In one embodiment, the simulated contour is used to measure CD values ​​at the same location as the measured data. For example, the simulated CD may be measured between the simulated contours (401a and 401b). Subsequently, the difference between the simulated CD value and the measured CD value is calculated. Based on the CD difference, the simulated contour is modified within the FOV so that the CD difference is minimized. In one embodiment, the difference is such that the size of the simulated contour is increased to the modified contour (411a, 411b) so that the CD difference is reduced (in one embodiment, minimized). Additionally, a metrology gauge is generated based on the modified contour (411). Using the generated metrology gauge, such as an EP gauge, the structural characteristics of the substrate can be accurately measured.

[0053] In another example, modification of a portion (302) of the simulated contour involves adjusting a threshold value associated with acquiring the simulated contour (e.g., used in a level-set method for acquiring the simulated contour). For example, in one embodiment, procedures P311, P313, and P315 may be used. Procedure (P311) includes the step of determining simulated data (312) related to the physical properties of the simulated contour of the structure based on a portion (302) of the simulated contour. Procedure (P313) includes the step of determining a difference (314) between the measured data and the simulated data (312) related to the physical properties of the structure. Procedure (P317) includes the step of adjusting a threshold value used to generate the simulated contour so that the difference (314) between the measured data (301) and the simulated data (312) is reduced based on the difference (314), and the adjusted threshold value modifies the portion (302) of the simulated contour. Therefore, the modified contour (304') is generated and can be further used in other applications associated with the patterning process (e.g., OPC) as described above.

[0054] In one embodiment, the measured data is the CD of the feature. In this case, in one example, the modification of the portion of the simulated contour (302) includes the steps of: determining the simulated CD value using the portion of the simulated contour (302) at a defined location on the substrate where the measured CD value is obtained; determining the difference (314) between the simulated CD value and the measured CD value; and adjusting a threshold value based on the difference (314) so ​​that the difference (314) between the CD values ​​is reduced (the adjusted threshold value modifies the portion of the simulated contour (302)).

[0055] FIG. 5 illustrates an example of a threshold value used to generate a modified contour and a signal (501) associated with the simulated contour. The signal can be imagined as a three-dimensional (e.g., x, y, z) mountain-like profile. For example, a patterning process simulation may include a level-set method that receives the signal (501), for example, an image intensity associated with the simulated pattern. Additionally, the level-set method uses a threshold value (510) in the form of a plane crossing the signal, for example. Then, the intersection of the signal and the plane generates the simulated contour. Different simulated contours may be generated depending on the threshold value. Thus, according to the present invention, the difference between the measured data and the simulated data from the simulated contour can be used to adjust the threshold value (510) to a different threshold value (520). The adjusted threshold value (520) is intended to generate the simulated contour such that the difference between the simulated data and the measured data associated with physical characteristics is reduced or minimized. For example, the threshold value (510) may be modified in relation to the difference between the simulated data and the measured data.

[0056] The procedure (P305) includes the step of creating a metrology gauge (e.g., an edge placement gauge) on or adjacent to the modified portion of the simulated contour, and the metrology gauge is placed to measure the physical properties of the simulated contour of the structure. In one embodiment, the step of creating the metrology gauge includes the step of designating a mark, such as a point on (or adjacent to) the modified portion of the simulated contour; and the step of exporting the location of the point as a measurement gauge (e.g., an edge placement gauge). In one embodiment, the location may be exported or output in a text file, a GDS file, or other format used for processing by a computer. FIG. 4b illustrates exemplary edge placement gauges (EP1,…EP10,…,EPn) created along the modified contour (411). In one embodiment, the edge placement gauge may be created by drawing a line from the simulated contour to the modified contour in a direction perpendicular to the modified contour.

[0057] In one embodiment, the method (300) may be modified to generate a modified contour from a simulated contour, and the modified contour is used to improve the patterning process. In one embodiment, the improvement of the patterning process includes the step of determining parameters of the patterning process based on a patterning process simulation (e.g., see FIG. 2).

[0058] In one embodiment, the method (300) may be modified as follows. The method includes the step of obtaining (i) measurement data (301) related to the physical properties of a structure printed on a substrate, and (ii) at least a portion (302) of a simulated contour of the structure (the portion (302) of the simulated contour is associated with the measurement data), as described in procedure (P301). Additionally, as described in relation to procedure (P303), the method includes the step of generating a modified contour of the portion (302) of the simulated contour of the structure based on the measurement data (301). In one embodiment, the modified contour may be generated by shifting the simulated contour based on the difference (314) between the measurement data (301) and the simulated data (312) (discussed in relation to P303). In one embodiment, the simulated contour is shifted to reduce the CD difference between the CD measured at a given location and the simulated CD value.

[0059] Additionally, the method includes the step of providing a modified contour to a model of a patterning process to determine parameters of the patterning process. For example, the modified contour may be provided to the etching model or the resist model of FIG. 2 to further improve the accuracy of the simulated etching contour or the simulated resist contour.

[0060] FIG. 6 is a flowchart of a method (600) for determining the location of a hot spot on a substrate. The method (600) may be an application of a metrology gauge, such as an EP gauge or a CD gauge. For example, an EP gauge generated by P305 may be used to determine the location of the hot spot. A hot spot detection algorithm may use EP gauges (e.g., EP1, …, EPn) to determine the pattern and location of the hot spot. In one embodiment, the hot spot is a pattern or process window that limits the pattern most likely to fail after imaging on the substrate. An exemplary method for determining the hot spot is described in procedures P601, P603, and P605. However, metrology gauges may be used in other hot spot detection algorithms configured to determine the hot spot based on metrology gauges and simulated contours.

[0061] The procedure (P601) includes the step of (i) obtaining a simulated contour (601) associated with one or more patterns (the simulated contour (601) is associated with measured data of physical properties of one or more patterns printed on a substrate) and (ii) obtaining a metrology gauge (602) associated with the simulated contour (601) (e.g., edge placement and / or CD gauge).

[0062] In one embodiment, the step of acquiring a metrology gauge (602) includes: determining a simulated contour (601) associated with one or more patterns by simulating a patterning process using measurement data; modifying at least a portion of the simulated contour (601) based on the measurement data associated with one or more patterns; and generating a metrology gauge (602) on or in the modified portion of the simulated contour (601). For example, the method (300) may be used to modify the simulated contour (601) and further generate a metrology gauge (602), such as an EP gauge.

[0063] The procedure (P603) includes the step of determining a value (604) of a physical property associated with one or more patterns based on a metrology gauge (602). In one embodiment, the step of determining the value (604) of the physical property includes the step of measuring the value (604) of the physical property at one or more metrology gauges (602). In one embodiment, the metrology gauge (602) may be used to measure the edge placement error (EPE) of a simulated contour for a reference pattern (e.g., a target pattern), a CD gauge, or other physical properties.

[0064] The procedure (P605) includes the step of determining a hot spot (606) or a hot spot location (606) on a substrate based on a physical characteristic value (604), wherein the hot spot or hot spot location refers to a pattern or location on the substrate where the physical characteristic value is smaller than a hot spot threshold value associated with one or more patterns.

[0065] In one embodiment, the step of determining a hotspot location (606) includes determining whether the value of a physical characteristic associated with one or more patterns violates a hotspot threshold; and in response to a violation of the threshold, identifying the location of a metrology gauge (602) associated with the violation of the threshold. For example, the hotspot threshold may be a minimum CD or EPE value of a feature to be printed on a substrate.

[0066] FIG. 7 is a flowchart of a method (700) for training a model associated with a patterning process. The method (700) is an exemplary application of a metrology gauge (702) generated using the method (300) of the present invention. As the metrology gauge (702) becomes more accurate, the process model associated with the patterning process trained based on the metrology gauge (702) will provide more accurate results (e.g., closely matching the measured data). The results of the model can be further used to determine improved parameters of the patterning process, thereby enabling higher yields in the actual patterning process. An exemplary procedure associated with the method (700) is discussed in detail below.

[0067] The procedure (P701) includes the step of obtaining (i) measurement data (701) related to the physical properties of a structure printed on a substrate, and (ii) a patterning process gauge (702) (e.g., EP gauge or CD gauge) related to a simulated contour of the structure (the simulated contour is associated with a defined location on the substrate where the physical properties are measured).

[0068] The procedure (P703) includes the step of training a model (704) using measurement data (701) and a metrology gauge (702) so that the performance metric of the patterning process is improved around a defined location on the substrate, and the performance metric is a function of the metrology gauge (702) and physical properties. The model after the training process is completed is referred to as the trained model (704).

[0069] In one embodiment, training of the model is an iterative process. The iteration includes the steps of: determining simulated data related to the physical properties of the simulated contour of the structure to be printed on the substrate and the simulated contour of the structure through model execution; determining a first difference between the simulated data and the measured data (701), and a second difference between points along the simulated contour and the metrology gauge (702); and determining model parameters such that the performance metric, which is a function of the first difference and the second difference, is minimized based on the slope of the performance metric having parameters of the patterning process.

[0070] Figure 8 illustrates an example of a model such as a CNN (convolutional neural network) containing multiple layers, where each layer is associated with model parameters such as weights and biases. When an input (e.g., a feature vector) passes through these layers, the input is weighted and biased according to the values ​​assigned to each layer, and an output (e.g., an output vector of simulated contours and federation process parameters) is generated.

[0071] As previously described, the training of a machine learning model such as a CNN (800) is an iterative process. The iteration includes the steps of initializing the model parameters of the CNN (800); predicting the values ​​of physical characteristics related to the substrate; and adjusting the model parameter values ​​of the CNN (800) so that the cost function is reduced.

[0072] In one embodiment, the adjustment of model parameter values ​​is based on the gradient of the cost function. In one embodiment, the cost function is minimized. In one embodiment, the adjustment of model parameter values ​​of the CNN (800) includes the step of determining a gradient map of the first cost function as a function of the model parameters. Subsequently, model parameter values ​​are determined such that the cost function is minimized based on the gradient map.

[0073] In one embodiment, the adjustment of model parameter values ​​includes the step of 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 of a CNN, and / or the number of layers of a CNN. In one embodiment, the number of layers is a hyperparameter of a CNN that can be pre-selected and may not be changed during the training process. In one embodiment, a series of training processes in which the number of layers can be modified may be performed.

[0074] In one embodiment, the cost function is the difference between the measured data and the simulated data (e.g., predicted by the CNN (800)). The difference is reduced by modifying the values ​​of the CNN model parameters (e.g., weights, biases, strides, etc.). In one embodiment, the gradient corresponding to the difference may be dcost / dparameter, where the cnn_parameters value may be updated based on an equation (e.g., parameter = parameter - learning_rate * gradient). In one embodiment, the parameter may be a weight and / or bias, and the learning_rate may be a hyperparameter used to tune the training process and may be selected by the user or computer to improve the convergence of the training process (e.g., faster convergence).

[0075] In one embodiment, the model may be one of a process model, such as an etching model configured to predict an etching image; or a resist model configured to predict a resist image.

[0076] Computational analysis of the etching process uses a calibrated predictive model capable of predicting the dimensions of the etched structure resulting from the etching process. As mentioned herein, the model associated with the etching process may be calibrated based on empirical measurements. The calibration process includes the steps of patterning a test wafer with various process parameters, measuring the critical dimension (CD) of the pattern on the test wafer after the etching process, and calibrating the model based on the measured CD. In practice, a fast and accurate model can be used to improve the performance of the patterning device, the patterning yield, the process window of the patterning process, or to increase design choices, for example, related to mask pattern determination.

[0077] After the etching process, the etching contour of the etching pattern deviates from the corresponding resist contour of the resist pattern on the substrate. The deviation varies depending on the pattern. A constant bias may not be applied to the resist contour to generate the etching contour. In etching modeling, the resist contour can be used as input, and the goal is to predict the etching bias values ​​to be applied to different points on the resist contour. In conventional modeling approaches, pattern-dependent etching bias values ​​are modeled by linear equations using multiple linear terms that describe pattern characteristics.

[0078] There are some limitations associated with the step of modeling pattern-dependent bias values ​​using linear equations. These limitations stem from the fact that etching processes (e.g., using dry etching) involve complex chemical reactions and physical particle impact. Therefore, a more accurate etching model must be developed to account for etching effects that cannot be accurately modeled by linear terms. In one embodiment, the etching model can be further used in various applications related to lithography. For example, the etching model can be used to determine the OPC associated with the mask pattern to improve patterning performance or yield.

[0079] Currently, an etching contour is generated by applying bias values ​​at different points on the resist contour (e.g., determined by an etching model). The bias values ​​are applied in a direction locally perpendicular to the resist contour. However, this approach tends to overcalculate the bias values ​​at points of high curvature, and consequently, the etching contour may exhibit non-physical behavior (e.g., a fish-mouth shape or unreasonably sharp ends as shown in FIGS. 10A-10C). The present invention describes a method for determining the etching contour and the bias direction to solve the aforementioned problems related to the etching contour.

[0080] FIG. 9 is an exemplary process (900) for training a machine learning model associated with a patterning process according to an embodiment of the present invention. The training is based on measurement data related to an image after development (ADI) and an image after etching (AEI). After training, the trained model can determine a bias value to which the ADI contour can be applied to generate an etching contour. The exemplary process (900) includes different procedures that will be described in detail later.

[0081] The procedure (P901) includes the step of obtaining (i) contour data (901) of a post-development image (ADI) pattern on a substrate, (ii) measured data (902) of a post-etching image (AEI) pattern printed on a substrate, and (iii) a reference bias value (903) based on the contour data (901) of the ADI pattern and the measured data (902) of the AEI pattern. For example, the reference bias value (903) is determined based on the difference between the measured values ​​of the ADI pattern and the AEI pattern.

[0082] In one embodiment, the contour data (901) may be represented in the form of an image of a contour associated with one or more features of an ADI pattern. In one embodiment, the image is generated from the simulated contour of the simulated ADI pattern. In an embodiment, the step of acquiring the contour data (901) includes executing one or more process models associated with a patterning process to generate a simulated ADI pattern using a design pattern to be printed on a substrate as input. The patterning process includes a resist process or a resist model for simulating a resist process. ADI contours can be extracted from the simulated ADI pattern. Each contour is a contour of a feature within the simulated ADI pattern. In one embodiment, one or more process models include at least one of an optical model configured to determine an aerial image and a resist model configured to determine a resist image. Examples of simulation processes using various models associated with the patterning process are described in relation to FIG. 2.

[0083] In one embodiment, the image may be obtained from a metrology device (e.g., SEM) configured to capture an image of the substrate after a resist process on the substrate. In the example, the contour may be a resist contour that can be extracted from a resist image, for example, an SEM image of a resist pattern printed on the substrate.

[0084] In one embodiment, the measured data (902) is obtained from a designated metrology gauge. As previously described, the metrology gauge may be an edge placement gauge, a critical dimension (CD) gauge associated with the AEI pattern, or both. For example, the data (902) measured from the metrology gauge may include the position of the edge placement gauge associated with the contour of the AEI pattern printed on the substrate; and / or the CD value associated with the AEI pattern printed on the substrate.

[0085] In one embodiment, when the metrology gauge is a CD gauge, a reference bias value (903) is obtained through a calibration process configured to determine a bias value associated with a given CD gauge. The bias value represents the amount of CD reduction to be applied to an ADI pattern to generate an AEI pattern. In one embodiment, the bias value is provided at the end of the given CD gauge. The bias value may differ at both ends; that is, the bias value may be asymmetric with respect to the center of the CD gauge.

[0086] In one embodiment, the calibration process includes the step of determining a bias model as a linear combination of a plurality of terms characterizing a pattern. The bias model can determine a bias value at a specific resist contour point. An example of a bias model is provided as a linear model as follows.

[0087]

[0088] Term_bias in the above equation i is a model term associated with point i of the ADI contour, and c i is a coefficient related to the Term_bias at point i. In one embodiment, the model term may be a linear expression or a physical term related to aspects of the patterning process (e.g., CD, dose, focus, MSD, resist thickness). In one embodiment, the bias model may be implemented together with a lithography simulation process (e.g., FIG. 2). In one embodiment, the resist contour is biased in the vertical direction using the model-predicted bias value to obtain the corresponding etching contour.

[0089] In one embodiment, the term bias model may be represented as CD, and point i represents the first or second end of the CD gauge (e.g., a horizontal or vertical line drawn across the contour to measure the CD of the contour). Thus, in one embodiment, the bias model can determine bias values ​​at the ends of the CD gauge. Since the bias is not always symmetric with respect to the center of the gauge, when working with the CD gauge, the bias values ​​are divided across the two ends of the CD gauge. The method for dividing the bias for the CD gauge uses the above-calibrated bias model, which can generate asymmetric bias values ​​for a given CD gauge. In one embodiment, the gauge center is used as a reference, and the bias values ​​are divided equally between the two ends of the CD gauge. Then, the CNN model is trained using the divided CD bias values. In one embodiment, when an edge placement (EP) gauge is used, there is no asymmetric division of the bias values. Bias values ​​are determined for each EP gauge, and these bias values ​​can be used directly to train the CNN model.

[0090] In one embodiment, the ADI pattern or the ADI contour extracted therefrom may first be converted into another image format before being used to train a model. For example, the image format may include a Filtered Downsample Resist Image (FDRI). For example, the FDRI may be a low-pass filter image generated by applying a low-pass filter to the contour extracted from the ADI pattern. In one embodiment, the contour may be a binary image, and if used directly to train the model, the training process may be very slow compared to using the FDRI. Additionally, the FDRI is a grayscale image that provides greater flexibility in modifying each pixel value during the training process so that the model output converges to the desired result at a faster rate. In one embodiment, the image may be generated by transforming the ADI contour in terms of the bias model term of the ADI contour or other mathematical transformations. The transformation may result in better correlation between the bias model term and the etching process.

[0091] The procedure (P903) includes the step of training a machine learning model to determine a bias value to be applied to an ADI contour using measurement data (902) and contour data (901) as training data. After the training process, a trained model (905) is generated. The trained model (905) may be further applied to one or more aspects of a patterning process to improve, for example, lithography performance, patterning yield, and parameter adjustment of the patterning process.

[0092] In one embodiment, training of the model involves adjusting the model parameters of the machine learning model so that the bias value falls within a specific range determined based on a reference bias value (903). The model (e.g., a convolutional neural network (CNN)) may be adjusted to generate a bias value such that the model falls within a specified range. In one embodiment, the specified range indicates that the model-generated bias value converges to the reference bias value (903). For example, the specified range may be defined at a given location of the ADI pattern (e.g., the reference bias value ± 0.1 nm). In one embodiment, the specified range may be defined as a value that deviates within 0-5% of each reference bias value.

[0093] In one embodiment, the training of a machine learning model is an iterative process. The iteration includes: (a) running a machine learning model using given values ​​of measured data (902), contour data (901), and model parameters to generate a bias map associated with the contour data (901) (the bias map includes bias values); (b) adjusting the model parameters of the machine learning model so that the difference is reduced based on the slope of the difference between the model-based bias values ​​and the reference bias values ​​(903); and (c) performing steps (a)-(b) until the difference is minimized.

[0094] In one embodiment, the model parameters are the weights and biases of the model. Adjusting the weights and biases of one or more layers of the model causes the model to generate a bias value that is nearly identical to a reference bias value (903). The reference bias value (903) induces the adjustment of the model parameter values. For example, the gradient can be a derivative map of the difference with respect to the model parameters. The map consists of peaks and valleys, where the valleys represent points of minimization. In one embodiment, the training process includes a step of adjusting the values ​​of the model parameters so that the difference is minimized. This minimization can be associated with the valleys of the gradient map. For example, minimization is achieved by changing the model parameter values ​​toward the valley's trough direction.

[0095] In one embodiment, a machine learning model is configured to generate a representation of a bias map for an ADI contour. In one embodiment, the bias map may be represented as a pixelated image, where each pixel represents a bias value. Additionally, pixel locations may be associated with coordinates of a target layout or coordinates of an ADI pattern. In one embodiment, the bias value may be positive, negative, or zero. A positive bias value may indicate that the ADI contour should be reduced, a negative bias value may indicate that the ADI contour should be increased, and vice versa.

[0096] In one embodiment, a bias map generated by a trained machine learning model includes an etching bias value applied to a resist contour to determine an etching contour to be printed on a substrate. In one embodiment, the bias map includes coordinates associated with the entire wafer or die. Each coordinate is associated with a bias value. In an embodiment, the etching bias value is applied to the resist contour in a local vertical direction. The local vertical direction is the direction perpendicular to the resist contour at a given point on the resist contour. Thus, each point on the resist counter has a different vertical direction. In one embodiment, the bias map is a pixelated image, and each pixel has an intensity value representing the bias value.

[0097] As described above in the examples, applying a bias value to the ADI contour in the local vertical direction can cause an unrealistic etching contour. FIGS. 10a-10c illustrate examples of conventional bias approaches and related problems.

[0098] In FIG. 10a, bias values ​​b1, b2, b3, b4, and b5 can be applied to different locations on the resist contour (1001). Bias values ​​b1-b5 are applied in a vertical direction to create an etching contour (1020). If the bias values ​​(b1-b5) are sufficiently large, this can cause phrase shapes, such as irregular shapes (1021), in the etching contour (1020). These phrase shapes (1021) are unrealistic representations of the etching pattern.

[0099] As illustrated in FIG. 10b, the bias values ​​intersect in the curvature region (1030). This intersecting of the bias causes a phrase image (1021). In one embodiment, a large bias value that may not intersect can cause sharp line-ends (e.g., as illustrated in FIG. 10C). FIG. 10C illustrates a resist contour (1050) to which bias values ​​b10, b11, and b12 can be applied to create an etching contour (1060). Bias values ​​b10 and b11 are large enough to cause knife-points such as sharp line-ends. Therefore, if the ADI contour is shifted in the local vertical direction by the bias values ​​calculated by the corrected bias model, an accurate AEI contour may not be produced. Thus, the method of FIG. 11 is provided for determining a bias vector that can be applied, for example, to a resist contour.

[0100] FIG. 11 is an exemplary process (1100) for determining a bias vector associated with a post-development image (ADI) pattern according to an embodiment of the present invention. In one embodiment, the bias vector includes a bias direction pointing to a bias value in a direction that does not cause an intersection of contour curvatures when biased. In one embodiment, the method (1100) includes the following procedure, which is discussed in detail below. In one embodiment, the bias value may be obtained from any given pattern, the bias vector of the method (1100), a user-defined bias value, or a trained model (e.g., 905) configured to generate a bias value for another bias determination algorithm or method.

[0101] The procedure (P1101) includes the step of obtaining (i) a probability distribution function (1101) (PDF) of particle deposition within an ADI pattern on a substrate, and (ii) a contour function (1102) characterizing an ADI contour associated with the ADI pattern.

[0102] In one embodiment, the PDF (1101) of the particle deposition is determined or calibrated based on measured substrate data. The measured substrate data may include deposition data of particles and a measured etching pattern. In one embodiment, the PDF (1101) of the particles characterizes the net deposition effect or net etching effect of the particles in contact with the ADI contour. In this embodiment, the embodiments use the terms "deposition" or "deposition rate" to describe in detail that the resulting contour is derived by applying an inward bias from the original contour. However, it will be understood that the disclosed mechanism for determining the bias direction can also be extended to applications where the resulting contour can be derived by applying an outward bias from the original contour and using a negative deposition rate. In one embodiment, the PDF (1101) may be a Gaussian distribution. However, this is merely an example, and any other suitable form of function may be used without departing from the scope of the invention. In one embodiment, the acquisition of the PDF (1101) includes the step of determining the variance or standard deviation (σ) of a Gaussian distribution that fits the measured data. Examples of how changes in the Gaussian distribution affect the bias direction and etching contour are described below in relation to FIG. 13 and FIG. 14a-14b.

[0103] The procedure (P1103) includes the step of determining a particle deposition rate (1103) at a specific location of the ADI contour based on a combination of the particle PDF (1101) and the contour function (1102) for a region of the ADI contour. In one embodiment, the deposition rate (1103) may be positive (e.g., corresponding to shrinkage of the contour) or negative (e.g., corresponding to expansion of the contour). In one embodiment, the determination of the particle deposition rate (1103) includes the step of convolving the contour function (1102) with the particle PDF (1101) and integrating it across a region of the ADI contour.

[0104] FIG. 12 illustrates an example of a particle effect on a resist contour represented by the contour function R(x,y). As illustrated, the bias direction at point (P) of the resist contour points to the particle location (indicated by an asterisk). In one embodiment, the particle location is characterized by the concentration of the particles. In one embodiment, the particles will be deposited on the resist wall, and thus the resist contour will decrease toward the direction of the particles. In one embodiment, the resist trench will contain etching particles whose diffusion is characterized, for example, by a Gaussian distribution G(r). In one embodiment, the resist contour R(x,y) is integrated with all particles across the region of the resist contour to find the final etching counter E(x,y). That is, the etching contour is not determined by a single particle, but by all particles in the resist trench.

[0105] In one embodiment, the deposition rate (1103), e.g. D(x,y), can be determined based on the following equation:

[0106]

[0107] In the above equation, R(u,v) is a contour function that characterizes the geometric shape of the contour (e.g., resist contour) in the ADI. G(xu,yv) is a deposition rate function for particles in the trench at a distance r to the resist wall. In one embodiment, the deposition rate function is a Gaussian function characterized by mean and variance. In one embodiment, the variation of the Gaussian function can be determined based on measurement data (e.g., etching contour on a printed substrate). In one embodiment, G(xu,yv) serves as a guide for the direction of the bias value. For example, FIGS. 14a and 14b illustrate the step of changing the variation of the Gaussian function that affects the bias direction and the final etching contour.

[0108] The procedure (P1105) includes the step of determining a bias vector (1105) associated with an ADI pattern based on a deposition rate (1103). When applied to the ADI contour of the ADI pattern, the bias vector (1105) creates an image after etching (AEI) contour. In one embodiment, the bias vector (1105) includes a bias direction at a specific location on the ADI contour. In one embodiment, the method may further include the step of applying a bias value along the bias direction to create an AEI contour. For example, the bias vector includes a bias direction in which a bias value can be applied at a specific location on the resist contour as discussed herein (see, for example, FIG. 14a-14b).

[0109] In one embodiment, determining the bias vector (1105) includes the step of determining the slope of the deposition rate (1103) for the first direction and the second direction of the ADI pattern. For example, the first direction (e.g., along the x-axis) and the second direction (e.g., along the y-axis) are perpendicular to each other.

[0110] In one embodiment, for the above deposition rate D(x,y), the slope of the deposition rate (1103) is determined based on the following equation:

[0111]

[0112] In the above equation, the slope ∇D of the deposition rate is expressed as a combination of the x and y components of the deposition rate in a given direction.

[0113] In one embodiment, the bias direction at each specific location on the ADI contour is associated with a bias value. When a bias value at a different location is applied to the ADI contour, the bias vectors (1105) at the different locations do not intersect each other. In one embodiment, the bias direction of the bias vector (1105) includes a direction that is not perpendicular to the ADI contour. In one embodiment, a variation in the Gaussian distribution of the particles causes the bias vector (1105) to change. Thus, in one embodiment, the deviation can be adjusted to generate a bias vector (1105) that does not cause an intersection of the ADI contour when a bias value is applied.

[0114] In an embodiment, when the ADI pattern includes a plurality of contours, the set of bias vectors (1105) is determined individually for each ADI contour. For example, the ADI pattern may include features on a first layer and a second layer on the first layer. In one example, one feature may be surrounded by neighboring features of the ADI pattern. In one example, the density or proximity of neighboring features may be incorporated to calculate the bias value. However, regardless of the density of neighboring features, the bias vector does not cause an intersection of the ADI contours after applying the bias value.

[0115] FIG. 13 illustrates an example of applying a bias value to a resist contour (RC1) in a vertical direction at different points on the resist contour to create a biased contour (EC1) (also referred to as the etching contour (EC1)). Additionally, the bias vectors intersect each other in the region (R1) at the curvature of the resist contour (RC1). As previously mentioned, these intersections cause irregular or non-physical behavior of the etching contour (EC1). For example, the resist contour (RC1) is shifted by the bias value so that the biased contour (EC1) has a phrase shape or a sharp line-end in the R1 region.

[0116] In one embodiment, the biased contour (EC1) may be similar to the contour generated by applying the method (1100) described above. For example, the biased contour (EC1) may be generated by setting the variance of the Gaussian function to approximately 0. The effect of the change in the variance of the Gaussian function is further illustrated in FIGS. 14a and 14b.

[0117] FIGS. 14a and FIGS. 14b are exemplary results of applying the method (1100) using Gaussian functions having variances of 30 and 60, respectively. In one embodiment, the method (1100) determines a bias vector based on a Gaussian function having a first variance and determines another bias vector based on a Gaussian function having a second variance that is relatively higher than the first variance. When the bias vector is applied to the resist contour (RC1), it generates biased contours (EC2 and EC3) without causing a crossover of the bias values.

[0118] As the variance of the Gaussian function increases, the intersection point of the bias value (related to the resist contour) shifts to the left. For example, the intersection point in the R3 region is relatively to the left of the intersection point in the R2 region. In the example, the intersection point indicates a relatively higher concentration of particles within the resist trench. Therefore, the bias value points to the intersection point.

[0119] Comparing the biased contours EC2 and EC3, it can be seen that the contour portions within R2 and R3 do not have sharp edges or phrase shapes. Additionally, the portion of the biased contour (EC2) (within R2) is relatively (partially) sharper than the portion of the biased contour (EC3) (within R3).

[0120] In the embodiment, the variance value of the Gaussian function can be calibrated based on measured data (e.g., etching contour data of a printed substrate) as previously discussed. Using the calibrated Gaussian function, the bias direction can be determined using method (1100). For example, the slope ∇D is determined. Additionally, an etching contour can be generated using the bias value determined using, for example, a trained model (905) (e.g., CNN) and the bias direction ∇D at each point of the resist contour.

[0121] In one embodiment, the method (900, 1100) can be used for various applications related to a patterning process. Exemplary applications include, but are not limited to, SMO, OPC, hot spot detection, defect detection, adjustment of parameters of a lithography device during a manufacturing process, adjustment of parameters of a post-lithography process, and other related applications.

[0122] In an OPC application, for example, a mask pattern may be used to generate a resist contour. Using the resist contour as an input to a trained model (905), a bias value may be determined. The bias value may be applied to the resist contour to determine an etching contour. In one embodiment, the bias value may be applied in a vertical direction or a bias direction determined by the method (1100). Additionally, an optical proximity correction for the mask pattern may be determined based on the difference between the etching contour and the target contour to be printed on the substrate. In one embodiment, the aforementioned steps may be repeated until the difference between the etching contour and the target contour is minimized.

[0123] In one embodiment, the method (1100) is not limited to a patterning process. The method (1100) can be extended to determine a biased contour for other applications. For example, modifications to the method (1100) are discussed as follows.

[0124] In one embodiment, FIG. 15 is a flowchart of an exemplary process (1500) for determining a bias vector for a contour. The method (1500) includes the following procedure.

[0125] The procedure (P1501) includes the step of obtaining (i) a probability distribution function (1501) (PDF) corresponding to a process to be performed on the contour, and (ii) a contour function (1502) that characterizes the shape of the contour. For example, the PDF (1501) may represent the behavior of a machining process through a machining tool, a measurement process through a metrology tool, a process related to the aforementioned lithography, guiding a robot device along the contour, or other processes including contour-based operations. In one example, the contour may be a geometric shape related to a component to be machined. In another example, the contour may characterize the tool travel path during the machining process, the tool travel path during the measurement process, the robot travel path, or the limits of other attributes related to the contour. In one embodiment, the PDF (1501) may represent attributes of the tool used in the process. For example, the PDF (1501) may specify a specific tool having specified dimensions, etching, robot component dimensions, or other attributes that affect the contour when the process is performed on the contour during the machining operation.

[0126] The procedure (P1503) includes the step of convolving a PDF (1501) and a contour function (1502) across an area of ​​the contour to determine a processing speed (1503) at a specific location of the contour. In one embodiment, the process causes the addition or removal of material on which the contour is formed, and the addition or removal causes a change in the shape of the contour. In one embodiment, the process speed characterizes the behavior of the addition or removal of material on which the contour is formed. For example, it may be the addition or removal of material during a machining process, or the addition or removal of material during an etching process associated with lithography. The PDF (1501) of the process may be a Gaussian function fitted based on measurement data related to the process performed on the contour.

[0127] The procedure (P1505) includes the step of determining a bias vector (1505) to be applied to a contour to create a biased contour that represents the effect of the process applied to the contour, based on the process speed (1503). For example, the bias vector (1505) includes a bias value applied inwardly or outwardly to the contour to create a biased profile. For example, in a removal process, the bias value may be applied inwardly. In an additional process, the bias value may be applied outwardly. The processes discussed herein, e.g., machining, etching, robotic movement, etc., are examples for illustrating concepts and do not limit the scope of the invention.

[0128] FIGS. 16a and 16b illustrate examples of contour-based processes. For example, FIG. 16a illustrates a machining operation performed on a die using a machining tool (e.g., a milling tool). The component includes a contour (1601) before the machining process is performed. After machining, a machined contour (1602) is obtained. This machined contour (1602) represents a biased contour determined through a PDF that characterizes the machining process using a tool of specified dimensions.

[0129] FIG. 16b illustrates another example of a contour-based process. For example, contour (1611) represents the initial contour of a part to be processed (or scanned) through a tool (MT1). After machining, a biased contour (1612) is obtained. In one embodiment, a tool path (indicated by horizontal and dashed lines inside the biased contour (1612)) may be determined based on contour (1611) and biased contour (1612). As illustrated, the tool (MT1) is a circular tool having a specific radius and machining speed used to create or trace the biased contour (1612). It will be understood that the invention is not limited to a specific tool. The tool used in the process may be a machining tool, an etching tool, a scanning tool, or other tools associated with a lithography process used to create or trace the biased contour.

[0130] In one embodiment, one or more procedures of methods 300, 600, 700, 900, 1100, and 1500 may be implemented on one or more processors of a computer system. In one embodiment, a computer program product comprising a non-transient computer-readable medium on which instructions are recorded is provided, and the instructions perform one or more procedures of the methods when executed by a computer.

[0131] For example, in one embodiment, a non-transient computer-readable medium comprises instructions that cause an operation, when executed by one or more processors, including (i) obtaining a probability distribution function (PDF) corresponding to a particle deposited within a post-development image (ADI) pattern of a substrate, and (ii) obtaining a contour function characterizing an ADI contour associated with the ADI pattern; determining a deposition rate of a particle at a specific location of the ADI contour based on a combination of the PDF of the particle and the contour function for a region of the ADI contour; and determining a bias vector associated with the ADI pattern (the bias vector generates a post-etching image (AEI) contour when applied to the ADI contour of the ADI pattern) based on the deposition rate.

[0132] In one embodiment, a non-transient computer-readable medium for obtaining a probability distribution function (PDF) of particles is based on measured substrate data, and the measured substrate data includes deposition data of particles and a measured etching pattern. In one embodiment, obtaining the PDF includes determining the variance of a Gaussian distribution fitted to the measured data.

[0133] In one embodiment, a non-transient computer-readable medium for determining the deposition rate of particles comprises the step of convolving the PDF and contour function of the particles across an area of ​​an instruction and an ADI contour. A non-transient computer-readable medium for determining a bias vector comprises determining the slope of the deposition rate for a first direction and a second direction of the ADI pattern, wherein the first direction and the second direction are perpendicular to each other.

[0134] In one embodiment, in a non-transient computer-readable medium, the bias vector includes a bias direction at the location of the ADI contour and further includes the step of applying a bias value to generate an AEI contour. In one embodiment, in a non-transient computer-readable medium, the bias direction is determined such that when bias values ​​at different locations are applied to the ADI contour, the bias vectors at different locations do not intersect each other. In one embodiment, the non-transient computer-readable medium includes a direction in which the bias direction is not perpendicular to the ADI contour.

[0135] In one embodiment, in a non-transient computer-readable medium, the PDF of the particles represents the deposition or etching process of the particles on the ADI contour, wherein the deposition rate is positive or negative. In one embodiment, in a non-transient computer-readable medium, it is obtained from a trained machine learning model configured to generate a bias map for a resist pattern given a bias value. In one embodiment, in a non-transient computer-readable medium, if the ADI pattern includes multiple contours, a set of bias vectors is determined individually for each ADI contour.

[0136] In one embodiment, a non-transient computer-readable medium is provided that comprises instructions configured to be executed by one or more processors to (i) obtain a probability distribution function (PDF) corresponding to a process to be performed on a contour, and (ii) obtain a contour function characterizing the shape of the contour; convolve the contour function with the PDF over a contour region to determine a processing rate at a specified location of the contour; and determine a bias vector to be applied to the contour to generate a biased contour representing the effect of the process applied to the contour based on the processing rate.

[0137] In one embodiment, in a non-transient computer-readable medium, the process causes the addition or removal of the contour-forming material, and the addition or removal causes a change in the shape of the contour. In one embodiment, in a non-transient computer-readable medium, the process speed characterizes the behavior of the addition or removal of the contour-forming material.

[0138] In one embodiment, the trained machine learning model may be used in various applications related to the patterning process to improve the yield of the patterning process. For example, the method (300) includes the step of predicting a substrate image for a design layout through the trained machine learning model; and the step of determining a mask layout to be used for manufacturing a mask for the patterning process through OPC simulation using the design layout and the predicted substrate image. In one embodiment, the OPC simulation includes the step of determining a simulated pattern to be printed on the substrate by simulating a patterning process model using the geometric shape of the design layout and corrections associated with a plurality of segments; and the step of determining an optical proximity correction for the design layout so as to reduce the difference between the simulated pattern and the design layout. In one embodiment, determining the optical proximity correction is an iterative process. The iteration includes the step of adjusting the shape and / or size of the geometric shape of the main features and / or one or more auxiliary features of the design layout so as to reduce the performance metric of the patterning process. In one embodiment, one or more assist features are extracted from the predicted post-OPC image of the machine learning model.

[0139] In some embodiments, the inspection device may be a scanning electron microscope (SEM) that generates an image of a structure (e.g., part or all of the structure of the device) exposed or transferred onto a substrate. FIG. 17 illustrates an example of a SEM tool. A primary electron beam (EBP) emitted from an electron source (ESO) is focused by a condensing lens (CL), passes through a beam deflector (EBD1), an E×B deflector (EBD2), and an objective lens (OL), and is focused and irradiated onto a substrate (PSub) on a substrate table (ST) for one hour.

[0140] When an electron beam (EBP) is irradiated onto a substrate (PSub), secondary electrons are generated from the substrate (PSub). The secondary electrons are deflected by an E x B deflector (EBD2) and detected by a secondary electron detector (SED). A two-dimensional electron beam image can be obtained by detecting electrons generated in a sample, for example, by two-dimensional scanning of the electron beam by a beam deflector (EBD1) or by synchronizing with the repetitive scanning of the electron beam (EBP) by the beam deflector (EBD1) with continuous movement of the substrate (PSub) by a substrate table (ST) in the X or Y direction, or in the other direction of the X or Y direction.

[0141] The signal detected by the secondary electron detector (SED) is converted into a digital signal by an analog-to-digital (A / D) converter (ADC), and the digital signal is transmitted to an image processing system IPU. In one embodiment, the image processing system (IPU) may have a memory (MEM) for storing all or part of a digital image for processing by a processing unit (PU). The processing unit PU (e.g., specially designed hardware or a combination of hardware and software) is configured to convert or process the digital image into a dataset representing the digital image. Additionally, the image processing system (IPU) may have a storage medium (STOR) configured to store the digital image and the corresponding dataset in a reference database. A display device (DIS) is connected to the image processing system (IPU) so that an operator can perform the necessary operations of the equipment through a graphical user interface.

[0142] As previously mentioned, SEM images can be processed to extract contours describing the edges of objects representing device structures within the image. These contours are subsequently quantified using metrics such as CD. Therefore, images of device structures are generally compared and quantified using simple metrics, such as CD (distance between edges) or simple pixel differences between images. Common contour models that detect object edges in images to measure CD utilize image gradients. In practice, these models rely on strong image gradients. However, in reality, images are typically noisy and have discontinuous boundaries. While techniques such as smoothing, adaptive thresholding, edge detection, erosion, and dilation can be used to process the results of image gradient contour models to handle noisy and discontinuous images, this ultimately results in low-resolution quantification of high-resolution images. Consequently, in most cases, mathematically manipulating images of device structures to reduce noise and automate edge detection leads to a loss of image resolution and information. As a result, low-resolution quantification is achieved, corresponding to a simple representation of a complex, high-resolution structure.

[0143] Accordingly, it is desirable to have a mathematical expression regarding whether a structure (e.g., circuit features, alignment marks, or metrological target portions (e.g., grid features), etc.) created or expected to be created using a patterning process is, for example, a latent resist image, a developed resist image, or transferred to a layer on a substrate by, for example, etching to describe the general shape of the structure while preserving resolution. In the context of lithography or other patterning processes, the structure may be a device being manufactured or a part thereof, and the image may be an SEM image of the structure. In some cases, the structure may be a feature of a semiconductor device, for example, an integrated circuit. In this case, the structure may be referred to as a pattern or a desired pattern comprising multiple features of the semiconductor device. In some cases, the structure may be an alignment mark or a part thereof (e.g., a grating of an alignment mark) used in an alignment measurement process to determine the alignment of an object (e.g., a substrate) and another object (e.g., a patterning device) or a metrology target, or a part thereof (e.g., a grating of a metrology target) used to measure parameters of a patterning process (e.g., overlay, focus, dose, etc.). In one embodiment, the metrology target is, for example, a diffraction grating used to measure an overlay.

[0144] FIG. 18 schematically illustrates an additional embodiment of an inspection device. The system is used to inspect a sample (90) (such as a substrate) at 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).

[0145] A charged particle beam generator (81) generates a primary charged particle beam (91). A condensing lens module (82) condenses the generated primary charged particle beam (91). A probe forming objective lens module (83) focuses the condensed primary charged particle beam onto a charged particle beam probe (92). A charged particle beam deflection module (84) scans the formed charged particle beam probe (92) across the surface of a region of interest on a sample (90) fixed to a sample stage (88). In one embodiment, the charged particle beam generator (81), the condensing lens module (82), and the probe forming objective lens module (83), or equivalent designs, alternative examples, or any combination thereof, together form a charged particle beam probe generator that generates a scanning charged particle beam probe (92).

[0146] A secondary charged particle detector module (85) detects secondary charged particles (93) emitted from a sample surface (along with other charged particles that may have been reflected or scattered from the sample surface) when struck by a charged particle beam probe (92), and generates 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, accordingly, form at least one scan image. In one embodiment, the secondary charged particle detector module (85) and the image forming module (86), or equivalent designs, alternative examples, or any combination thereof, together form an image forming device that forms a scan image from the detected secondary charged particles emitted from a sample (90) struck by a charged particle beam probe (92).

[0147] In one embodiment, a monitoring module (87) is coupled to an image forming module (86) of an image forming device to perform monitoring, control, etc. of a patterning process using a scanned image of a sample (90) received from the image forming module (86), and / or derive parameters for designing, controlling, monitoring, etc. of the patterning process. Accordingly, in one embodiment, the monitoring module (87) is configured or programmed to cause the execution of the method described herein. In one embodiment, the monitoring module (87) includes a computing device. In one embodiment, the monitoring module (87) includes a computer program that provides a function therein and is encoded on a computer-readable medium that forms the monitoring module (87) or is placed therein.

[0148] In one embodiment, as with the electron beam inspection tool of FIG. 17 that inspects a substrate using a probe, the electron current of the system of FIG. 18 is significantly larger than that of the CD SEM as illustrated in FIG. 17, for example, so the probe spot is sufficiently large and the inspection speed can be fast. However, the resolution may not be as high as that of the CD SEM due to the large probe spot. In one embodiment, the aforementioned inspection device may be a single-beam or multi-beam device without limiting the scope of the present invention.

[0149] For example, SEM images from the system of FIG. 17 and / or FIG. 18 can be processed to extract contours describing the edges of objects representing device structures in the images. These contours are then typically quantified through metrics such as CD at user-defined cut-lines. Thus, images of device structures are typically compared and quantified through metrics such as the distance between edges (CD) measured from the extracted contours or simple pixel differences between images.

[0150] FIG. 19 is a block diagram illustrating a computer system (100) that may be helpful in implementing the methods and flows disclosed herein. The computer system (100) includes a bus (102) or other communication device for transmitting information, and a processor (104) [or multiple processors (104 and 105)] coupled to the bus (102) for processing information. Additionally, the computer system (100) includes a main memory (106) coupled to the bus (102), such as a random access memory (RAM) or other dynamic storage device, for storing information and instructions to be executed by the processor (104). Additionally, the main memory (106) may be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor (104). Additionally, the computer system (100) further includes a ROM (read-only memory: 108) or other static storage device coupled to a bus (102) that stores static information and instructions for a processor (104). A storage device (110), such as a magnetic disk or an optical disk, is provided and coupled to the bus (102) to store information and instructions.

[0151] A computer system (100) may be coupled via a bus (102) to a display (112), such as a cathode ray tube (CRT) or a flat panel or touch panel display, to show information to a computer user. An input device (114), including alphanumeric keys and other keys, is coupled to the bus (102) to transmit information and command selections to the processor (104). Another type of user input device is a cursor control unit (116), such as a mouse, trackball, or cursor arrow keys, to transmit directional information and command selections to the processor (104) and to control cursor movement on the display (112). This input device typically has two degrees of freedom on a first axis (e.g., x) and a second axis (e.g., y), which are two axes that allow the device to specify positions in a plane. Additionally, a touch panel (screen) display may be used as an input device.

[0152] According to one embodiment, parts of the process may be performed by a computer system (100) in response to a processor (104) executing one or more sequences of one or more instructions contained in main memory (106). These instructions may be read into main memory (106) from another computer-readable medium, such as a storage device (110). Execution of sequences of instructions contained in main memory (106) causes the processor (104) to perform the process steps described herein. Additionally, one or more processors of a multi-processing arrangement may be adopted to execute sequences of instructions contained in main memory (106). In an alternative embodiment, hard-wired circuitry may be used in combination with or instead of software instructions. Accordingly, the description in this specification is not limited to any specific combination of hardware circuitry and software.

[0153] As used herein, the term “computer-readable medium” refers to any medium involved in providing instructions to a processor (104) for execution. Such media may 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 devices (110). Volatile media include dynamic memory such as main memory (106). Transmission media include coaxial cables, copper wires, and optical fibers, including wires including a bus (102). 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 having a pattern of holes, RAM, PROMs, and EPROMs, FLASH-EPROMs, and any other memory chips or cartridges.

[0154] Various forms of computer-readable media may be involved in transmitting one or more sequences of one or more instructions to the processor (104) for execution. For example, the instructions may initially be stored (bear) on the magnetic disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system (100) may receive data over the telephone line and use an infrared transmitter to convert the data into an infrared signal. An infrared detector coupled to the bus (102) may receive the data transmitted as an infrared signal and place the data on the bus (102). The bus (102) transmits the data to the main memory (106) where the processor (104) retrieves and executes the instructions. The instructions received by the main memory (106) may be optionally stored in a storage device (110) before or after execution by the processor (104).

[0155] The computer system (100) preferably includes a communication interface (118) coupled to a bus (102). The communication interface (118) is coupled to a network link (120) connected to a local network (122) to provide two-way data communication. For example, the communication interface (118) may be an ISDN (Integrated Services Digital Network) card or a modem providing a data communication connection to a corresponding type of telephone line. As another example, the communication interface (118) may be a LAN (Local Area Network) card providing a data communication connection to a compatible LAN. Additionally, a wireless link may be implemented. In any such implementation, the communication interface (118) transmits and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0156] Typically, a network link (120) provides data communication to other data devices through one or more networks. For example, the network link (120) may provide a connection to a host computer (host computer: 124) or data equipment operated by an ISP (Internet Service Provider: 126) through a local network (122). In turn, the ISP (126) provides data communication services through a worldwide packet data communication 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 transmit digital data streams. Signals through various networks, and signals on the network link (120) through a communication interface (118) that transmits digital data to and from the computer system (100), are exemplary forms of carrier waves that transmit information.

[0157] A computer system (100) can transmit messages and receive data including program code through network(s), network links (120), and communication interfaces (118). In an internet example, a server (130) can transmit requested code for an application program through the internet (128), an ISP (126), a local network (122), and communication interfaces (118). One such downloaded application can provide, for example, lighting optimization of the embodiment. The received code can be executed by a processor (104) upon receipt and / or stored in a storage device (110) or other non-volatile storage for subsequent execution. In this way, the computer system (100) can obtain the application code in the form of a carrier wave.

[0158] FIG. 20 schematically illustrates an exemplary lithography projection apparatus in which the techniques described herein may be utilized. The apparatus is:

[0159] - A lighting system (IL) that conditions a radiation beam (B) - In this specific case, the lighting system also includes a radiation source (SO) - ;

[0160] - A patterning device holder is provided for holding a patterning device (MA) (e.g., a reticle), and a first object table (e.g., a patterning device table) (MT) is connected to a first positioner that accurately positions the patterning device with respect to an item (PS);

[0161] - A substrate holder is provided for holding a substrate (W) (e.g., a resist-coated silicon wafer), and a second object table (substrate table) (WT) connected to a second positioner that accurately positions the substrate with respect to an item (PS); and

[0162] - Includes a projection system ("lens") (PS) [e.g., a refractive, catoptric, or catadiooptic optical system] for imaging an irradiated portion of a patterning device (MA) onto a target portion (C) of a substrate (W) (e.g., comprising one or more dies).

[0163] As described in this specification, the device is configured as a transmissive type (i.e., having a transmissive patterning device). However, generally, it may also be configured as a reflective type, for example (having a reflective patterning device). The device may adopt a patterning device of a different type from a typical mask; examples include a programmable mirror array or an LCD matrix.

[0164] A source (SO) [e.g., a mercury lamp or excimer laser, or an LPP (laser-generated plasma) EUV source] generates a radiation beam. This beam is supplied directly or, after passing through a conditioning means such as, for example, a beam expander (Ex), to an illumination system (illuminator) (IL). The illuminator (IL) may include a conditioning means (AD) for setting the outer radius and / or inner radius of the intensity distribution within the beam (typically referred to as outer-σ and inner-σ, respectively). Additionally, it will generally include various other components such as an integrator (IN) and a condenser (CO). In this way, the beam (B) incident on the patterning device (MA) has the desired uniformity and intensity distribution across its cross-section.

[0165] With respect to FIG. 20, it should be noted that the source (SO) may be located within the housing of the lithography projection device [often as in the case where the source (SO) is, for example, a mercury lamp], but may also be located far away from the lithography projection device, and the radiation beam it generates may enter the device (for example, with the help of a suitable directional mirror); this latter scenario is often the case where the source (SO) is an excimer laser [for example, based on KrF, ArF, or F2 lasing].

[0166] Subsequently, the beam (B) passes through (intercepts) the patterning device (MA) held on the patterning device table (MT). Once it has crossed the patterning device (MA), the beam (B) passes through the lens (PS), which focuses the beam (B) onto the target portion (C) of the substrate (W). With the help of the second positioning means [and the interferometer measuring means (IF)], the substrate table (WT) can be moved precisely to position, for example, a different target portion (C) within the path of the beam (B). Similarly, the first positioning means can be used to accurately position the patterning device (MA) with respect to the path of the beam (B), for example, after mechanical retrieval of the patterning device (MA) from the patterning device library or during scanning. Generally, the movement of the object tables (MT, WT) will be realized with the help of a long-stroke module (rough positioning) and a short-stroke module (fine positioning), which is not clearly illustrated in FIG. 20. However, [in contrast to a step-and-scan tool] in the case of a stepper, the patterning device table (MT) can be connected to or fixed only to a short-stroke actuator.

[0167] The illustrated tool can be used in two different modes:

[0168] - In step mode, the patterning device table (MT) is basically kept in a stationary state, and the entire patterning device image is projected onto the target portion (C) at once [i.e., in a single "flash"]. Then, the substrate table (WT) is shifted in the x and / or y directions so that a different target portion (C) can be irradiated by the beam (B).

[0169] - In scan mode, the same scenario applies in principle, except that the given target portion (C) is not exposed in a single "flash". Instead, the patterning device table (MT) is movable in a given direction (so-called "scan direction," e.g., the y direction) at a speed v, so that the projection beam (B) scans across the patterning device image; concurrently, the substrate table (WT) is moved simultaneously in the same direction or the opposite direction at a speed V = Mv, where M is the magnification of the lens (PS) (typically, M = 1 / 4 or 1 / 5). In this way, a relatively wide target area (C) can be exposed without reducing the resolution.

[0170] FIG. 21 schematically illustrates another exemplary lithography projection device (1000) comprising:

[0171] - Source collector module (SO) for providing radiation;

[0172] - A lighting system (illuminator) (IL) configured to condition a radiation beam (B) (e.g., EUV radiation) from a source collector module (SO);

[0173] - A support structure (e.g., mask table) (MT) connected to a first positioner (PM) configured to support a patterning device (e.g., mask or reticle) (MA) and to accurately position the patterning device;

[0174] - A substrate table (e.g., wafer table) (WT) connected to a second positioner (PW) configured to hold a substrate (e.g., resist-coated wafer) (W) and to accurately position the substrate; and

[0175] - Includes a projection system (e.g., a reflection projection system) (PS) configured to project a pattern applied to a radiation beam (B) by a patterning device (MA) onto a target portion (C) of a substrate (W) (e.g., including one or more dies).

[0176] As described in this specification, the device (1000) is configured to be reflective (e.g., adopting a reflective mask). It should be noted that, since most materials are absorbent within the EUV wavelength range, the patterning device may have multilayer reflectors, for example, including a multilayer stack of molybdenum and silicon. In one example, the multilayer stack reflector has 40 layers of molybdenum and silicon pairs, where the thickness of each layer is a quarter wavelength. Much smaller wavelengths may be generated by X-ray lithography. Since most materials are absorbent in EUV and X-ray wavelengths, a thin layer of the patterned absorbent material on the patterning device topography (e.g., TaN absorber on the top of the multilayer reflector) defines the locations of features to be printed (positive resist) or not printed (negative resist).

[0177] Referring to FIG. 21, an illuminator (IL) receives an extreme ultraviolet radiation beam from a source collector module (SO). Methods for generating EUV radiation include, but are not limited to, the step of converting a material having at least one element, such as xenon, lithium, or tin, having one or more emission lines within the EUV range into a plasma state. In one such method, commonly referred to as a laser-generated plasma (“LPP”), the plasma can be generated by irradiating a fuel, such as a droplet, stream, or cluster of a material having a line-emitting element, with a laser beam. The source collector module (SO) may be part of an EUV radiation system that includes a laser (not shown in FIG. 21) that provides a laser beam to excite the fuel. The resulting plasma emits output radiation, such as EUV radiation, which is collected using a radiation collector placed in the source collector module. For example, if a CO2 laser is used to provide the laser beam for fuel excitation, the laser and the source collector module may be separate entities.

[0178] In this case, the laser is not considered to form part of the lithography device, and the radiation beam is passed from the laser to the source-collector module with the help of a beam delivery system, for example, including suitable directional mirrors and / or a beam expander. In other cases, for example, where the radiation source is a discharge-generating plasma EUV generator, commonly referred to as a DPP radiation source, the radiation source may be an integrated part of the source-collector module.

[0179] The illuminator (IL) may include a regulator for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer radius and / or inner radius of the intensity distribution within the pupil plane of the illuminator (typically referred to as outer-σ and inner-σ, respectively) may be adjusted. Additionally, the illuminator (IL) may include various other components, such as facetted field and pupil mirror devices. The illuminator may be used to condition the radiation beam to have a desired uniformity and intensity distribution across the cross-section of the radiation beam.

[0180] A radiation beam (B) is incident on a patterning device (e.g., mask) (MA) held on a support structure (e.g., mask table) (MT) and is patterned by the patterning device. After being reflected from the patterning device (e.g., mask) (MA), the radiation beam (B) passes through a projection system (PS), which focuses the beam onto a target portion (C) of a substrate (W). With the help of a second positioner (PW) and a position sensor (PS2) (e.g., an interferometer, a linear encoder, or a capacitive sensor), the substrate table (WT) can be moved precisely to position different target portions (C), for example, within the path of the radiation beam (B). Similarly, a first positioner (PM) and another position sensor (PS1) can be used to accurately position the patterning device (e.g., mask) (MA) with respect to the path of the radiation beam (B). A patterning device (e.g., a mask) (MA) and a substrate (W) can be aligned using patterning device alignment marks (M1, M2) and substrate alignment marks (P1, P2).

[0181] The illustrated device (1000) can be used in at least one of the following modes:

[0182] 1. In step mode, the support structure (e.g., mask table) (MT) and the substrate table (WT) are basically kept in a stationary state, while the entire pattern imparted to the radiation beam is projected onto the target portion (C) at once [i.e., single static exposure]. Then, the substrate table (WT) is shifted in the X and / or Y directions so that a different target portion (C) can be exposed.

[0183] 2. In scan mode, the support structure (e.g., mask table) (MT) and the substrate table (WT) are scanned synchronously while the pattern applied to the radiation beam is projected onto the target portion (C) [i.e., single dynamic exposure]. The speed and orientation of the substrate table (WT) relative to the support structure (e.g., mask table) (MT) can be determined by the magnification (reduction) and image inversion characteristics of the projection system (PS).

[0184] 3. In another mode, the support structure (e.g., mask table) (MT) is kept in a basically stationary state by holding the programmable patterning device, and the substrate table (WT) is moved or scanned while the pattern imparted by the radiation beam is projected onto the target portion (C). In this mode, a pulsed radiation source is typically employed, and the programmable patterning device is updated as needed after each movement of the substrate table (WT) or between continuous radiation pulses during scanning. This mode of operation can be easily applied to maskless lithography using a programmable patterning device such as a programmable mirror array of the type mentioned above.

[0185] FIG. 22 illustrates the device (1000) in more detail, including a source collector module (SO), an illumination system (IL), and a projection system (PS). The source collector module (SO) is configured and positioned so that a vacuum environment can be maintained within the enclosing structure (220) of the source collector module (SO). An EUV radiation-emitting plasma (210) can be formed by a discharge-generating plasma radiation source. EUV radiation can be generated by a gas or vapor, for example, Xe gas, Li vapor, or Sn vapor, which generates a very hot plasma (210) to emit radiation within the EUV range of the electromagnetic spectrum. The very hot plasma (210) is generated, for example, by an electrical discharge that causes at least partially ionized plasma. For efficient generation of 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 of excited tin (Sn) is provided to generate EUV radiation.

[0186] Radiation emitted by the superheated plasma (210) passes from the source chamber (211) into the collector chamber (212) through an optional gas barrier or contaminant trap (230) (also referred to as a contaminant barrier or foil trap in some cases) located within or behind the opening of the source chamber (211). The contaminant trap (230) may include a channel structure. Additionally, the contaminant trap (230) may include a gas barrier, or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier (230) further described herein includes at least a channel structure as known in the art.

[0187] The collector chamber (212) 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 crossing the collector (CO) can be reflected from a grating spectral filter (240) and focused to a virtual source point (IF) along an optical axis indicated by the dashed line 'O'. The virtual source point (IF) is typically referred to as an intermediate focus, and the source collector module is positioned so that the intermediate focus (IF) is located at or near an opening (221) in the enclosure structure (220). The virtual source point (IF) is an image of the radiation-emitting plasma (210).

[0188] Subsequently, radiation traverses an illumination system (IL), which may include a faceted field mirror device (22) and a faceted pupil mirror device (24) positioned to provide a desired angular distribution of the radiation beam (21) in the patterning device (MA) as well as a desired uniformity of radiation intensity in the patterning device (MA). Upon reflection of the radiation beam (21) in the patterning device (MA) held by a support structure (MT), a patterned beam (26) is formed, and the patterned beam (26) is imaged onto a substrate (W) held by a substrate table (WT) through reflection elements (28, 30) by a projection system (PS).

[0189] Generally, more elements than shown may exist within the illumination optical unit (IL) and projection system (PS). A grating spectrum filter (240) may be optionally present depending on the type of lithography device. Additionally, more mirrors may exist than shown in the drawings, and, for example, one to six additional reflective elements may exist within the projection system (PS) than shown in FIG. 22.

[0190] A collector optical device (CO) as illustrated in FIG. 22 is shown as a nested collector having grazing incident reflectors (253, 254, and 255) as just one example of a collector (or collector mirror). The grazing incident reflectors (253, 254, and 255) are arranged axially around an optical axis (O), and this type of collector optical device (CO) can preferably be used in combination with a discharge generating plasma source.

[0191] Alternatively, the source collector module (SO) may be part of an LPP radiation system as illustrated in FIG. 23. A laser (LAS) is positioned to deposit laser energy into a fuel such as xenon (Xe), tin (Sn), or lithium (Li) to generate a highly ionized plasma (210) having an electron temperature of tens of eV. Intense energetic radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by a near normal incidence collector optic (CO), and focused onto an opening (221) of an enclosure structure (220).

[0192] Embodiments of the present invention will be further described in the following claims:

[0193] 1. A method for generating a metrology gauge for measuring the physical properties of a structure printed on a substrate,

[0194] (i) a step of obtaining measurement data related to the physical properties of a structure printed on a substrate, and (ii) at least a portion of a simulated contour of the structure—the portion of the simulated contour is related to the measurement data;

[0195] A step of modifying a portion of the simulated contour of a structure based on measurement data; and

[0196] A method comprising the step of generating a metrology gauge on or adjacent to a modified portion of a simulated contour—the metrology gauge is placed to measure the physical properties of the simulated contour of a structure.

[0197] 2. The method of claim 1, wherein a portion of the simulated contour is a portion of the simulated contour within a defined area surrounding measurement data associated with the structure.

[0198] 3. In claim 1, the step of acquiring a portion of the simulated contour is:

[0199] A step of defining an area of ​​a substrate around a defined location associated with measurement data; and

[0200] A method comprising the step of simulating a patterning process of a structure within a defined area of ​​a substrate to obtain a portion of the simulated contour of the structure.

[0201] 4. In any one of claims 1 to 3, the step of modifying a portion of the simulated contour is:

[0202] A step of determining simulated data associated with the physical properties of the simulated contour of a structure based on a portion of the simulated contour;

[0203] A step of determining the difference between the measured data and the simulated data associated with the physical characteristics of the structure; and

[0204] A method comprising the step of modifying a portion of a simulated contour based on the difference so as to reduce the difference between the measured data and the simulated data.

[0205] 5. A method according to any one of claims 1 to 4, wherein the measurement data is a CD value at a defined location associated with a structure.

[0206] 6. A method according to any one of claims 1 to 5, wherein the step of modifying a portion of the simulated contour is based on the difference between the simulated CD value and the measured CD value associated with the structure.

[0207] 7. In any one of claims 1 to 6, the step of modifying a portion of the simulated contour is:

[0208] A step of determining simulated data associated with the physical properties of the simulated contour of a structure based on a portion of the simulated contour;

[0209] A step of determining the difference between the measured data and the simulated data associated with the physical characteristics of the structure; and

[0210] A method comprising the step of adjusting a threshold adopted to generate a simulated contour based on the difference so that the difference between the measured data and the simulated data is reduced—the adjusted threshold modifies a part of the simulated contour.

[0211] 8. In any one of claims 1 to 7, the step of modifying a portion of the simulated contour is:

[0212] A step of determining a simulated CD value at a defined location associated with a measured CD value using a portion of the simulated contour;

[0213] A step of determining the difference between the simulated CD value and the measured CD value; and

[0214] A method comprising the step of adjusting a threshold based on the difference so that the difference between CD values ​​is reduced—the adjusted threshold modifies a portion of the simulated contour.

[0215] 9. In any one of claims 1 to 8, the step of generating a metrology gauge is:

[0216] Step of refining points along the modified portion of the simulated contour; and

[0217] A method comprising the step of exporting the location of a point to a metrology gauge.

[0218] 10. A method according to any one of claims 1 to 9, wherein the measurement data is obtained through a metrology tool.

[0219] 11. In claim 9, the measurement tool is a scanning electron microscope (SEM) and the measured data is obtained from the SEM image.

[0220] 12. A method according to any one of claims 1 to 11, wherein the metrology gauge is an edge placement gauge and / or a CD gauge.

[0221] 13. A method for determining a hotspot location associated with a substrate, comprising: (i) a simulated contour associated with one or more patterns, wherein the simulated contour is associated with measurement data of physical properties of one or more patterns printed on the substrate; and (ii) a step of acquiring a metrology gauge associated with the simulated contour; a step of determining a value of a physical property associated with one or more patterns based on the metrology gauge; a step of determining a hotspot location on the substrate based on the value of the physical property; and a step of determining a hotspot location on the substrate (the hotspot location is a location on the substrate where the value of the physical property is smaller than a hotspot threshold associated with one or more patterns) based on the value of the physical property.

[0222] 14. The method of claim 13, wherein the step of acquiring a metrology gauge comprises: determining a simulated contour associated with one or more patterns by simulating a patterning process using measurement data; modifying at least a portion of the simulated contour based on the measurement data associated with one or more patterns; and generating a metrology gauge on or on the modified portion of the simulated contour.

[0223] 15. The method according to claim 13 or 14, wherein the step of determining the value of a physical characteristic includes the step of measuring the value of a physical characteristic at one or more metrology gauges.

[0224] 16. The method of claim 15, wherein the step of determining a hotspot location (606) comprises: determining whether the value of a physical characteristic associated with one or more patterns violates a hotspot threshold; and identifying the location of a metrology gauge (602) associated with the violation of the threshold in response to the violation of the threshold.

[0225] 17. A method for training a model associated with a patterning process, comprising: (i) obtaining measurement data associated with physical properties of a structure printed on a substrate, and (ii) obtaining a metrology gauge associated with a simulated contour of a structure to be printed on a substrate (the simulated contour is a defined location on the substrate where physical properties are measured); and training a model using the measurement data and the metrology gauge so as to improve a performance metric of the patterning process around a defined location on the substrate—the performance metric is a function of the metrology gauge and physical properties.

[0226] 18. The method of claim 17, wherein the training of the model is an iterative process, and the iteration comprises: determining simulated data related to the physical properties of the simulated contour of the structure to be printed on a substrate and the simulated contour of the structure through model execution; determining a first difference between the simulated data and the measured data, and a second difference between points along the simulated contour and a metrology gauge; and determining model parameters such that a performance metric, which is a function of the first difference and the second difference, is minimized based on the slope of a performance metric having parameters of the patterning process.

[0227] 19. The method of claim 18, wherein the model comprises at least one of an etching model configured to predict an etching image; or a resist model configured to predict a resist image.

[0228] 20. A method for generating a metrology gauge for measuring physical properties of a structure on a substrate, comprising: (i) measurement data relating to physical properties of a structure printed on a substrate, and (ii) at least a portion of a simulated contour of the structure (a portion of the simulated contour relating to the measurement data); a step of modifying a portion of the simulated contour of the structure based on the measurement data; and a step of generating a metrology gauge—the metrology gauge being placed to measure physical properties of the simulated contour of the structure—on or adjacent thereto on or of the modified portion of the simulated contour.

[0229] 21. In claim 20, the step of generating a modified contour of a portion of the simulated contour is:

[0230] A step of determining simulated data associated with the physical properties of the simulated contour of a structure based on a portion of the simulated contour;

[0231] A step of determining the difference between the measured data and the simulated data associated with the physical characteristics of the structure; and

[0232] A method comprising the step of modifying a portion of a simulated contour based on the difference so as to reduce the difference between the measured data and the simulated data.

[0233] 22. A computer program product comprising a non-transient computer-readable medium on which instructions are recorded, wherein the instructions implement any one of the methods of claims 1 through 21 when executed by a computer.

[0234] 23. A method for training a machine learning model associated with a patterning process, comprising: (i) contour data of a post-development image (ADI) pattern on a substrate, (ii) measurement data of a post-etching image (AEI) pattern printed on the substrate, and (iii) obtaining a reference bias value based on the contour data of the ADI pattern and the measurement data of the AEI pattern; and training a machine learning model using the measurement data and the contour data as training data to determine a bias value to be applied to the ADI contour.

[0235] 24. The method of claim 23, wherein the training comprises the step of adjusting the model parameters of a machine learning model so that the bias value is within a specified range determined based on a reference bias value.

[0236] 25. The method of claim 23, wherein the machine learning model is configured to generate a representation of a bias map for an ADI contour.

[0237] 26. The method of claim 23, wherein the contour data represents an image of a contour associated with one or more features of an ADI pattern.

[0238] 27. The method of claim 26, wherein the image is generated from a simulated contour of a simulated ADI pattern and / or obtained from a metrology device configured to capture an image of the substrate after performing a resist process on the substrate.

[0239] 28. In any one of claims 23 to 27, the step of acquiring contour data is:

[0240] A step of executing one or more process models associated with a patterning process to generate a simulated ADI pattern including a resist process, using a design pattern to be printed on a substrate as input; and

[0241] A method comprising the step of extracting contours from a simulated ADI pattern, wherein each contour is a contour of a feature within the simulated ADI pattern.

[0242] 29. The method of claim 28, wherein one or more process models comprise: an optical model configured to determine an aerial image; and at least one of a resist model configured to determine a resist image.

[0243] 30. A method according to any one of claims 23 through 29, wherein the measurement data is obtained from a metrology gauge, and the metrology gauge is an edge placement gauge, and / or a critical dimension (CD) gauge associated with an AEI pattern.

[0244] 31. The method of claim 28, wherein the data measured by the metrology gauge is the position of the edge placement gauge associated with the contour of the AEI pattern printed on the substrate; and / or the CD value associated with the AEI pattern printed on the substrate.

[0245] 32. The method of claim 28, wherein, when the metrology gauge is a CD gauge, a reference bias value is obtained through a calibration process configured to determine a bias value associated with a given CD gauge (the bias value represents the amount of CD reduction to be applied to an ADI pattern to generate an AEI pattern).

[0246] 33. In claim 32, the bias value is provided at the end of a given CD gauge, and the bias value is not equal or asymmetric with respect to the center of the CD gauge.

[0247] 34. A method according to any one of claims 23 to 33, wherein the training of a machine learning model is an iterative process, and the iteration comprises: (a) running a machine learning model using given values ​​of measured data (902), contour data (901), and model parameters to generate a bias map associated with the contour data (901) (the bias map includes bias values); (b) adjusting the model parameters of the machine learning model so as to reduce the difference based on the slope of the difference between the model-based bias values ​​and the reference bias values ​​(903); and (c) performing steps (a)-(b) until the difference is minimized.

[0248] 35. A method according to any one of claims 23 to 34, wherein the bias map generated through a trained machine learning model includes an etching bias value applied to a resist contour to determine an etching contour to be printed on a substrate.

[0249] 36. In claim 35, the etching bias value is applied in a direction locally perpendicular to the resist contour.

[0250] 37. A method according to any one of claims 23 to 36, wherein the bias map is a pixelated image and each pixel has an intensity value representing a bias value.

[0251] 38. A method for determining a bias vector associated with an image after development (ADI) pattern, the method comprising: (i) obtaining a probability distribution function (PDF) corresponding to a particle deposited within an ADI pattern on a substrate, and (ii) obtaining a contour function characterizing an ADI contour associated with the ADI pattern; determining a deposition rate of a particle at a specific location of the ADI contour based on a combination of the PDF of the particle and the contour function for a region of the ADI contour; and determining a bias vector associated with the ADI pattern based on the deposition rate, wherein the bias vector, when applied to the ADI contour of the ADI pattern, generates an image after etching (AEI) contour.

[0252] 39. The method of claim 38, wherein the step of obtaining a probability distribution function (PDF) of particles is based on measured substrate data, and the measured substrate data includes deposition data of particles and a measured etching pattern.

[0253] 40. The method of claim 39, wherein the step of obtaining the PDF includes the step of determining the variance of a Gaussian distribution fitted to the measurement data.

[0254] 41. A method according to any one of claims 38 to 40, wherein the step of determining the deposition rate of particles comprises: convolving the PDF of the particles and the contour features; and integrating across the region of the ADI contour.

[0255] 42. A method according to any one of claims 38 to 41, wherein the step of determining the bias vector comprises the step of determining the slope of the deposition rate with respect to the first direction and the second direction of the ADI pattern, wherein the first direction and the second direction are perpendicular to each other.

[0256] 43. The method of claim 38, wherein the bias vector includes a bias direction at the location of the ADI contour, and further comprises the step of applying a bias value to generate an AEI contour.

[0257] 44. A method according to claim 43, wherein when bias values ​​at different positions are applied to an ADI contour, the bias direction is determined such that bias vectors at different positions do not intersect each other.

[0258] 45. The method of claim 44, wherein the bias direction includes a direction not perpendicular to the ADI contour.

[0259] 46. ​​A method according to any one of claims 38 to 45, wherein the PDF of the particles represents a deposition or etching process of particles on an ADI contour, and the deposition rate is negative or positive.

[0260] 47. A method according to any one of claims 43 to 46, wherein the bias value is obtained from a trained machine learning model configured to generate a bias map for a given resist pattern.

[0261] 48. A method according to any one of claims 38 to 47, wherein, when the ADI pattern comprises a plurality of contours, the set of bias vectors is determined individually for each ADI contour.

[0262] 49. A method for determining a bias vector for a contour, comprising: (i) obtaining a probability distribution function (PDF) corresponding to a process to be performed on the contour, and (ii) obtaining a contour function that characterizes the shape of the contour; convolving the contour function with the PDF over a region of the contour to determine a processing speed at a specific location of the contour; and determining a bias vector to be applied to the contour based on the process speed to generate a biased contour representing the effect of the process applied to the contour.

[0263] 50. In claim 49, the process causes the addition or removal of the material on which the contour is formed, and the addition or removal causes a change in the shape of the contour.

[0264] 51. The method of claim 50, wherein the process speed characterizes the behavior of adding or removing the material on which the contour is formed.

[0265] 52. A non-transient computer-readable medium containing instructions, wherein the instructions are executed by one or more processes;

[0266] A non-transient computer-readable medium configured to perform operations including: (i) contour data of a post-development image (ADI) pattern on a substrate, (ii) measurement data of a post-etching image (AEI) pattern printed on the substrate, and (iii) obtaining a reference bias value based on the contour data of the ADI pattern and the measurement data of the AEI pattern; and training a machine learning model using the measurement data and contour data as training data to determine a bias value to be applied to the ADI contour.

[0267] 53. A non-transient computer-readable medium, wherein the training comprises the step of adjusting the model parameters of a machine learning model so that the bias value is within a specified range determined based on a reference bias value.

[0268] 54. In claim 52, a non-transient computer-readable medium configured such that a machine learning model generates a representation of a bias map for an ADI contour.

[0269] 55. In claim 52, the contour data is a non-transient computer-readable medium representing an image of a contour associated with one or more features of an ADI pattern.

[0270] 56. In claim 55, a non-transient computer-readable medium in which the image is generated from a simulated contour of a simulated ADI pattern and / or obtained from a metrology device configured to capture an image of the substrate after performing a resist process on the substrate.

[0271] 57. In any one of claims 52 to 56, the step of acquiring contour data is,

[0272] A step of executing one or more process models associated with a patterning process to generate a simulated ADI pattern including a resist process, using a design pattern to be printed on a substrate as input; and

[0273] A non-transient computer-readable medium comprising the step of extracting contours from a simulated ADI pattern, wherein each contour is a contour of a feature within the simulated ADI pattern.

[0274] 58. In claim 57, a non-transient computer-readable medium comprising at least one of the following process models: an optical model configured to determine an aerial image; and a resist model configured to determine a resist image.

[0275] 59. A non-transient computer-readable medium, wherein, in any one of claims 52 through 58, the measurement data is obtained from a metrology gauge, and the metrology gauge is an edge placement gauge and / or a critical dimension (CD) gauge associated with an AEI pattern.

[0276] 60. A non-transient computer-readable medium, wherein the data measured by the metrology gauge is the position of the edge placement gauge associated with the contour of the AEI pattern printed on the substrate; and / or the CD value associated with the AEI pattern printed on the substrate.

[0277] 61. A non-transient computer-readable medium, wherein, in claim 57, when the metrology gauge is a CD gauge, the reference bias value is obtained through a calibration process configured to determine the bias value associated with the given CD gauge (the bias value represents the amount of CD reduction to be applied to the ADI pattern to generate the AEI pattern).

[0278] 62. In claim 57, a non-transient computer-readable medium in which a bias value is provided at the end of a given CD gauge, and the bias value is not equal or asymmetric with respect to the center of the CD gauge.

[0279] 63. A non-transient computer-readable medium, wherein the training of a machine learning model is an iterative process, and the iteration comprises: (a) running the machine learning model using given values ​​of measured data (902), contour data (901), and model parameters to generate a bias map associated with the contour data (901) (the bias map includes bias values); (b) adjusting the model parameters of the machine learning model so as to reduce the difference based on the slope of the difference between the model-based bias values ​​and the reference bias values ​​(903); and (c) performing steps (a)-(b) until the difference is minimized.

[0280] 64. A non-transient computer-readable medium according to any one of claims 52 to 63, wherein the bias map generated through a trained machine learning model comprises an etching bias value applied to a resist contour to determine an etching contour to be printed on a substrate.

[0281] 65. In claim 64, a non-transient computer-readable medium in which the etching bias value is applied locally perpendicular to the resist contour.

[0282] 66. A non-transient computer-readable medium, wherein, in any one of claims 52 to 66, the bias map is a pixelated image and each pixel has an intensity value representing a bias value.

[0283] 67. A non-transient computer-readable medium comprising instructions, wherein the instructions are a method for determining a bias vector associated with an image after development (ADI) pattern when executed by one or more processors, the method comprising: (i) obtaining a probability distribution function (PDF) corresponding to a particle deposited within an ADI pattern on a substrate, and (ii) obtaining a contour function characterizing an ADI contour associated with the ADI pattern; determining a deposition rate of a particle at a specific location of the ADI contour based on a combination of the PDF of the particle and the contour function for a region of the ADI contour; and determining a bias vector associated with the ADI pattern based on the deposition rate, wherein the bias vector, when applied to the ADI contour of the ADI pattern, generates an image after etching (AEI) contour.

[0284] 68. In claim 67, the step of obtaining a probability distribution function (PDF) of particles is based on measured substrate data, wherein the measured substrate data comprises deposition data of particles and a measured etching pattern, a non-transient computer-readable medium.

[0285] 69. A non-transient computer-readable medium, wherein the step of acquiring the PDF in claim 68 includes the step of determining the variance of a Gaussian distribution fitted to the measurement data.

[0286] 70. A non-transient computer-readable medium, wherein, in any one of claims 67 to 69, the step of determining the deposition rate of particles comprises: convolving the PDF of the particles and the contour features; and integrating across the region of the ADI contour.

[0287] 71. A non-transient computer-readable medium, wherein, in any one of claims 67 to 70, the step of determining a bias vector comprises the step of determining a slope of the deposition rate for a first direction and a second direction of an ADI pattern, and the first direction and the second direction are perpendicular to each other.

[0288] 72. A non-transient computer-readable medium according to claim 67, wherein the bias vector includes a bias direction at the location of the ADI contour and further comprises the step of applying a bias value to generate an AEI contour.

[0289] 73. A non-transient computer-readable medium in which, in the manner of claim 72, when bias values ​​at different positions are applied to an ADI contour, the bias direction is determined such that bias vectors at different positions do not intersect each other.

[0290] 74. A non-transient computer-readable medium, wherein the bias direction comprises a direction not perpendicular to the ADI contour in claim 73.

[0291] 75. A non-transient computer-readable medium, wherein in any one of claims 67 to 74, the PDF of the particles represents a deposition or etching process of particles on an ADI contour, and the deposition rate is negative or positive.

[0292] 76. A non-transient computer-readable medium, wherein in any one of claims 67 through 75, the bias value is obtained from a trained machine learning model configured to generate a bias map for a given resist pattern.

[0293] 77. A non-transient computer-readable medium, wherein, in any one of claims 67 through 76, the ADI pattern comprises a plurality of contours, and the set of bias vectors is determined individually for each ADI contour.

[0294] 78. A non-transient computer-readable medium comprising instructions, wherein the instructions, when executed by one or more processors, perform a method comprising: (i) obtaining a probability distribution function (PDF) corresponding to a process to be performed on a contour, and (ii) obtaining a contour function characterizing the shape of the contour; convolving the contour function with the PDF over a region of the contour to determine a processing speed at a specific location of the contour; and determining a bias vector to be applied to the contour based on a process speed to generate a biased contour representing the effect of the process applied to the contour.

[0295] 79. In claim 78, a non-transient computer-readable medium in which the process causes the addition or removal of the material on which the contour is formed, and the addition or removal causes a change in the shape of the contour.

[0296] 80. In claim 79, a non-transient computer-readable medium in which the process speed characterizes the behavior of adding or removing the material on which the contour is formed.

[0297] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging subwavelength features and may be particularly useful for new imaging technologies capable of generating increasingly smaller wavelengths. New technologies already in use include EUV (extreme ultraviolet) lithography, which can generate 193 nm wavelengths using an ArF laser and up to 157 nm wavelengths using a fluorine laser. Furthermore, EUV lithography can generate wavelengths within the 20-5 nm range by using a synchrotron or by colliding a material (solid or plasma) with high-energy electrons to generate photons within this range.

[0298] It should be understood that while the concept disclosed herein may be used for imaging on a substrate such as a silicon wafer, the disclosed concept may be used with any type of lithography imaging system, for example, a system used for imaging on a substrate other than a silicon wafer.

[0299] While specific references may be made in this specification regarding the use of the embodiments in the manufacture of ICs, it should be understood that the embodiments of this specification may have many other possible applications. For example, they may be used in the manufacture of guidance and sensing patterns for integrated optical systems, magnetic domain memory, liquid crystal displays (LCDs), thin-film magnetic heads, micromechanical systems (MEMs), etc. In the context of such alternative applications, the use of the terms “reticle,” “wafer,” or “die” in this specification refers to a “patterning device,” “substrate,” or “target part,” respectively. The substrate mentioned in this specification may be processed before or after exposure, for example, by a track (a tool that generally applies a resist layer to a substrate and develops the exposed resist) or by a metrology or inspection tool. Where applicable, the disclosures of this specification may be applied to such tools and other substrate processing tools. Additionally, since the substrate may be processed one or more times, for example to create a multilayer IC, the term “substrate” as used herein may refer to a substrate comprising a number of already processed layers.

[0300] In this specification, the terms “radiation” and “beam” include all types of electromagnetic radiation, including ultraviolet radiation (e.g., having wavelengths of about 365, about 248, about 193, about 157, or about 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having wavelengths in the range of 5-20 nm), as used herein, as well as particle beams such as ion beams or electron beams.

[0301] As used herein, the term "optimization" refers to or means adjusting a patterning device (e.g., lithography device), a patterning process, etc., so that the result and / or process have more desirable characteristics, such as higher accuracy of the design pattern on the substrate, a larger process window, etc. Accordingly, as used herein, the term "optimization" refers to or means a process of identifying one or more values ​​for one or more parameters that provide an improvement, such as local optimization, by comparing one or more values ​​for one or more parameters in at least one relevant metric with an initial set of such values. "Optimization" and other related terms should be interpreted accordingly. In one embodiment, the optimization step may be applied iteratively to provide further improvement in one or more metrics.

[0302] Aspects of the present invention may be implemented in any convenient form. For example, an embodiment may be implemented by one or more suitable computer programs that can be executed on a suitable carrier medium, which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). An embodiment of the present invention may be implemented using a suitable device that specifically takes the form of a programmable computer executing a computer program configured to implement the method described herein. Accordingly, an embodiment of the present invention may be implemented in hardware, firmware, software, or any combination thereof. An embodiment of the present invention may also be implemented as instructions stored on a machine-readable medium that can 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 Read Only Memory (ROM); Random Access Memory (RAM); magnetic disk storage medium; optical storage medium; flash memory device; electrical, optical, acoustic, or other forms of radio signals (e.g., carrier waves, infrared signals, digital signals, etc.) and others. Additionally, firmware, software, routines, and instructions may be described herein as performing specific actions. However, it should be understood that such description is for convenience only and that such actions actually originate from computing devices, processors, controllers, or other devices executing firmware, software, routines, instructions, etc.

[0303] In block diagrams, the illustrated components are depicted as separate functional blocks, but embodiments are not limited to systems in which the functions described herein are configured as illustrated. The functions provided by each component may be provided by software or hardware modules configured differently from those currently illustrated, and, for example, such software or hardware may be mixed, combined, replicated, decomposed, distributed (within a data center or geographically), or configured differently. The functions described herein may be provided by one or more processors of one or more computers executing code stored on a type of non-transient 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 this case, the information (e.g., content) may be provided, or within the scope provided, the information may be provided through instructions to retrieve said information from the content delivery network.

[0304] Unless otherwise specifically stated, as is evident from the discussion, it will be understood that the discussion throughout this specification using terms such as "processing," "calculating," "calculating," "determining," etc., refers to the operation or process of a specific device, such as a special-purpose computer or a similar special-purpose electronic processing / computing device.

[0305] It should be understood that this application describes various inventions. Instead of separating these inventions into several separate patent applications, they have been grouped into a single document because it is economically beneficial for the application of the relevant subject matter. However, the apparent advantages and aspects of such inventions should not be confused. It should be understood that while some embodiments address all the defects mentioned herein, the invention is useful independently, and some embodiments address only a subset of these problems or provide other unmentioned advantages that would be apparent to those skilled in the art reviewing the invention. Due to cost constraints, some inventions disclosed herein may not be claimed at present and may be claimed in subsequent applications, such as continuation applications or amendments to the claims of the invention. Similarly, due to space constraints, the summary or description of the invention in this document should not be construed as containing a comprehensive list of all such inventions or all aspects of such inventions.

[0306] It should be understood that the description and drawings are not intended to limit the invention to the specific form disclosed, but rather, on the contrary, encompass all modifications, equivalents, and alternatives that fall within the scope and spirit of the invention as defined by the appended claims.

[0307] Various modifications and alternative embodiments of the present invention will be apparent to those skilled in the art from the description of the invention. Accordingly, such description and drawings are to be interpreted merely as illustrative and are intended to inform those skilled in the art of the general manner of carrying out the invention. The forms of the invention shown and described herein should be understood as being taken as examples of embodiments. Elements and materials may be substituted with those exemplified and described herein, parts and processes may be reversed or omitted, specific features may be utilized independently, and features of embodiments or embodiments may be combined, all of which will be apparent to those skilled in the art after taking advantage of this description. Modifications to the elements described herein may be made without departing from the spirit and scope of the invention as described in the following claims. Titles used herein are for compositional purposes only and are not intended to limit the scope of the description.

[0308] As used throughout this application, the word “may” is used in a permissive sense (i.e., potential sense) rather than an obligatory sense (i.e., must). Words such as “including” and “to include” mean that they include, but are not limited to. As used throughout this application, the singular forms “a,” “an,” and “the” include multiple referents unless the content explicitly indicates otherwise. Thus, for example, a reference to an element “an” or an element “a” includes a combination of two or more elements, despite the use of other terms and phrases for one or more elements, such as “one or more.” The term “or” is non-exclusive unless otherwise specified, i.e., includes both “and” and “or.” Terms describing conditional relationships, such as "response to X, Y," "X, Y," "if X, Y," and "if X, Y," include causal relationships where the antecedent is a necessary causal condition, a sufficient causal condition, or a contributing causal condition. Consequently, for example, "state X occurs when condition Y is acquired" is generally understood as "X occurs only in Y" and "X occurs in Y and Z." These conditional relationships are not limited to results immediately following an acquisition, as some results may be delayed and the antecedent in the conditional statement is linked to the result; for example, the antecedent relates to the likelihood of the result occurring. Unless otherwise specified, a statement in which multiple attributes or functions map to multiple objects (e.g., one or more processors performing steps A, B, C, and D) includes all attributes or functions mapped to all such objects and a subset of attributes or functions mapped to a subset of attributes or functions (e.g., all processors each perform step AD, processor 1 performs step A, processor 2 performs steps B and part of step C, and processor 3 performs step Perform part of C and step D).Additionally, unless otherwise specified, a statement that one value or behavior is "based" on another condition or value includes both cases where the condition or value is the sole factor and cases where the condition or value is one of multiple factors. Unless otherwise specified, a statement that "each" instance of some set has some attribute should not be understood to exclude cases where some other identical or similar configurations of a larger set do not have that attribute. A reference to a selection within a range includes the last part of the range.

[0309] In the foregoing description, every process, description, or block of the flowchart should be understood as representing a module, segment, or portion of code containing one or more executable instructions for implementing a specific logical function or step of the process, and as understood by those skilled in the art, alternative implementations are included within the scope of exemplary embodiments of the present invention in which functions may be executed differently from the order shown or discussed, including substantially simultaneously or in reverse order, depending on the relevant functions.

[0310] To the extent that specific U.S. patents, U.S. patent applications, or other materials (e.g., articles) are included by reference, the text of such U.S. patents, U.S. patent applications, and other materials does not conflict with interest with the statements and drawings set forth herein. Where such conflict exists, the text of the U.S. patents, U.S. patent applications, and other materials included by reference that conflicts with interest is not included by reference herein.

[0311] Although specific embodiments have been described, these embodiments are presented merely as examples and are not intended to limit the scope of the invention. In practice, the novel methods, apparatuses, and systems described herein may be implemented in various other forms. Furthermore, various omissions, substitutions, and modifications to the forms of methods, apparatuses, and systems described herein may be made without departing from the spirit of the invention. The appended claims and their equivalents are intended to include such forms or modifications that fall within the scope and spirit of the invention.

Claims

Claim 1 A metrology method comprising: (i) obtaining measurement data related to physical properties of a structure printed on a substrate, and (ii) obtaining at least a portion of a simulated contour of the structure—the portion of the simulated contour being related to the measurement data; modifying the portion of the simulated contour of the structure based on the obtained measurement data; and generating a metrology gauge—the metrology gauge being placed to measure physical properties of the simulated contour of the structure—on or adjacent to the modified portion of the simulated contour, wherein the measurement data is a CD value at a defined location associated with the structure, and the metrology gauge is an edge placement gauge and a CD gauge. Claim 2 A method according to claim 1, wherein the portion of the simulated contour is a portion of the simulated contour within a defined area around the measurement data associated with the structure. Claim 3 In claim 2, the step of obtaining a portion of the simulated contour comprises: defining an area of ​​the substrate around a defined location associated with the measurement data; and simulating a patterning process of the structure within the defined area of ​​the substrate to obtain a portion of the simulated contour of the structure. Claim 4 A method according to claim 1, wherein the step of modifying a portion of the simulated contour comprises: determining simulated data associated with the physical properties of the simulated contour of the structure based on the portion of the simulated contour; determining the difference between the measurement data and the simulated data associated with the physical properties of the structure; and modifying the portion of the simulated contour based on the difference so as to reduce the difference between the measurement data and the simulated data. Claim 5 delete Claim 6 In claim 1, the step of modifying a portion of the simulated contour is based on the difference between the simulated CD value and the measured CD value associated with the structure. Claim 7 A method according to claim 1, wherein the step of modifying a portion of the simulated contour comprises: determining simulated data associated with the physical properties of the simulated contour of the structure based on the portion of the simulated contour; determining the difference between the measurement data and the simulated data associated with the physical properties of the structure; and adjusting a threshold value adopted to generate the simulated contour based on the difference so as to reduce the difference between the measurement data and the simulated data, wherein the adjusted threshold value modifies the portion of the simulated contour. Claim 8 A method according to claim 1, wherein the step of modifying a portion of the simulated contour comprises: determining a simulated CD value at a defined location associated with a measured CD value using the portion of the simulated contour; determining a difference between the simulated CD value and the measured CD value; and adjusting a threshold value based on the difference so as to reduce the difference between the simulated CD value and the measured CD value, wherein the adjusted threshold value modifies the portion of the simulated contour. Claim 9 A method according to claim 1, wherein the step of generating the metrology gauge comprises: the step of specifying a point along the modified portion of the simulated contour; and the step of exporting the location of the point to the metrology gauge. Claim 10 A method according to claim 1, wherein the measurement data is obtained through a metrology tool. Claim 11 In claim 10, the method wherein the metrology tool is a scanning electron microscope (SEM) and the measurement data is obtained from an SEM image. Claim 12 delete Claim 13 A method according to claim 3, comprising the step of determining parameters of the patterning process by providing the modified contour to a model of the patterning process. Claim 14 In claim 3, the method further comprises the step of training a machine learning model associated with a patterning process, wherein the method comprises the step of training the machine learning model so that, using the measurement data and the metrology gauge, a performance metric of the patterning process around the defined location on the substrate—the performance metric being a function of the metrology gauge and the physical properties, and the machine learning model being an etching model or a resist model—is improved. Claim 15 One or more non-transient computer-readable media having instructions recorded thereon, wherein the instructions, when executed by one or more processors, cause the one or more processors to implement the method of any one of claims 1 through 4, 6 through 11, and 13 through 14.

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