Methods for training machine learning models for improving patterning processes

Abstract

This paper describes a method for training a machine learning model configured to predict values ​​of physical properties associated with a substrate for adjusting a patterning process. The method involves: obtaining a reference image; determining a first set of model parameter values ​​for the machine learning model such that a first cost function is reduced from an initial value of a cost function obtained using the initial set of model parameter values, wherein the first cost function is the difference between the reference image and an image generated by the machine learning model; and training the machine learning model using the first set of model parameter values ​​such that a combination of the first cost function and a second cost function, the second cost function being the difference between a measured value and a predicted value, is iteratively reduced.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. application No. 62 / 886,058, filed on August 13, 2019, and the entire contents of said U.S. application are incorporated herein by reference. Technical Field

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

[0004] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that case, a pattern forming device (which is alternatively referred to as a mask or reticle) can be used to produce a circuit pattern corresponding to a single layer of an IC, and such a pattern can be imaged onto a target portion (e.g., including a portion of a die, one or several dies) on a substrate (e.g., a silicon wafer) having a layer of radiation-sensitive material (resist). Typically, a single substrate will contain a network of adjacent target portions that are exposed in succession. Known lithographic apparatus include: a so-called stepper, in which each target portion is irradiated by exposing the entire pattern to the target portion at one time; and a so-called scanner, in which each target portion is irradiated by scanning the substrate synchronously in parallel or antiparallel to a given direction (the "scanning" direction) while scanning the pattern via the beam.

[0005] Before the circuit pattern is transferred to the substrate from the pattern forming device, the substrate can undergo various processes, such as primer, resist coating and soft baking. After exposure, the substrate can undergo other processes, such as post-exposure baking (PEB), developing, hard baking, and measurement / inspection of the circuit pattern after transfer. This process array is the basis for the single layer of the device (e.g., IC) used for manufacturing. The substrate can then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., which are intended to refine the single layer of the device. If several layers are needed in the device, the whole process or its variant is repeated for each layer. Eventually, the device will be present in each target portion on the substrate. Then these devices are separated from each other by techniques such as cutting or slicing, so that a separate device can be mounted on a carrier, connected to a pin, etc.

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

[0007] In an embodiment, a method of training a machine learning model is provided, the machine learning model being configured to predict a value of a physical property associated with a substrate for use in adjusting a patterning process. The method involves: obtaining a reference image associated with a desired pattern to be printed on the substrate; determining a first set of model parameter values ​​for the machine learning model such that a first cost function is reduced from an initial value of the cost function obtained using an initial set of model parameter values, wherein the first cost function is the difference between the reference image and an image generated via the machine learning model; and training the machine learning model using the first set of model parameter values ​​such that a combination of the first cost function and a second cost function is iteratively reduced. In an embodiment, the second cost function is the difference between a measured value and a predicted value of a physical property associated with the desired pattern, the predicted value being predicted via the machine learning model.

[0008] Furthermore, in an embodiment, a computer program product is provided, including a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the aforementioned method when executed by a computer. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0010] Figure 1 A block diagram showing various subsystems of a lithography system according to an embodiment;

[0011] Figure 2 depicts an example flow chart for modeling and / or simulating at least a portion of a patterning process according to an embodiment;

[0012] Figure 3is a flow chart of a method of training a machine learning model configured to predict a value of a physical property associated with a substrate for use in adjusting a patterning process in accordance with an embodiment;

[0013] Figure 4 FIG. 1 shows a method for implementing a method according to an embodiment of the present invention. Figure 3 An example of a machine learning model with multiple layers trained using the methods in ;

[0014] Figure 5A and Figure 5B illustrates example pattern shifts relative to a grid resulting in grid-dependent errors according to an embodiment;

[0015] Figure 6 schematically depicts an embodiment of a scanning electron microscope (SEM) according to an embodiment;

[0016] Figure 7 schematically depicts an embodiment of an electron beam inspection apparatus according to an embodiment;

[0017] Figure 8 is a block diagram of an example computer system according to an embodiment;

[0018] Fig. 9 is a schematic diagram of a lithographic projection apparatus according to an embodiment;

[0019] Fig.10 is a schematic diagram of an extreme ultraviolet (EUV) lithography projection apparatus according to an embodiment;

[0020] Fig.11 According to the embodiment Fig.10 A more detailed view of the devices in the

[0021] Fig.12 According to the embodiment Fig.10 and Fig.11 A more detailed view of the source collector module of a device. DETAILED DESCRIPTION

[0022] Before describing the embodiments in detail, it is instructive to present an example environment in which the embodiments may be implemented.

[0023] Figure 1An exemplary lithographic projection apparatus 10A is shown. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other type of source including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have a radiation source); an illumination optical device, which, for example, defines a partial coherence (denoted as sigma or σ) and may include optical devices 14A, 16Aa and 16Ab that shape the radiation from source 12A; a patterning device 18A; and a transmission optical device 16Ac that projects an image of a patterned device pattern onto a substrate plane 22A. An adjustable filter or hole 20A at the pupil plane of the projection optical device can limit the range of beam angles incident on the substrate plane 22A, where the maximum possible angle defines the numerical aperture NA of the projection optical device = nsin(Θmax), where n is the refractive index of the medium between the substrate and the final element of the projection optical device, and Θmax is the maximum angle of the beam leaving the projection optical device that can still be incident on the substrate plane 22A.

[0024] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a pattern forming device, and a projection optical device guides and shapes the illumination onto a substrate via the pattern forming device. The projection optical device may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. An aerial image (AI) is a distribution of radiation intensity at the substrate level. A resist layer on the substrate is exposed, and the aerial image is transferred to the resist layer to serve as a potential "resist image" (RI) therein. A resist image may be defined as a spatial distribution of the solubility of the resist in the resist layer. A resist model may be used to calculate a resist image from an aerial image, and such an example may be found in U.S. Patent Application Publication No. US2009-0157360, the entire contents of which are hereby incorporated herein by reference. A resist model is only about the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of the lithographic projection apparatus (e.g., the properties of the source, the pattern forming device, and the projection optical device) dominate the aerial image. Since a patterning device used in a lithographic projection apparatus can be varied, it may be desirable to decouple the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the source and projection optics.

[0025] In an embodiment, assist features (sub-resolution assist features and / or printable resolution assist features) may be placed in a design layout based on how the design layout is optimized according to the methods of the present disclosure. For example, in an embodiment, the method employs a machine learning based model to determine the pattern of the pattern forming device. The machine learning model may be a neural network, such as a convolutional neural network, which may be trained in some manner (e.g., as described in Figure 3 ) to obtain accurate predictions at fast rates, thus enabling full-chip simulation of the patterning process.

[0026] A neural network can be trained (i.e., parameters of the neural network are determined) using a set of training data. The training data may include or consist of a set of training samples. Each sample may be a pair including an input object (typically a vector, which may be referred to as a feature vector) and a desired output value (also referred to as a management signal), or consisting of the input object and the desired output value. The training algorithm analyzes the training data and adjusts the behavior of the neural network by adjusting the parameters of the neural network (e.g., the weights of one or more layers) based on the training data. The neural network after training can be used to map new samples.

[0027] In the context of determining a pattern of a patterning device, the feature vector may include one or more characteristics of a design layout included 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 size, refractive index, material composition, etc.), and one or more characteristics of the illumination used in the lithography process (e.g., wavelength). The management signal may include one or more characteristics of the pattern of the patterning device (e.g., CD, profile, etc. of the pattern of the patterning device).

[0028] Given a structure of the form {(x1,y1),(x2,y2),…,(x N ,y N )}, so that x i is the feature vector of the i-th example and y i To manage the signal, the training algorithm looks for a neural network g:X→Y, where X is the input space and Y is the output space. A feature vector is an n-dimensional vector that represents a numerical feature of some object. The vector space associated with these vectors is often called the feature space. Sometimes it is convenient to do the following: Use a scoring function f:X× to represent g, so that g is defined to return the y value that gives the highest score: Let F denote the space of scoring functions.

[0029] The neural network can be probabilistic, where g takes the form of a conditional probability model g(x)=P(y|x), or f takes the form of a joint probability model f(x,y)=P(x,y).

[0030] There are two basic approaches to choosing f or g: empirical risk minimization and structural risk minimization. Empirical risk minimization seeks the neural network that best fits the training data. Structural risk minimization includes a penalty function that controls the bias / variance tradeoff. For example, in an embodiment, the penalty function can be based on a cost function, which can be squared error, number of defects, EPE, etc. The function (or weights within the function) can be modified so that the variance is reduced or minimized.

[0031] In both cases, the training set is assumed to consist of independent and identically distributed pairs (x i ,y i One or more samples of or consisting of one or more samples of the pair. In an embodiment, in order to measure how well the function fits the training data, a loss function is defined For the training sample (x i ,y i , predicted value The loss is

[0032] Define the risk R(g) of a function g as the expected loss of g. This can be estimated from the training data as

[0033] In an embodiment, a machine learning model of a patterning process may be trained to predict, for example, contours, patterns, CDs of mask patterns, and / or contours, CDs, edge positioning (e.g., edge positioning errors) in resist and / or etched images on a wafer, etc. The goal of the training is to achieve accurate predictions of, for example, contours, spatial image intensity slopes, and / or CDs of printed patterns on a wafer, etc. The intended design (e.g., a wafer target layout to be printed on a wafer) is typically defined as a pre-OPC design layout that may be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0034] Figure 212 is an exemplary flow chart for modeling and / or simulating multiple parts of a patterning process. As will be appreciated, the models can represent different patterning processes and need not include all of the models described below. The source model 1200 represents the optical characteristics of the illumination of the patterning device (including the radiation intensity distribution, bandwidth, and / or phase distribution). The source model 1200 can represent the optical characteristics of the illumination, including but not limited to the numerical aperture setting, the illumination sigma (σ) setting, and any specific illumination shape (e.g., off-axis radiation shape, such as annular, quadrupole, dipole, etc.), where σ (or sigma) is the outer radial extent of the illuminator.

[0035] The projection optics model 1210 represents the optical properties of the projection optics (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics). The projection optics model 1210 may represent the optical properties of the projection optics, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0036] 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 detailed physical properties of the patterning device, as described, for example, in U.S. Pat. No. 7,587,704, which is incorporated herein by reference in its entirety. In an embodiment, the patterning device / design layout model module 1220 represents the optical properties of a design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.) (including changes in radiation intensity distribution and / or phase distribution caused by a given design layout), which is a representation of the arrangement of features on or by the patterning device. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the illumination and projection optical devices. The purpose of the simulation is typically to accurately predict, for example, edge positioning and CD, which can then be compared with the device design. The device design is typically defined as a pre-OPC patterning device layout and will be provided in a standardized digital file format such as GDSII or OASIS.

[0037] An aerial image 1230 can be simulated from the source model 1200, the projection optics model 1210, and the patterning device / design layout model 1220. The aerial image (AI) is the radiation intensity distribution at the substrate level. The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, patterning device, and projection optics) govern the aerial image.

[0038] The resist layer on the substrate is exposed by an aerial image, and the aerial image is transferred to the resist layer to be therein as a potential "resist image" (RI). The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. A resist model 1240 can be used to simulate a resist image 1250 from an aerial image 1230. The resist model can be used to calculate a resist image from an aerial image, an example of which can be found in U.S. patent application publication number US 2009-0157360, the entire disclosure of which is hereby incorporated by reference herein. The resist model typically describes the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB) and development, so as to predict, for example, the profile of a resist feature formed on a substrate, and therefore it typically only relates to such properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking and development). In an embodiment, the optical properties of the resist layer (eg, refractive index, film thickness, propagation, and polarization effects) may be captured as part of the projection optics model 1210 .

[0039] Therefore, in general, the connection between the optical model and the resist model is the simulated spatial image intensity within the resist layer, which is caused by the projection of radiation onto the substrate, the refraction at the resist interface, and the multiple reflections in the resist film stack. The radiation intensity distribution (spatial image intensity) becomes a potential "resist image" through the absorption of the incident energy, which is further modified by diffusion processes and various loading effects. For full-chip applications, efficient simulation methods that are fast enough approximate the true 3D intensity distribution in the resist stack through a 2D spatial (and resist) image.

[0040] In an embodiment, the resist image may be used as an input to the post-pattern transfer process model module 1260. The post-pattern transfer process model 1260 defines the performance of one or more post-resist development processes (eg, etching, developing, etc.).

[0041] The simulation of the patterning process can, for example, predict the profile, CD, edge positioning (e.g., edge positioning error), etc. in the resist and / or etched image. Therefore, the purpose of the simulation is to accurately predict, for example, the edge positioning and / or the slope of the spatial image intensity and / or the CD, etc. of the printed pattern. These values ​​can be compared with the expected design to, for example, correct the patterning process, identify the locations where defect points are predicted to occur, etc. The expected design is generally defined as a pre-OPC design layout that can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0042] Thus, the model formula describes most, if not all, of the known physical and chemical effects of the overall process, and each of the model parameters desirably corresponds to a different physical or chemical effect. The model formula thus sets an upper bound on how well the model can be used to simulate the overall manufacturing process.

[0043] In a patterning process (e.g., photolithography, electron beam lithography, guided self-assembly, etc.), an energy sensitive material (e.g., resist) deposited on a substrate typically undergoes a pattern transfer step (e.g., via exposure). After the pattern transfer step, various post-steps such as resist baking and subtractive processes such as resist development, etching, etc. are applied. These post-exposure steps or processes exert various effects on the substrate that cause the patterned layer or etch to have structures (which have dimensions different from the target dimensions).

[0044] The computational analysis of the patterning process uses a predictive model that, when properly calibrated, can produce an accurate prediction of the size output from the patterning process. The model of the post-exposure process is typically calibrated based on empirical measurements. The calibration process includes running a test wafer with different process parameters, measuring the critical dimensions after the post-exposure process, and calibrating the model to the measurement results. In practice, a well-calibrated model makes fast and accurate predictions of the size for improving device performance or yield, enhancing the process window, or increasing design options. In an example, modeling the post-exposure process using a deep convolutional neural network (CNN) produces a model accuracy comparable to or better than that produced using traditional techniques, which typically involve modeling using physical term expressions or closed form equations. Compared to traditional modeling techniques, deep learning convolutional neural networks reduce the requirements for process knowledge in model development and increase the reliance on engineers' personal experience in model tuning. In short, the deep CNN model for the post-exposure process consists of input and output layers and multiple hidden layers such as convolutional layers, normalization layers, and pooling layers. The parameters of the hidden layers are optimized to give the minimum value of the loss function. In an embodiment, a CNN model may be trained to model the behavior of any process or combination of processes related to the patterning process.

[0045] Figure 3Flowchart of a method 300 for training a machine learning model 305 (e.g., a CNN) configured to predict values ​​of physical properties associated with a substrate for use in adjusting a patterning process. The training method is a more accurate training method compared to existing methods. For example, the training is based on reducing specific errors associated with model predictions (e.g., via a first cost function, a second cost function, grid-dependent errors, edge location errors, etc. in one or more training steps) by applying specific weight factors, such as in a CNN, wherein weights are associated with these errors, thereby improving the overall modeling quality.

[0046] After training, the machine learning model 305 may be referred to as a trained machine learning model 305'. Training the machine learning model 305' may also be performed to determine the physical property. Additionally, patterning process parameters (e.g., dose, focus, OPC, etc.) may be adjusted based on the physical property values ​​to improve the patterning process.

[0047] The method involves training a machine learning model 305 in successive steps to model a process (e.g., a post-exposure process) of a patterning process. Successive steps refer to training the machine learning model 305 using a first cost function to determine an initial set of model parameter values, and using such initial model parameter values ​​to further train the machine learning model 305 using a second cost function. Such successive step training facilitates faster convergence and produces a more accurate model compared to a single-step training process involving a single cost function. The method 300 is discussed in further detail below.

[0048] Process P301 involves obtaining a reference image 301 associated with a desired pattern to be printed on a substrate. In an embodiment, obtaining the reference image 301 involves executing a process model configured to produce the reference image 301 as an output, wherein the process model models a portion of a patterning process. In an embodiment, the process model is a calibrated model of an optical device model, a resist model, and / or an etching model of the patterning process. Thus, in an embodiment, the reference image 301 is an aerial image, a resist image, and / or an etching image of the desired pattern.

[0049] Process P303 involves determining a first set of model parameter values ​​303 for the machine learning model 305 such that the first cost function is reduced from an initial value of the cost function obtained using the initial set of model parameter values. In an embodiment, the first cost function is the difference between the reference image 301 and the image generated via the machine learning model 305. In an embodiment, the reference image 301 and the generated image are pixelated images. Therefore, the first cost function can be the difference in intensity values ​​of the pixelated image. The intensity of a pixel indicates the presence or absence of a feature. For example, a peak intensity signal indicates the edge of a feature (e.g., a contact hole) in an image.

[0050] In an embodiment, determining the first set of model parameter values ​​303 of the machine learning model 305 is an iterative process. The iteration involves: generating an image by executing the machine learning model 305 using the desired pattern; determining the difference between the generated image and the reference image 301; and adjusting the model parameter values ​​of the machine learning model 305 so that the difference is reduced. In an embodiment, the difference between the generated image and the reference image 301 is minimized.

[0051] Therefore, using the first initial set of model values, the machine learning model 305 ("model 305" refers to the machine learning model 305 with model parameter values ​​303) can accurately predict the aerial image, resist image, or etching image associated with the substrate. In addition, the contour and physical properties of the pattern can be obtained from the predicted image for further analysis or improvement of the patterning process.

[0052] In an embodiment, the model parameters are weights and / or biases associated with one or more layers of the machine learning model 305. In an embodiment, the machine learning model 305 is a convolutional neural network comprising a plurality of layers, each layer being associated with weights and / or biases.

[0053] In addition, process P305 involves training a machine learning model 305″ using a first set of model parameter values ​​303 so that a combination of the first cost function and the second cost function is reduced. In an embodiment, the combination of the first cost function (CF1) and the second cost function (CF2) is calculated using the expression c1*CF1+c2*CF2, where c1 and c2 are coefficients that can be adjusted to minimize the combination.

[0054] In an embodiment, the second cost function is the difference between the measured value 304 and the predicted value of the physical property associated with the desired pattern, which is predicted via the machine learning model 305". After the training process is completed, a trained machine learning model 305' is obtained that is configured to determine the physical property of the pattern to be imaged in the substrate.

[0055] In an embodiment, the physical property determined from the predicted image is a critical dimension or edge positioning error associated with the desired pattern. In an embodiment, the physical property is determined using the contour of the pattern in the predicted image of the model. For example, an algorithm can be used to define meter points along the contour, and a cutting line that intersects the contour at the meter location. In addition, to determine the CD, the distance between the meter points can be measured. Similarly, the EPE can be measured using meter points relative to a reference contour (e.g., a reference contour associated with the reference image 301).

[0056] In an embodiment, the measurement value 304 is a CD value obtained, for example, via a metrology tool configured to measure the desired printed pattern of the substrate. In an embodiment, the metrology tool is a scanning electron microscope (SEM) (see, for example, Figure 6 to Figure 7 ) and the measured values ​​are obtained from the SEM image. In an embodiment, the measured values ​​304 are intensity values ​​of the aerial image associated with the desired pattern. Therefore, during the training process, the measured values ​​304 (e.g., CD) are compared with the predicted physical properties (e.g., predicted CD). The training is performed so that the predicted values ​​closely match the measured values ​​304.

[0057] In an embodiment, the training of the machine learning model 305 is an iterative process. The iteration involves: initializing the model parameters of the machine learning model 305 using a first set of model parameter values ​​303; predicting the value of the physical property associated with the substrate by executing the machine learning model 305" using the desired pattern; obtaining the measured value 304 of the physical property of the desired printed pattern on the substrate via a metrology tool; and adjusting the model parameter values ​​of the machine learning model 305" so that the combination of the first cost function and the second cost function is reduced.

[0058] In an embodiment, adjusting the model parameter values ​​is based on a gradient descent of a combination of a first cost function and a second cost function. In an embodiment, the sum of the first cost function and the second cost function is minimized. In an embodiment, adjusting the model parameter values ​​of the machine learning model 305 involves determining a gradient graph of the sum of the first cost function and the second cost function as a function of the model parameters. Subsequently, based on the gradient graph, the model parameter values ​​are determined such that the sum of the cost functions is minimized.

[0059] In an embodiment, adjusting the model parameter values ​​includes adjusting the following values: one or more weights of a layer of a convolutional neural network, one or more biases of a layer of a convolutional neural network, a hyperparameter of the CNN, and / or the number of layers of the CNN. In an embodiment, the number of layers is a hyperparameter of the CNN, which may be pre-selected and may not be changed during the training process. In an embodiment, a series of training processes may be performed in which the number of layers may be modified. Figure 4 An example of a CNN is shown in Figure 2.

[0060] In an embodiment, training (e.g., Figure 4CNN) involves: determining the value of a first cost function; and gradually adjusting the weights of one or more layers of the CNN so that the first cost function is reduced (in one embodiment, minimized). In an embodiment, the first cost function is the difference between a predicted resist image or a predicted spatial image (e.g., an output vector of the CNN) and a real resist image obtained from a printed substrate (e.g., using an SEM tool). The first cost function or the difference is reduced by modifying the values ​​of CNN model parameters (e.g., weights, biases, strides, etc.). In an embodiment, the first cost function is calculated as CF1=f(reference image-CNN(input, cnn_parameters). In such a step, the input of the CNN includes a measured image or a simulated image (e.g., AI / RI) and cnn_parameters has an initial value that can be arbitrarily selected. After several iterations of training, the optimized cnn_parameters values ​​are obtained and further used as a first set of model parameter values ​​303 for further training.

[0061] In further training, after reducing (or minimizing) the first cost function, physical properties can be obtained from the predicted image of the machine learning model 305. For example, CD or EPE values ​​can be obtained from the predicted resist image or intensity values ​​can be obtained from the predicted aerial image. These predicted CD, EPE and / or intensity values ​​are compared with the measured values ​​304 to further train the machine learning model 305 using a second cost function associated with the physical properties in addition to the first cost function.

[0062] For example, the second cost function may be an edge positioning error (EPE). In such a case, the second cost function is determined using the measured values ​​of the EPE and the predicted EPE. In an embodiment, the second cost function may be expressed as: CF2=f(measured values-CNN(input,cnn_parameters), where CF2 may be EPE, and the function f(.) performs contour acquisition from the predicted pattern (e.g., by CNN) and further determines the difference. In an embodiment, the input of such a CNN includes the predicted image (e.g., AI / RI). cnn_parameters may be the weights and biases of the CNN and the values ​​of cnn_parameters are the initial model parameter values ​​obtained based on the first cost function.

[0063] In an embodiment, the gradient corresponding to the cost function (e.g., the first cost function and / or the second cost function) may be dcost / dparameter, where the value of cnn_parameters may be updated based on an equation (e.g., parameter=parameter-learning_rate*gradient). In an embodiment, the parameter may be a weight and / or a bias, and the learning_rate may be a hyperparameter for tuning the training process and may be selected by a user or a computer to improve the convergence of the training process (e.g., faster convergence).

[0064] In an embodiment, the trained machine learning model 305' (e.g. Fig. 9 The trained CNN) can also be used to correct the simulated pattern or any of its characteristics.

[0065] In an embodiment, the method 300 may also involve a process P305 of adopting a third cost function for further training the trained machine learning model 305'. The process P305 involves training the machine learning model 305' using the first set of model parameter values ​​303 so that the combination of the first cost function, the second cost function, and the third cost function is reduced (in one embodiment, minimized). In an embodiment, the third cost function is a grid-dependent function.

[0066] Grid-dependent errors are related to the simulation mechanism (e.g., image-based) used during the simulation of the patterning process. In an embodiment, the simulation of one or more process models is image-based, wherein a grid can be placed on an image (e.g., an image of a substrate pattern) and only features on the grid are evaluated during the simulation, while off-grid features are interpolated. Such interpolation may result in inaccurate simulation results (e.g., substrate pattern). In addition, the grid size may affect the simulation speed and the accuracy of the results. A small grid size gives accurate simulation results, but significantly slows down the simulation. Therefore, a larger grid can be used for faster simulations, which may adversely affect the accuracy of the simulation results (e.g., the simulated substrate pattern).

[0067] Typically, simulation is an iterative process, so any shift in the pattern placement relative to the grid in each iteration will induce errors in the predicted pattern. Therefore, simulation results including grid-dependent errors can be used to determine parameters of the patterning process (e.g., dose, focus, mask pattern, etc.), for example to improve the patterning process. Due to the grid-dependent errors, the determined parameters may not lead to the desired yield of the patterning process. Therefore, the grid-dependent errors should be removed or minimized. According to the present disclosure, such grid-dependent errors are handled via a third cost function.

[0068] FIG. 5A to FIG. 5BAn example pattern shift relative to a grid resulting in grid-dependent errors is illustrated. The figure shows predicted contours 501 / 511 (dashed lines) and input contours 502 / 512 (eg, designed or desired contours). Figure 5A In , the entire input contour 501 lies on the grid, however, in Figure 5B , a portion of the input contour 511 is off-grid, for example at a corner. This results in a difference in the model predicted contours 502 and 512. In embodiments, such as LMC or OPC applications, the same pattern may be iteratively presented at different locations on the grid, and it is desirable to have an invariant model prediction regardless of the location of the pattern. However, no model can achieve perfect shift invariance. Some ill-conditioned models may produce large contour differences between pattern shifts.

[0069] In an embodiment, grid dependent (GD) error may be measured as follows. To measure the GD error, the pattern along the contour and the meter are shifted together in sub-pixel steps. For example, for pixel size = 14nm, the pattern / meter may be shifted by 1nm per step along the x and / or y direction. With each shift, the model predicted CD is measured along the meter. Subsequently, the variance in the set of model predicted CDs indicates the grid dependent error.

[0070] In an embodiment, the training machine learning model can be used for various applications related to the patterning process to improve the yield of the patterning process. For example, method 300 also involves predicting a substrate image of a design layout via a trained machine learning model; determining a mask layout to be used to manufacture a mask for a patterning process via an OPC simulation using the design layout and the predicted substrate image. In an embodiment, the OPC simulation involves simulating a patterning process model using the geometry of the design layout and corrections associated with multiple sections, determining a simulated pattern to be printed on a substrate; and determining an optical proximity correction for the design layout so that the difference between the simulated pattern and the design layout is reduced. In an embodiment, determining the optical proximity correction is an iterative process. Iteration involves adjusting the shape and / or size of the geometry of the main features and / or one or more auxiliary features of the design layout so that the performance index of the patterning process is reduced. In an embodiment, the one or more auxiliary features are obtained from the predicted OPC-post image of the machine learning model.

[0071] In some embodiments, the inspection device may be a scanning electron microscope (SEM) that produces images of structures exposed or transferred on the substrate (eg, some or all of the structures of the device). Figure 6An embodiment of a SEM tool is depicted.A primary electron beam EBP emitted from an electron source ESO is focused by a condenser lens CL and then passes through a beam deflector EBD1 , an E×B deflector EBD2 and an objective lens OL to illuminate a substrate PSub on a substrate stage ST at a focal point.

[0072] When the substrate PSub is irradiated with the electron beam EBP, secondary electrons are generated from the substrate PSub. The secondary electrons are deflected by the E×B deflector EBD2 and detected by the secondary electron detector SED. A two-dimensional electron beam image can be obtained by detecting the electrons generated from the sample in synchronization with, for example, two-dimensional scanning of the electron beam by the beam deflector EBD1 or in synchronization with repeated scanning of the electron beam EBP in the X or Y direction by the beam deflector EBD1, and continuously moving the substrate PSub in the other of the X or Y directions by the substrate stage ST.

[0073] The signal detected by the secondary electron detector SED is converted into a digital signal by an analog / digital (A / D) converter ADC, and the digital signal is sent to the image processing system IPU. In an embodiment, the image processing system IPU may have a memory MEM to store all or part of the digital image for processing by the 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 data set representing the digital image. In addition, the image processing system IPU may have a storage medium STOR configured to store the digital image and the corresponding data set in a reference database. The display device DIS can be connected to the image processing system IPU so that the operator can perform necessary operations of the equipment with the help of a graphical user interface.

[0074] As mentioned above, SEM images can be processed to obtain contours describing the edges of objects representing device structures in the image. These contours are then quantified via indicators such as CD. Therefore, images of device structures are typically compared and quantified via simplified indicators such as edge-to-edge distance (CD) or simple pixel differences between images. Typical contour models for detecting the edges of objects in images in order to measure CD use image gradients. In practice, those models rely on strong image gradients. But in practice, images are typically noisy and have discontinuous boundaries. Techniques such as smoothing, adaptive thresholding, edge detection, corrosion, and expansion can be used to process the results of image gradient contour models to solve noisy and discontinuous images, but will ultimately result in low-resolution quantization of high-resolution images. Therefore, in most cases, mathematical operations are performed on the images of device structures to reduce noise, and automating edge detection results in a loss of resolution of the image, thereby resulting in a loss of information. Therefore, the result is a low-resolution quantization of a simplified representation of a complex high-resolution structure.

[0075] Thus, it is desirable to have a mathematical representation of a structure (e.g., a circuit feature, an alignment mark, or a portion of a measurement target (e.g., a grating feature), etc.) produced or expected to be produced using a patterning process, regardless of, for example, where the structure is in a latent resist image, in a developed resist image, or in a layer transferred to a substrate, such as by etching, which can maintain resolution and also describe the general shape of the structure. In the context of a lithography or other patterning process, the structure can be a device being manufactured or a portion thereof, and the image can be a SEM image of the structure. In some cases, the structure can be a feature of a semiconductor device (e.g., an integrated circuit). In this case, the structure can be referred to as a pattern or expected pattern comprising multiple features of a semiconductor device. In some cases, the structure can be an alignment mark or a portion thereof (e.g., a grating of an alignment mark) used in an alignment measurement process to determine the alignment of an object (e.g., a substrate) with another object (e.g., a patterning device), or a measurement target or a portion thereof (e.g., a grating of a measurement target) used to measure parameters of a patterning process (e.g., overlay, focus, dose, etc.). In an embodiment, the measurement target is a diffraction grating used to measure, for example, overlay.

[0076] Figure 7 Another embodiment of the inspection apparatus is schematically illustrated. The system is used to inspect a sample 90 (such as a substrate) on a sample platform 88 and includes a charged particle beam generator 81, a condenser lens module 82, a probe forming objective lens module 83, a charged particle beam deflection module 84, a secondary charged particle detector module 85 and an image forming module 86.

[0077] The charged particle beam generator 81 generates a primary charged particle beam 91. The condenser lens module 82 condenses the generated primary charged particle beam 91. The probe forming objective lens module 83 focuses the condensed primary charged particle beam into a charged particle beam probe 92. The charged particle beam deflection module 84 scans the formed charged particle beam probe 92 across the surface of the area of ​​interest on the sample 90 fixed on the sample platform 88. In an embodiment, the charged particle beam generator 81, the condenser lens module 82 and the probe forming objective lens module 83 or their equivalent designs, alternatives or any combination thereof together form a charged particle beam probe generator that generates a scanning charged particle beam probe 92.

[0078] The secondary charged particle detector module 85 detects the secondary charged particles 93 emitted from the sample surface (possibly together with other reflected or scattered charged particles from the sample surface) immediately after being bombarded by the charged particle beam probe 92 to generate a secondary charged particle detection signal 94. An image forming module 86 (e.g., a computing device) is coupled to the secondary charged particle detector module 85 to receive the secondary charged particle detection signal 94 from the secondary charged particle detector module 85 and thereby form at least one scanned image. In an embodiment, the secondary charged particle detector module 85 and the image forming module 86 or their equivalent designs, alternatives, or any combination thereof together form an image forming device that forms a scanned image from the detected secondary charged particles emitted from the sample 90 bombarded by the charged particle beam probe 92.

[0079] In an embodiment, the monitoring module 87 is coupled to the image forming module 86 of the image forming device to monitor, control, etc. the patterning process using the scanned image of the sample 90 received from the image forming module 86, and / or derive parameters for patterning process design, control, monitoring, etc. Therefore, in an embodiment, the monitoring module 87 is configured or programmed to perform the methods described herein. In an embodiment, the monitoring module 87 includes a computing device. In an embodiment, the monitoring module 87 includes a computer program to provide the functionality herein and is encoded on a computer readable medium that forms the monitoring module 87 or is disposed within the monitoring module 87.

[0080] In an embodiment, similar to using a probe to inspect a substrate Figure 6 Electron beam inspection tools, Figure 7 The electron current in a system such as Figure 6 The probe spot is significantly larger than the CD SEM depicted in , so that the probe spot is large enough to enable fast inspection speed. However, due to the large probe spot, the resolution may not be as high as compared to the CD SEM. In embodiments, the inspection device discussed above may be a single beam or multi-beam device, without limiting the scope of the present disclosure.

[0081] Can process from e.g. Figure 6 and / or Figure 7 The SEM images of the system are acquired to obtain contours describing the edges of objects representing device structures in the image. These contours are then typically quantified via an indicator such as CD at a user-defined cut line. Thus, the images of device structures are typically compared and quantified via an indicator such as edge-to-edge distance (CD) measured on the acquired contours or a simple pixel difference between the images.

[0082] Figure 81 is a block diagram illustrating a computer system 100 that can assist in implementing the methods and processes disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing information and instructions to be executed by the processor 104. The main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0083] The computer system 100 can be coupled to a display 112, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display, via the bus 102 for displaying information to a computer user. An input device 114 including alphanumeric keys and other keys is coupled to the bus 102 for transmitting information and command selections to the processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for transmitting direction information and command selections to the processor 104 and for controlling cursor movement on the display 112. Such an input device typically has two degrees of freedom on two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0084] According to one embodiment, portions of a process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In alternative embodiments, hardwired circuitry may be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuitry and software.

[0085] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to the processor 104 for execution. Such a medium can be in 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 fiber optics, including wires containing bus 102. Transmission media can also be in the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, floppy disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with hole patterns, RAMs, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cassettes, carrier waves as described below, or any other media that can be read by a computer.

[0086] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may be initially carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions via a telephone line using a modem. A modem local to the computer system 100 may receive the data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to the bus 102 may receive the data carried in the infrared signal and place the data on the bus 102. The bus 102 carries the data to the main memory 106, from which the processor 104 retrieves and executes the instructions. The instructions received by the main memory 106 may optionally be stored on the storage device 110 before or after being executed by the processor 104.

[0087] The computer system 100 also desirably includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupled to a network link 120, which is connected to a local area network 122. For example, the communication interface 118 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection with a corresponding type of telephone line. As another example, the communication interface 118 can be a local area network (LAN) card to provide a data communication connection with a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 118 sends and receives electrical signals, electromagnetic signals, or optical signals that carry digital data streams representing various types of information.

[0088] The network link 120 typically provides data communication to other data equipment via one or more networks. For example, the network link 120 may provide a connection from a local area network 122 to a host computer 124 or to a data device operated by an Internet Service Provider (ISP) 126. The ISP 126 in turn provides data communication services via a global packet data communication network, now commonly referred to as the "Internet" 128. Both the local area network 122 and the Internet 128 use electrical, electromagnetic or optical signals that carry digital data streams. The signals via the various networks and the signals on the network link 120 and via the communication interface 118, which carry the digital data to and from the computer system 100, are example forms of carrier waves that transport the information.

[0089] The computer system 100 can send messages and receive data including program code through the network, network link 120 and communication interface 118. In the Internet example, the server 130 can transmit the requested code for the application through the Internet 128, ISP 126, local area network 122 and communication interface 118. One such downloaded application can provide, for example, the irradiation optimization of the embodiment. The received code can be executed by the processor 104 when it is received, and / or stored in the storage device 110 or other non-volatile storage for later execution. In this way, the computer system 100 can obtain application code in the form of a carrier wave.

[0090] Fig. 9 An exemplary lithographic projection apparatus that can be used in conjunction with the techniques described herein is schematically depicted. The apparatus comprises:

[0091] - an illumination system IL, said illumination system being used to condition the radiation beam B. In such a particular case, the illumination system also comprises a radiation source SO;

[0092] a first stage (e.g. patterning device table) MT provided with a patterning device holder for holding a patterning device MA (e.g. a reticle) and connected to a first positioner for accurately positioning the patterning device relative to the object PS;

[0093] a second stage (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a silicon wafer coated with resist) and connected to a second positioner for accurately positioning the substrate relative to the article PS;

[0094] - A projection system ("lens") PS (eg a refractive, reflective or catadioptric optical system) for imaging the illuminated portion of the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

[0095] As depicted herein, the device is of the transmissive type (i.e., with a transmissive patterning device). However, in general, the device may also be of the reflective type, for example (with a reflective patterning device). The device may employ a patterning device of a different kind than a classical mask; examples include a programmable mirror array or an LCD matrix.

[0096] A source SO (e.g., a mercury lamp or an excimer laser, a laser produced plasma (LPP) EUV source) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, for example, directly or after having traversed a conditioning device such as a beam expander Ex. The illuminator IL may include an adjustment device AD ​​for setting the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the beam. In addition, the illuminator will typically 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 a desired uniformity and intensity distribution in its cross section.

[0097] about Fig. 9 It should be noted that the source SO can be inside the housing of the lithographic projection device (for example, this is usually the case when the source SO is a mercury lamp), but the source SO can also be remote from the lithographic projection device, and the radiation beam it generates is guided into the device (for example, with the aid of suitable directional reflectors); the latter is usually the case when the source SO is an excimer laser (for example, based on KrF, ArF or F2 lasers).

[0098] The beam PB then intercepts the patterning device MA held on the patterning device table MT. Having traversed the patterning device MA, the beam B passes through a lens PL which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning device (and the interferometry device IF), the substrate table WT can be accurately moved, for example in order to position a different target portion C in the path of the beam PB. Similarly, the first positioning device can be used to accurately position the patterning device MA relative to the path of the beam B, for example after mechanical retrieval of the patterning device MA from a patterning device library or during a scan. Typically, the patterning device MA will be accurately positioned with the aid of the second positioning device (and the interferometry device IF) not in the substrate table. Fig. 9 Movement of the stage MT, WT is achieved by a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) explicitly depicted in FIG. 2. However, in the case of a stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to the short-stroke actuator only, or may be fixed.

[0099] The depicted tools can be used in two different modes:

[0100] - in step mode, the patterning device table MT is kept substantially stationary and the entire patterning device image is projected onto a target portion C at once (i.e. a single "flash"). The substrate table WT is then shifted in the x and / or y direction so that a different target portion C can be irradiated by the beam PB;

[0101] - In scan mode, essentially the same situation applies, except that a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT may be moved at a speed v in a given direction (the so-called "scanning direction", e.g. the y-direction) so as to scan the projection beam B over the patterning device image; while the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, where M is the magnification of the lens PL (typically M=1 / 4 or 1 / 5). In this way, a relatively large target portion C may be exposed without having to compromise resolution.

[0102] Fig.10 Another exemplary lithographic projection apparatus 1000 is schematically depicted, comprising:

[0103] - A source collector module SO for providing radiation.

[0104] - an illumination system (illuminator) IL configured to condition the radiation beam B (eg EUV radiation) coming from the source collector module SO.

[0105] a support structure (e.g., mask table) MT configured to support a patterning device (e.g., mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0106] a substrate table (eg wafer stage) WT configured to hold a substrate (eg resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

[0107] - a projection system (eg, a reflective projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0108] As depicted here, the apparatus 1000 is of the reflective type (e.g., employing a reflective mask). It should be noted that since most materials are absorptive in the EUV wavelength range, the patterning device can have a multilayer reflector comprising, for example, multiple stacked layers of molybdenum and silicon. In one example, the multiple stacked layer reflector has 40 layers of molybdenum and silicon pairs, where each layer is a quarter wavelength thick. Even smaller wavelengths can be produced using X-ray lithography. Since most materials are absorptive at EUV and x-ray wavelengths, a thin sheet of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of a multilayer reflector) defines where features will be printed (positive resist) or not (negative resist).

[0109] refer to Fig.10 , the illuminator IL receives a beam of extreme ultraviolet radiation from a source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, utilizing one or more emission lines in the EUV range to convert a material into a plasma state having at least one element (e.g., xenon, lithium, or tin). In one such method, often referred to as laser produced plasma ("LPP"), a plasma may be generated by irradiating a fuel (e.g., a droplet, stream, or cluster of a material having a line emitting element) with a laser beam. The source collector module SO may be a laser ( Fig.10 The laser is used to provide a laser beam for exciting the fuel. The resulting plasma emits output radiation (e.g., EUV radiation) which is collected using a radiation collector disposed in a source collector module. For example, when a CO2 laser is used to provide a laser beam for fuel excitation, the laser and source collector module may be separate entities.

[0110] In such cases, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system comprising, for example, suitable directional mirrors and / or a beam expander. In other cases, for example, when the radiation source is a discharge produced plasma EUV generator (commonly referred to as a DPP radiation source), the radiation source may be an integral part of the source collector module.

[0111] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as σ-outer and σ-inner, respectively) may be adjusted. Furthermore, the illuminator IL may include various other components, such as a faceted field mirror arrangement and a faceted pupil mirror arrangement. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0112] The radiation beam B is incident on a patterning device (e.g. a mask) MA held on a support structure (e.g. a mask table) MT and is patterned by the patterning device. After reflection from the patterning device (e.g. a mask) MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g. an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example so that a different target portion C is positioned in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor PS1 can be used to accurately position the patterning device (e.g. a mask) MA relative to the path of the radiation beam B. The patterning device (e.g. a mask) MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0113] The depicted device 1000 may be used in at least one of the following modes:

[0114] 1. In step mode, the support structure (e.g. mask table) MT and the substrate table WT are kept substantially stationary while the entire pattern imparted to the radiation beam is projected at once onto a target portion C (i.e. a single static exposure). Next, the substrate table WT is shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0115] 2. In scan mode, the support structure (e.g. mask table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure (e.g. mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0116] 3. In another mode, the support structure (e.g., mask table) MT is kept substantially stationary so as to hold the programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation may be readily applicable to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type mentioned above.

[0117] Fig.11The apparatus 1000 is shown in more detail, and the apparatus includes a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and arranged so that a vacuum environment can be maintained in a closed structure 220 of the source collector module SO. A plasma 210 for emitting EUV radiation can be formed by a discharge to generate a plasma radiation source. EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), wherein a very hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, a very hot plasma 210 is generated by a discharge that generates an at least partially ionized plasma. In order to efficiently generate radiation, a partial pressure of, for example, 10Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required. In an embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0118] The radiation emitted by the hot plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via an optionally present gas barrier or contaminant trap 230 (also referred to as a contaminant barrier or foil trap in some cases) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant barrier 230 further indicated herein includes at least a channel structure.

[0119] The collector chamber 211 may include a radiation collector CO which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from the grating spectral filter 240 to be focused into a virtual source point IF along the optical axis indicated by the dash-dot line "O". The virtual source point IF is often referred to as an intermediate focus, and the source collector module is arranged so that the intermediate focus IF is located at or near an opening 221 in the enclosure 220. The virtual source point IF is an image of the plasma 210 for emitting radiation.

[0120] The radiation then traverses an illumination system IL which may include a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24 which are arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of radiation intensity at the patterning device MA. After reflection of the radiation beam 21 at the patterning device MA held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by a substrate table WT.

[0121] There may typically be more elements than shown in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, a grating spectral filter 240 may optionally be present. In addition, there may be more mirrors than shown in the figures, for example more than 100 mirrors may be present in the projection system PS. Fig.11 1 to 6 additional reflective elements beyond those shown.

[0122] like Fig.11 The collector optics CO illustrated in FIG. 1 is depicted as a nested collector with grazing incidence reflectors 253, 254 and 255, merely as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254 and 255 are arranged axisymmetrically around the optical axis O, and this type of collector optics CO is desirably used in combination with a discharge produced plasma radiation source.

[0123] Alternatively, the source collector module SO may be as follows Fig.12 . The laser LAS is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li), thereby producing a highly ionized plasma 210 with an electron temperature of several tens of eV. The energetic radiation produced during the deexcitation and recombination of these ions is emitted from the plasma, collected by the near normal incidence collector optics CO, and focused onto an opening 221 in a closed structure 220.

[0124] The concepts disclosed herein can simulate or mathematically model any conventional imaging system for imaging sub-wavelength features, and may be particularly useful for emerging imaging technologies that can produce wavelengths of increasingly smaller sizes. Emerging technologies already in use include extreme ultraviolet (EUV) lithography that can produce 193nm wavelengths using ArF lasers and even 157nm wavelengths using fluorine lasers. In addition, EUV lithography can produce wavelengths in the range of 20nm to 5nm by using a synchrotron or by using high energy electrons to bombard materials (solid or plasma) in order to produce photons in this range.

[0125] Although the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts may be used with any type of lithography imaging system, for example, a lithography imaging system for imaging on substrates other than silicon wafers.

[0126] Although the use of embodiments in the manufacture of ICs may be specifically referred to herein, it should be understood that the embodiments herein may have many other possible applications. For example, it may be used in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film heads, micromechanical systems (MEMs), etc. Those skilled in the art will appreciate that in the context of such alternative applications, any use of the terms "reticle", "wafer" or "die" herein may be considered synonymous with or interchangeable with the more general terms "patterning device", "substrate" or "target portion", respectively. The substrates mentioned herein may be processed in, for example, a track or coating development system (a tool that typically applies a resist layer to a substrate and develops the exposed resist) or a measurement or inspection tool before or after exposure. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, the substrate may be processed more than once, for example, to produce, for example, a multilayer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0127] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of about 365 nm, about 248 nm, about 193 nm, about 157 nm, or about 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm to 20 nm), as well as particle beams, such as ion beams or electron beams.

[0128] As used herein, the term "optimizing" and "optimization" refers to or means adjusting a pattern forming device (e.g., a lithographic device), a patterning process, etc., so that the result and / or process has more desired characteristics, such as higher accuracy of projection of a design pattern on a substrate, a larger process window, etc. Therefore, as used herein, the term "optimizing" and "optimization" refers to or means a process of identifying one or more values ​​of one or more parameters that provide an improvement in at least one related indicator, such as a local optimum, compared to an initial set of one or more values ​​for those one or more parameters. "Optimal" and other related terms should be interpreted accordingly. In an embodiment, the optimization step can be applied iteratively to provide further improvement of one or more indicators.

[0129] 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, which may be carried on a suitable carrier medium that may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Suitable devices may be used to implement embodiments of the present invention, which may specifically be in the form of a programmable computer that runs a computer program arranged to implement the method described herein. Therefore, embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form that is read by a machine (e.g., a computing device). For example, a machine-readable medium may include: a read-only memory (ROM); a random access memory (RAM); a disk storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic, or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), etc. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are merely for convenience and that such actions are actually caused by a computing device, processor, controller, or other device executing firmware, software, routines, instructions, etc.

[0130] In the block diagram, the illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems that organize the functionality described herein as illustrated. The functionality provided by each of these components can be provided by software or hardware modules that are organized in a manner different from that currently depicted, such as being doped, combined, replicated, decomposed, distributed (e.g., in a data center or geographically), or organizing such software or hardware in another different manner. The functionality described herein can be provided by one or more processors of one or more computers executing program codes stored on a tangible, non-temporary machine-readable medium. In some cases, a third-party content distribution network may host some or all of the information communicated via the network, in which case, to the extent that information (e.g., content) is allegedly supplied or otherwise provided, the information can be provided by sending instructions to obtain information from the content distribution network.

[0131] Unless otherwise specifically stated, as is clear from the discussion, it should be understood that throughout this specification, discussions utilizing terms such as "processing," "computing," "calculating," "determining," etc., refer to the actions or processes of a specific apparatus such as a special purpose computer or similar special purpose electronic processing / computing device.

[0132] The embodiments of the present disclosure can be further described by the following aspects.

[0133] 1. A method of training a machine learning model, the machine learning model being configured to predict a value of a physical property associated with a substrate for use in adjusting a patterning process, the method comprising:

[0134] obtaining a reference image associated with a desired pattern to be printed on the substrate;

[0135] determining a first set of model parameter values ​​for the machine learning model such that a first cost function is reduced from an initial value of the cost function obtained using an initial set of model parameter values, wherein the first cost function is a difference between the reference image and an image generated via the machine learning model; and

[0136] training the machine learning model using the first set of model parameter values ​​so as to iteratively reduce a combination of the first cost function and the second cost function,

[0137] Wherein the second cost function is the difference between a measured value and a predicted value of a physical property associated with the desired pattern, the predicted value being predicted via the machine learning model.

[0138] 2. The method according to claim 1, wherein obtaining the reference image comprises:

[0139] A process model configured to generate the reference image as an output is executed, wherein the process model models a portion of the patterning process.

[0140] 3. The method of clause 2, wherein the process model is a calibrated model of an optical device model, a resist model and / or an etch model of the patterning process.

[0141] 4. A method according to any one of aspects 1 to 3, wherein the reference image is an aerial image, a resist image and / or an etching image of the desired pattern.

[0142] 5. The method according to any one of aspects 1 to 4, wherein determining the first set of model parameter values ​​of the machine learning model is an iterative process, the iteration comprising:

[0143] generating the image by executing the machine learning model using the desired pattern;

[0144] determining a difference between the generated image and the reference image; and

[0145] Adjust the model parameter values ​​of the machine learning model so that the difference is reduced.

[0146] 6. A method according to any one of aspects 1 to 5, wherein the difference between the generated image and the reference image is minimized.

[0147] 7. The method according to any one of aspects 1 to 6, wherein training the machine learning model is an iterative process, the iteration comprising:

[0148] Initializing the model parameters of the machine learning model using the first set of model parameter values;

[0149] predicting a value of a physical property associated with the substrate by executing the machine learning model using the desired pattern;

[0150] obtaining, via a metrology tool, measurements of physical properties of a desired printed pattern on the substrate; and

[0151] Adjust model parameter values ​​of the machine learning model so that a combination of the first cost function and the second cost function is reduced.

[0152] 8. The method of clause 7, wherein adjusting the model parameter value is based on gradient descent of a combination of the first cost function and the second cost function.

[0153] 9. A method according to any one of aspects 1 to 8, wherein the sum of the first cost function and the second cost function is minimized.

[0154] 10. A method according to any one of aspects 1 to 9, wherein the model parameters are weights and / or biases associated with one or more layers of the machine learning model.

[0155] 11. A method according to any one of aspects 1 to 10, wherein the machine learning model is a convolutional neural network.

[0156] 12. The method of any one of clauses 1 to 11, wherein the parameter associated with the substrate is a critical dimension or edge positioning error associated with the desired pattern.

[0157] 13. A method according to any one of aspects 10 to 12, wherein the weights of the convolutional neural network are adjusted to reduce the edge positioning error or model error associated with the model of the patterning process being trained.

[0158] 14. The method of any one of clauses 1 to 13, wherein the measured value is a CD value obtained via the metrology tool configured to measure a desired printed pattern of the substrate.

[0159] 15. The method according to any one of aspects 7 to 14, wherein the metrology tool is a scanning electron microscope (SEM) and the measurements are obtained from SEM images.

[0160] 16. A method according to any one of aspects 1 to 15, wherein the measured values ​​are intensity values ​​of an aerial image associated with the desired pattern.

[0161] 17. The method according to any one of aspects 1 to 11, further comprising:

[0162] training the machine learning model using the first set of model parameter values ​​such that a combination of the first cost function, the second cost function, and a third cost function is reduced,

[0163] The third cost function is a grid-dependent function.

[0164] 18. The method according to any one of aspects 1 to 17, further comprising:

[0165] Predicting a substrate image for design layout via a trained machine learning model;

[0166] A mask layout to be used to fabricate a mask for a patterning process is determined through an OPC simulation using the design layout and the predicted substrate image.

[0167] 19. The method of clause 17, wherein the OPC simulation comprises:

[0168] determining a simulated pattern to be printed on a substrate by simulating a patterning process model using the geometry of the design layout and corrections associated with the plurality of sections; and

[0169] An optical proximity effect correction for the design layout is determined such that a difference between the simulated pattern and the design layout is reduced.

[0170] 20. The method of clause 19, wherein the determining of the optical proximity effect correction is an iterative process, the iteration comprising:

[0171] The shape and / or size of the geometry of the main features and / or one or more auxiliary features of the design layout are adjusted so that the performance index of the patterning process is reduced.

[0172] 21. A method according to aspect 20, wherein the one or more auxiliary features are obtained from the predicted post-OPC image of the machine learning model.

[0173] 22. A method according to any one of aspects 1 to 21, wherein the combination of the first cost function (CF1) and the second cost function (CF2) is calculated using the expression c1*CF1+c2*CF2, wherein c1 and c2 are coefficients that can be adjusted to minimize the combination.

[0174] 23. A computer program product, comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the method of any one of the above aspects when executed by a computer.

[0175] It should be understood that the description and drawings are not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

[0176] In view of this specification, those skilled in the art will understand the modifications and alternative embodiments of various aspects of the present invention. Therefore, this specification and the accompanying drawings should be understood to be illustrative only and for the purpose of teaching those skilled in the art to perform the common mode of the present invention. It should be understood that the form of the present invention shown and described herein should be regarded as an example of an embodiment. Each element and material can replace those elements and materials illustrated and described herein, each part and process can be reversed or omitted, certain features can be utilized independently, and the features of the embodiments or embodiments can be combined, and those skilled in the art will understand all of these after obtaining the benefits of this specification. Changes can be made to the elements described herein without departing from the spirit and scope of the present invention as described in the appended claims. The titles used herein are only for organizational purposes and are not intended to limit the scope of this specification.

[0177] As used throughout this application, the word "may" is used in a permissive sense (i.e., meaning the possibility) rather than in a mandatory sense (i.e., meaning must). The words "include, including, and includes," and the like mean including, but not limited to. As used throughout this application, the singular forms "a," "an," and "the" include plural referents unless the context clearly indicates otherwise. Thus, for example, reference to "an" element or "a" element includes combinations of two or more elements, although other terms and phrases, such as "one or more," may also be used with respect to one or more elements. Unless otherwise indicated, the term "or" is non-exclusive, i.e., covers both "and" and "or." Terms describing conditional relationships, such as "in response to X, Y", "under X, then Y", "if X, then Y", "when X, Y", etc., encompass causal relationships where the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributing causal condition to the effect, e.g., "under condition Y, then state X occurs" is hypernymous to "only under Y, then X occurs" and "under Y and Z, then X occurs". Such conditional relationships are not limited to effects that are obtained immediately following the antecedent, since some effects may be delayed, and in the conditional statement, the antecedent is connected to its effect, e.g., the antecedent is related to the likelihood of the effect occurring. Unless otherwise indicated, a statement that multiple attributes or functions are mapped to multiple objects (e.g., one or more processors that perform steps A, B, C, and D) encompasses both all such attributes or functions mapped to all such objects and subsets of attributes or functions mapped to subsets of attributes or functions (e.g., all processors each perform steps A to D, and both the case where processor 1 performs step A, processor 2 performs step B and part of step C, and processor 3 performs part of step C and step D). In addition, unless otherwise indicated, a statement that a value or action is "based on" another condition or value encompasses both the case where the condition or value is the only factor and the case where the condition or value is one factor among multiple factors. Unless otherwise indicated, a statement that "each" instance of a certain aggregate has some property should not be read to exclude the case where some otherwise identical or similar members of the larger aggregate do not have the property (i.e., each does not necessarily mean each and all). References to selections from a range include the endpoints of the range.

[0178] In the above description, any process, description or block in the flowchart should be understood to represent a module, segment or portion of a program code, which includes one or more executable instructions for implementing specific logical functions or steps in the process, and alternative implementations are included in the scope of the exemplary embodiments of the present invention, in which functions may be executed out of the order shown or discussed, including approximately simultaneously or in reverse order, depending on the functionality involved, as will be understood by those skilled in the art.

[0179] To the extent that certain U.S. patents, U.S. patent applications, or other materials (e.g., papers) have been incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is incorporated by reference only to the extent that there is no conflict between such materials and the statements and drawings set forth herein. In the event of such a conflict, any such conflicting text in such U.S. patents, U.S. patent applications, and other materials incorporated by reference is expressly not incorporated by reference herein.

[0180] Although certain embodiments have been described, these embodiments are presented only as examples and are not intended to limit the scope of the present disclosure. Indeed, the novel methods, devices, and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions, and changes in the form of the methods, devices, and systems described herein may be made without departing from the spirit of the present disclosure. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the present disclosure.

Claims

1. A method of training a machine learning model, the machine learning model being configured to predict a value of a physical property associated with a substrate for use in adjusting a patterning process, the method comprising: obtaining a reference image associated with a desired pattern to be printed on the substrate; determining a first set of model parameter values ​​for the machine learning model such that a first cost function decreases from a first value of the first cost function obtained by using the first set of model parameter values, wherein the first cost function represents a difference between the reference image and an image generated via the machine learning model; as well as training the machine learning model based on a combination of the first cost function and a second cost function using the first set of model parameter values, The second cost function represents a difference between a measured value and a predicted value of a physical property associated with the desired pattern, wherein the predicted value is predicted via the machine learning model.

2. The method according to claim 1, wherein obtaining the reference image comprises: A process model is executed to model a portion of the patterning process and is configured to generate the reference image as an output, wherein the process model models a portion of the patterning process. 3 . The method of claim 2 , wherein the process model is a calibrated model of an optical device model, a resist model and / or an etch model of the patterning process. 4 . The method according to claim 1 , wherein the reference image is an aerial image, a resist image and / or an etching image of the desired pattern.

5. The method of claim 1 , wherein determining the first set of model parameter values ​​for the machine learning model is an iterative process, the iteration comprising: generating the image by executing the machine learning model using the desired pattern; determining said difference between the generated image and said reference image; as well as Adjust the model parameter values ​​of the machine learning model so that the difference is reduced.

6. The method of claim 1, wherein training the machine learning model is an iterative process, the iterations comprising: Initializing the model parameters of the machine learning model using the first set of model parameter values; predicting a value of a physical property associated with the substrate by executing the machine learning model using the desired pattern; obtaining measurements of physical properties of a desired printed pattern on the substrate; and Adjust model parameter values ​​of the machine learning model so that a combination of the first cost function and the second cost function is reduced. The method of claim 6 , wherein the adjusting the model parameter value is based on a gradient descent of a combination of the first cost function and the second cost function.

8. The method of claim 1, wherein the machine learning model is a convolutional neural network, and wherein the model parameters are weights and / or biases associated with one or more layers of the convolutional neural network.

9. The method of claim 1, wherein the parameter associated with the substrate is a critical dimension or an edge positioning error associated with the desired pattern, and wherein the measured value is a CD value obtained via a metrology tool.

10. The method of claim 1, wherein the measured values ​​are intensity values ​​of an aerial image associated with the desired pattern.

11. The method according to claim 1, further comprising: The machine learning model is trained using the first set of model parameter values ​​such that a combination of the first cost function, the second cost function, and a third cost function is reduced, The third cost function is a grid-dependent function.

12. The method according to claim 1, further comprising: Predicting a substrate image for design layout via a trained machine learning model; and A mask layout to be used to fabricate a mask for a patterning process is determined through an OPC simulation using the design layout and the predicted substrate image.

13. The method of claim 12, wherein the OPC simulation comprises: determining a simulated pattern to be printed on a substrate; and An optical proximity effect correction for the design layout is determined such that a difference between the simulated pattern and the design layout is reduced.

14. The method of claim 12, wherein the determining comprises obtaining one or more auxiliary features from the predicted post-OPC image of the machine learning model.

15. The method according to claim 1, wherein the combination of the first cost function (CF1) and the second cost function (CF2) is calculated using the expression c1*CF1+c2*CF2, where c1 and c2 are coefficients.

16. The method of claim 8, wherein the weights of the convolutional neural network are adjusted to reduce edge location errors or model errors associated with a model of the patterning process being trained.

17. A computer program product comprising a non-transitory computer-readable medium having recorded thereon instructions, the instructions implementing the method according to any one of claims 1 to 16 when executed by a computer.

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