Prediction method, information processing apparatus, film forming apparatus, article manufacturing method and non-transitory storage medium

Abstract

A prediction method for predicting the behavior of droplets of a curable composition in a process of forming a film of the curable composition from a plurality of droplets of the curable composition disposed on a first member, the method comprising predicting the behavior of the droplets using a learning model, wherein the input to the learning model includes first information indicating the position of the droplets of the curable composition to be disposed on the first member.

Description

Technical Field

[0001] This invention relates to prediction methods, information processing equipment, membrane forming equipment, article manufacturing methods, and non-transitory storage media. Prior Technology

[0002] A film formation technology exists for forming a film made of a curable component on a substrate. This involves placing the curable component on the substrate, bringing the curable component into contact with a mold, and curing the curable component. This film formation technology is applied to imprinting and planarization techniques. In imprinting, a patterned mold is used, and the pattern of the mold is transferred to the curable component on the substrate by bringing the curable component on the substrate into contact with the pattern of the mold and curing the curable component. In planarization, a film with a flat upper surface is formed by using a mold with a flat surface, and the curable component on the substrate is brought into contact with the flat surface and cured.

[0003] A curable component is disposed on a substrate in the form of droplets, and then a mold is pressed onto the droplets. This causes the droplets of curable component to diffuse across the substrate, thereby forming a film of the curable component. At this point, it is important to form a film of the curable component with a uniform thickness and without leaving air bubbles within the film. To achieve this, the arrangement pattern of the droplets of the curable component, the method and conditions for pressing the mold onto the curable component, etc., must be adjusted. Implementing this adjustment operation through trial and error using the equipment requires a significant amount of time and cost. To address this problem, a simulator supporting such adjustment operations needs to be developed.

[0004] Japanese Patent No. 5599356 discloses a simulation method for predicting the wetting, diffusion, and aggregation of a plurality of droplets disposed on a patterning surface, and a method for generating droplet configuration patterns using this prediction. Japanese Patent No. 5599356 also discloses a simulator for predicting the behavior of droplets in a curable composition through physical calculations.

[0005] In traditional techniques, physical calculations are used to predict the behavior of droplets in a curable component. However, adjusting the droplet configuration pattern of the curable component, as well as the methods and conditions for pressing the mold onto the curable component, requires repeated simulations. In particular, when adjusting the droplet configuration pattern of the curable component, the simulations, including physical calculations, require a significant amount of computation time due to the vast number of possible droplet configuration patterns. Summary of the Invention

[0006] []

[0007] This invention provides a technique that facilitates the prediction of the behavior of droplets of a curable composition during the process of forming a film of the curable composition.

[0008] According to one aspect of the present invention, a prediction method is provided for predicting the behavior of droplets of a curable composition in a process in which a film of a curable composition is formed from a plurality of droplets of the curable composition disposed on a first member. The method includes using a learning model to predict the behavior of the droplets, wherein the input to the learning model includes first information indicating the position of the droplets of the curable composition to be disposed on the first member.

[0009] Other aspects of the invention will become apparent from the following description of exemplary embodiments with reference to the accompanying drawings. Simple Explanation of the Diagram

[0010] []

[0011] [Figure 1A] and [Figure 1B] are views illustrating a membrane forming apparatus according to an embodiment of the present invention.

[0012] Figures 2A to 2F show views of droplets of the curable component spreading on a substrate.

[0013] [Figure 3] is a view showing the configuration of a prediction system according to an embodiment of the present invention.

[0014] [Figure 4] is a block diagram showing the hardware configuration of the prediction server.

[0015] [Figure 5] is a view explaining graphical convolutional networks.

[0016] [Figure 6] is a view that explains in detail the weights between layers in a graphical neural network.

[0017] [Figure 7] is a flowchart used to explain the procedure for generating learning models using graph neural networks.

[0018] [Figure 8] shows a view of the program that generates the graphics.

[0019] [Figure 9] shows a view of the procedure for assigning feature quantities to a graph.

[0020] [Figure 10A] and [Figure 10B] are views illustrating the procedure for generating learning data from measurement data.

[0021] [Figure 11] is a view showing an example of a graphical neural network set up as a learning model.

[0022] [Figure 12] is a flowchart for explaining the procedure used to predict the behavior of droplets in a curable component.

[0023] [Figure 13A] and [Figure 13B] are views illustrating examples of prediction results from input parameters.

[0024] [Figure 14] is a view showing an example of a neural network.

[0025] [Figure 15A] and [Figure 15B] are views illustrating the input data used for prediction using neural networks.

[0026] [Figure 16A] and [Figure 16B] are views illustrating learning materials used for learning with neural networks.

[0027] Figures 17A to 17F are views used to describe the method of manufacturing the article. Implementation

[0028] []

[0029] In the following, embodiments will be described in detail with reference to the accompanying drawings. Note that the following embodiments are not intended to limit the scope of the claimed invention. Multiple features are described in the embodiments, but the invention is not limited to requiring all such features, and multiple such features may be suitably combined. Furthermore, in the accompanying drawings, the same reference numerals denote the same or similar constructions, and repeated descriptions thereof are omitted.

[0030] Figures 1A and 1B are views illustrating an embodiment of the film forming apparatus IMP of the present invention. The film forming apparatus IMP performs a process of forming a film of a curable composition IM from a plurality of droplets disposed on a substrate S. For example, it is a process of forming a film of the curable composition IM in the space between the substrate S and the mold M by contacting a plurality of droplets of the curable composition IM with each other. The film forming apparatus IMP can be configured as, for example, an imprinting apparatus or a planarization apparatus.

[0031] Here, the substrate S and the mold M are interchangeable, and a film of the curable composition IM can be formed in the space between the mold M and the substrate S by contacting a plurality of droplets of curable composition IM disposed on the mold M with the substrate S. Therefore, the film forming apparatus IMP is generally an apparatus that performs a procedure of contacting a plurality of droplets of curable composition IM disposed on a first component with a second component, thereby forming a film of curable composition IM in the space between the first component and the second component. This embodiment provides a description assuming the first component is the substrate S and the second component is the mold M. However, it is possible to assume the first component is the mold M and the second component is the substrate S. In this case, the substrate S and the mold M described below are interchangeable.

[0032] An imprinting apparatus uses a patterned mold M to transfer the pattern of the mold M onto a curable composition IM on a substrate S. The imprinting apparatus uses a mold M having a patterned area MP on which the pattern is formed. As an imprinting process, the imprinting apparatus contacts the curable composition IM on the substrate S with the patterned area MP of the mold M, fills the space between the mold M and the area on the substrate S where the pattern will be formed with the curable composition IM, and then cures the curable composition IM. In this way, the pattern in the patterned area IM of the mold M is transferred to the curable composition IM on the substrate S. For example, the imprinting apparatus forms a pattern made of the cured product of the curable composition IM in each of a plurality of injection areas on the substrate S.

[0033] As a planarization process, the planarization equipment uses a mold M with a flat surface to contact the curable component IM on the substrate S with the flat surface of the mold M, and cures the curable component IM to form a film with a flat upper surface. If a mold M with a size covering the entire area of ​​the substrate S is used, the planarization equipment forms a film made of the cured product of the curable component IM over the entire area of ​​the substrate S. Note that the planarization equipment can perform a process in which a film of the curable component IM is formed on the substrate S by a plurality of droplets disposed on the substrate S without contacting the mold M with the plurality of droplets.

[0034] As a curable composition, a material that will be cured by receiving curing energy is used. Examples of curing energy used are electromagnetic waves, heat, etc. As electromagnetic waves, for example, infrared light, visible light, ultraviolet light, etc., selected from the wavelength range of 10 nm (inclusive) to 1 mm (inclusive) are used. Therefore, the curable composition is a composition that is cured by light irradiation or heating. Depending on the need, a light-curable composition that is cured by light irradiation contains at least a polymerizable compound and a photopolymerization initiator, and may contain a non-polymerizable compound or solvent. The non-polymerizable compound is a material selected from the group containing at least one sensitizer, hydrogen donor, internal release agent, surfactant, antioxidant, polymer component, etc. The viscosity of the curable composition (viscosity at 25°C) is, for example, from 1 mPa·s (inclusive) to 100 mPa·s (inclusive).

[0035] Materials used as substrates include glass, ceramics, metals, semiconductors, and resins. Depending on the requirements, components made of a material different from the substrate material can be formed on the surface of the substrate. More specifically, examples of substrates include silicon wafers, semiconductor compound wafers, and silicon glass.

[0036] In the specification and accompanying drawings, directions are indicated on the XYZ coordinate system, where the direction parallel to the surface of substrate S is defined as the XY plane. The directions parallel to the X, Y, and Z axes of the XYZ coordinate system are the X direction, Y direction, and Z direction, respectively. Rotation about the X-axis, rotation about the Y-axis, and rotation about the Z-axis are θX, θY, and θZ, respectively. Control or drive systems for the X, Y, and Z axes refer to control or drive in directions parallel to the X-axis, parallel to the Y-axis, and parallel to the Z-axis, respectively. Furthermore, control or drive systems for the θX-axis, θY-axis, and θZ-axis refer to control or drive in rotation about axes parallel to the X-axis, rotation about axes parallel to the Y-axis, and rotation about axes parallel to the Z-axis, respectively. Position is information explicitly indicated based on coordinates on the X, Y, and Z axes, while direction is information explicitly indicated by values ​​on the θX-axis, θY-axis, and θZ-axis. Positioning refers to controlling position and / or direction. Alignment includes control over the position and / or orientation of at least one of the substrate S and the mold M.

[0037] The film forming apparatus (IMP) includes a substrate holding unit 102 for holding a substrate S, a substrate driving mechanism 105 for driving the substrate S by driving the substrate holding unit 102, a base 104 for supporting the substrate driving mechanism 105, and a position measuring unit 103 for measuring the position of the substrate holding unit 102. The substrate driving mechanism 105 includes, for example, a motor such as a linear motor.

[0038] The film forming apparatus IMP includes a sensor 151 that measures the substrate driving force (alignment load) required by the substrate driving mechanism 105 to drive the substrate S (substrate holding unit 102) during alignment. The substrate driving force during alignment, performed when the curable composition IM on the substrate S is in contact with the patterned area MP of the mold M, corresponds to, for example, a shear force acting between the substrate S and the mold M. The shear force is primarily a force acting in the planar direction of the substrate S and the mold M. The substrate driving force during alignment is, for example, related to the magnitude of the current supplied to the substrate driving mechanism 105 (its motor) during alignment. Therefore, the sensor 151 can obtain the substrate driving force by detecting the magnitude of the current supplied to the substrate driving mechanism 105. In this way, the sensor 151 serves as a sensor for measuring the influence (shear force) experienced by the mold M during patterning. Note that the drive request (command value) output from the control unit 110 (described later) to the substrate driving mechanism 105 is called the stage control value.

[0039] The membrane forming apparatus (IMP) includes a mold holding unit 121 for holding a mold M, a mold driving mechanism 122 for driving the mold M by driving the mold holding unit 121, and a support structure 130 for supporting the mold driving mechanism 122. The mold driving mechanism 122 includes, for example, a motor such as a voice coil motor.

[0040] The film forming apparatus IMP includes a sensor 152 for measuring demolding force (separation load) and / or pressure (imprinting force). Demolding force is the force required to separate (separate) the cured product of the imprinting material IM on the substrate S from the mold M. Pressure is the force that presses the mold M to bring it into contact with the curable composition IM on the substrate S. Both demolding force and pressure are forces acting in directions perpendicular to the plane of the substrate S and the mold M. Each of the demolding force and pressure is, for example, related to the magnitude of the current supplied to the mold drive mechanism 122 (its motor). Therefore, sensor 152 can obtain the demolding force and / or pressure by detecting the magnitude of the current supplied to the mold drive mechanism 122. In this way, sensor 152 serves as a sensor for measuring the effects (demolding force and / or pressure) experienced by the mold M during pattern formation. Note that the drive request (command value) output from control unit 110 (described later) to mold drive mechanism 122 is called a stage control value.

[0041] The substrate driving mechanism 105 and the mold driving mechanism 122 form a relative driving mechanism for driving at least one of the substrate S and the mold M to adjust the relative position between the substrate S and the mold M. The adjustment of the relative position between the substrate S and the mold M through the relative driving mechanism includes driving to contact the curable component IM on the substrate S with the mold M and driving to separate the mold M from the cured curable component IM (pattern of the cured product) on the substrate S. Additionally, the adjustment of the relative position between the substrate S and the mold M through the relative driving mechanism includes alignment between the substrate S and the mold M. The substrate driving mechanism 105 is configured to drive the substrate S relative to a plurality of axes (e.g., three axes including the X-axis, Y-axis, and θZ-axis, and preferably six axes including the X-axis, Y-axis, Z-axis, θX-axis, θY-axis, and θZ-axis). The mold drive mechanism 122 is configured to drive the mold M relative to a plurality of axes (e.g., three axes including the Z-axis, θX-axis and θY-axis, and preferably six axes including the X-axis, Y-axis, Z-axis, θX-axis, θY-axis and θZ-axis).

[0042] The membrane forming apparatus IMP includes a mold transport mechanism 140 for transporting a mold M and a mold cleaner 150. The mold transport mechanism 140 is configured, for example, to transport the mold M to a mold holding unit 121 and from the mold holding unit 121 to a storage container (not shown) or the mold cleaner 150. The mold cleaner 150 cleans the mold M using ultraviolet light, chemical solutions, etc.

[0043] The film forming apparatus IMP includes a window member 125 for forming a pressure control space CS on the side of the rear surface of the mold M (the surface opposite the patterned region MP of the mold M). The window member 125 is formed of a material that transmits curing energy from the curing unit 107 and allows curing energy to be applied to the curable composition IM on the substrate S. The film forming apparatus IMP includes a deformation mechanism 123 that deforms the patterned region MP of the mold M into a convex shape toward the substrate S by controlling the pressure in the pressure control space CS (hereinafter referred to as "cavity pressure"), as schematically shown in FIG1B.

[0044] The film forming apparatus (IMP) includes an alignment measurement system 106 that illuminates alignment marks respectively disposed on a substrate S (its shot region) and a mold M, and captures images of the alignment marks to measure the relative positions between the marks. The IMP may include a plurality of alignment measurement systems 106 to simultaneously observe multiple alignment marks disposed on the substrate S and the mold M. For example, the IMP may include four alignment measurement systems 106 that observe alignment marks disposed at the four corners of the shot region of the substrate S and at the four corners of the mold M. The alignment measurement system 106 can be positioned according to the position of the alignment marks by means of a drive mechanism (not shown). Note that the images captured by the alignment measurement system 106 are also called alignment images. Alignment images include, for example, images obtained by capturing reflected light from the alignment marks on the substrate S and the mold M, images obtained by capturing images formed by the moire of the alignment marks on the substrate S and the mold M, etc.

[0045] The film forming apparatus IMP includes a curing unit 107 for curing a curable component IM on a substrate S. The curing unit 107 cures the curable component IM by irradiating it with energy for curing the curable component IM, for example, by irradiating the curable component IM with ultraviolet light through an optical component 111.

[0046] The film forming apparatus IMP includes an image capturing unit 112, which captures images of the mold M, the substrate S, and the curable component IM on the substrate S through optical components 111 and window components 125. Note that the images captured by the image capturing unit 112 can also be referred to as spread images.

[0047] The film forming apparatus IMP includes a dispenser 108 for distributing, supplying, or distributing a curable component IM onto a substrate S. The dispenser 108 discharges the curable component IM to dispose droplets of the curable component IM onto the substrate S according to, for example, a configuration pattern indicating the positions on the substrate S where droplets of the curable component IM will be disposed.

[0048] The membrane forming apparatus IMP includes a control unit 110, which operates the membrane forming apparatus IMP by comprehensively controlling the various units of the membrane forming apparatus IMP. The control unit 110 is formed by, for example, a PLD (Programmable Logic Device) such as FPGA (Field Programmable Gate Array), ASIC (Application Specific Integrated Circuit), a general-purpose computer with a program installed, or all or some of these components.

[0049] Figures 2A to 2F show views of the diffusion of droplets of curable composition IM on the curable composition IM during the process of pressing the mold M onto the substrate S. Figure 2A shows the state immediately after the droplets of curable composition IM are disposed on the substrate S from the dispenser 108. Referring to Figure 2A, in the state immediately after the droplets of curable composition IM are disposed, the individual droplets are small and separated from each other. By pressing the mold M, the droplets of curable composition IM disposed on the substrate S gradually diffuse from the state shown in Figure 2A to the states shown in Figures 2B to 2E, and adjacent droplets come into contact with each other. Finally, the droplets of curable composition IM disposed on the substrate S diffuse across the entire area (pattern area MP) of the mold M.

[0050] In the process of diffusion of the curable composition IM on the substrate S, as shown in Figure 2E, bubbles 201 are formed (trapped) between adjacent droplets of the curable composition IM. If the curable composition IM cures in the presence of bubbles 201, the portion where bubbles 201 are present becomes a defect. Therefore, in order to improve the production performance of the film forming apparatus IMP, it is important to reduce the size of the bubbles 201 formed between adjacent droplets of the curable composition IM and to make the bubbles 201 disappear in a short time.

[0051] Therefore, in this embodiment, a prediction system (simulation system) is provided to predict the behavior of droplets of curable composition IM in a process executed in a film forming apparatus IMP. The prediction system uses machine learning instead of physical calculations to predict the complex behavior involving the occurrence of bubbles 201 and the interactions between droplets in the process of forming a film of curable composition IM in the space between the substrate S and the mold M, for example, in an imprinting process.

[0052] Figure 3 is a view showing the configuration of the prediction system 300, which predicts the behavior of droplets of curable composition IM disposed on substrate S. The prediction system 300 includes a measurement device 301, a data collection server 302, and a prediction server 303 (analog server).

[0053] The prediction server 303 is an information processing device (simulation device) that uses machine learning to predict the behavior of droplets of a curable component IM disposed on a substrate S. Data required for machine learning performed by the prediction server 303 is collected from the data collection server 302 via network 304.

[0054] Measuring device 301 is a device for measuring (inspecting) the state of the substrate S processed by the film forming equipment IMP, that is, the state (defects, etc.) of the film of the curable composition IM formed on the substrate. The measurement results measured by measuring device 301 are accumulated in data collection server 302 via network 304.

[0055] The data collection server 302 receives measurement results from the measurement device 301 via the network 304 and accumulates the measurement results into measurement data. In addition, the data collection server 302 transmits the measurement data to the prediction server 303 via the network 304.

[0056] The film forming apparatus IMP adjusts the droplet configuration pattern of the curable composition IM based on the behavior of the droplets predicted by the prediction server 303, and the method and conditions for pressing the mold M onto the curable composition IM.

[0057] Figure 4 is a block diagram showing the hardware configuration of the prediction server 303. The prediction server 303 includes a system bus 401, a CPU 402, a ROM 403, a RAM 404, an HDD 405, a GPU 406, a communication unit 407, an input unit 408, and a display unit 409. Each unit of the prediction server 303 operates (performs its function) according to the program.

[0058] CPU 402 executes calculations according to a program to control the various units of the prediction server 303 connected to system bus 401. ROM 403 is read-only data memory. ROM 403 stores programs and data. RAM 404 is read / write data memory and is used to store programs and data. RAM 404 is also used to temporarily store data such as the results of calculations performed by CPU 402.

[0059] HDD 405 is used as a storage area for programs of the operating system (OS) of the predictive server 303, as well as a temporary storage area for programs and data. HDD 405 inputs and outputs data at a slower speed than RAM 404, but can store a large amount of data. HDD 405 is preferably a non-volatile storage device capable of permanently storing data, allowing data to be referenced for a long period. In this embodiment, HDD 405 is configured as a storage device, but the invention is not limited thereto, and devices for reading data from and writing data to external media such as CDs, DVDs, or memory cards loaded onto the device may also be provided.

[0060] GPU 406 is a computing device capable of performing more parallel computing operations than CPU 402. In this embodiment, GPU 406 performs some inference and learning processes in machine learning according to the program content.

[0061] Communication unit 407 performs data communication via network 304 using communication protocols such as TCP / IP. Communication unit 407 is used when communicating with another device. Input unit 408 includes devices such as various keyboards and mice, and is used to input information (e.g., characters, data, etc.) required by prediction server 303. Display unit 409 includes devices such as CRTs and LCD monitors, and is used to display information required for the operation of prediction server 303, processing results (prediction results), etc.

[0062] As described above, the prediction server 303 uses machine learning to predict the behavior of droplets of the curable composition IM disposed on the substrate S. Here, using a graph neural network as the learning model is effective in predicting the relationships between adjacent droplets of the curable composition IM.

[0063] Figure 5 is a view illustrating a graph convolutional network as an example of a graph neural network. The graph neural network consists of an input layer 5010, one or more intermediate layers (hidden layers) 5020 and 5030, and an output layer 5040. Each layer includes a plurality of graphs as elements, and the nodes of each graph have feature values.

[0064] Learning in graph neural networks is performed by updating the weights that associate the layers. These weights are represented by matrices. For example, weight 502 represents the weights between graph 501 in the input layer 5010 and graph 503 in the intermediate layer 5020. During the learning process of a graph neural network, the weights are updated based on the error between the learned data and the predictions made from the learned data (the predicted results).

[0065] In this way, each layer in a graph neural network includes graphs as elements. During the learning process, the weights between layers are updated to reduce the error between the learning data and the predictions of the graph neural network.

[0066] Figure 6 is a view that explains in detail the weights between layers in a graph neural network. The intermediate layer N, which serves as the preceding layer, includes graph 601, and the intermediate layer N+1, which serves as the following layer, includes graphs 602 and 603. In Figure 6, the weights between graphs 601 and 602 are indicated by solid arrows, and the weights between graphs 601 and 603 are indicated by dashed arrows.

[0067] Graph 601 is formed by four nodes h[N, 0, 0], h[N, 0, 1], h[N, 0, 2], and h[N, 0, 3], with each node holding a feature value. Graph 602 is formed by four nodes h[N+1, 0, 0], h[N+1, 0, 1], h[N+1, 0, 2], and h[N+1, 0, 3], with each node holding a feature value. Similarly, graph 603 is formed by four nodes h[N+1, 1, 0], h[N+1, 1, 1], h[N+1, 1, 2], and h[N+1, 1, 3], with each node holding a feature value.

[0068] Note that the four nodes h[N, 0, 0], h[N, 0, 1], h[N, 0, 2], and h[N, 0, 3] that form graph 601 will be referred to as nodes h10, h11, h12, and h13, respectively, in the following text. Similarly, the four nodes h[N+1, 0, 0], h[N+1, 0, 1], h[N+1, 0, 2], and h[N+1, 0, 3] that form graph 602 will be referred to as nodes h20, h21, h22, and h23, respectively, in the following text. Similarly, the four nodes h[N+1, 1, 0], h[N+1, 1, 1], h[N+1, 1, 2] and h[N+1, 1, 3] that form graph 603 are referred to as nodes h30, h31, h32 and h33 respectively in the following text.

[0069] A specific example of the weights between graphs is the weight 604 between node h10 in intermediate layer N and its corresponding node h20 in intermediate layer N+1. In addition, nodes in intermediate layer N+1 also apply weights from the nodes adjacent to their corresponding nodes in intermediate layer N. For example, node h20 in intermediate layer N+1 could hold a value represented by the sum of the value of its corresponding node h10 in intermediate layer N multiplied by weight 604 and the values ​​of its adjacent nodes h11, h12, and h13 multiplied by weight 605. Alternatively, node h20 in intermediate layer N+1 could hold a value obtained by applying some aggregation operation to this sum and using a nonlinear function as the starting function. Thus, the feature quantity of each node in intermediate layer N+1 includes information about the feature quantities of its neighboring nodes in intermediate layer N. More specifically, node h20 in intermediate layer N+1 is influenced by the feature quantities of nodes h11, h12, and h13 in intermediate layer N plus the feature quantity of its corresponding node h10.

[0070] In this way, in graph convolutional networks, the corresponding nodes in the previous layer and their neighboring nodes are input to the nodes in the subsequent layer. This allows machine learning to consider the influence of neighboring nodes and nodes in a wider region.

[0071] Figure 7 is a flowchart illustrating the procedure for generating a learning model using a graph neural network. The procedure for generating the learning model is executed by the prediction server 303.

[0072] In step S701, conditions (program conditions) are set for the process (e.g., an imprinting process) required to form a film of curable composition IM in the space between the substrate S and the mold M. Program conditions include, for example, a configuration pattern indicating the positions of droplets of curable composition IM to be placed on the substrate S, the shape of the pattern on the mold M, a target value for the thickness of the film of curable composition IM to be formed on the substrate S, and the depth of the pattern (groove) in the patterned area MP of the mold M.

[0073] In step S702, measurement data corresponding to the program conditions set in step S701 is obtained from the data collection server 302, that is, measurement data of the state of the substrate S (the state of the film of the curable composition IM formed on the substrate) processed using these program conditions. More specifically, the prediction server 303 requests the measurement data corresponding to the processing conditions set in step S701 from the data collection server 302 via the network 304. In response to the request from the prediction server 303, the data collection server 302 extracts the measurement data (data group) corresponding to the processing conditions set in step S701 from the accumulated measurement data, which is a database. Then, the data collection server 302 creates a list of the measurement data extracted from the database and transmits the list to the prediction server 303 via the network 304.

[0074] In step S703, the graphs included in each layer of the graph neural network are generated.

[0075] Here, referring to FIG8, the procedure for generating the graphic will be described. FIG8a shows a configuration pattern 801 of droplets of the curable component IM set as processing conditions in step S701. As shown in FIG8a, the configuration pattern 801 includes information (first information) of the coordinates (positions) of each droplet of the curable component IM.

[0076] In this embodiment, the pattern shown in 8b is generated based on the droplet configuration pattern 801 of the curable component IM. In the pattern shown in 8b, each line connecting the positions of the individual droplets of the curable component IM included in the configuration pattern 801, that is, each line connecting adjacent droplets (nodes) with the center position of the droplet as a node, is set as link 802. An example of a method for generating such a pattern is to use the Delaunay diagram method while setting each droplet of the curable component IM as a node.

[0077] Furthermore, in this embodiment, the pattern shown in 8c is generated based on the droplet configuration pattern 801 of the curable composition IM. In the pattern shown in 8c, nodes 804 are configured in the region surrounded by the droplets of the curable composition IM. In other words, nodes 804 are positioned at locations within the region defined by adjacent droplets of the plurality of droplets of the curable composition IM. Note that nodes 804 are preferably configured at the midpoint between adjacent droplets of the curable composition IM (the centroid of the region defined by adjacent droplets). An example of a method for generating such a pattern is to use a Voronoi diagram while setting each droplet of the curable composition IM as a node. A Voronoi diagram is a diagram that divides a plane based on the nearest point. 8c shows the boundary lines 803 (Voronoi boundaries) of the regions obtained through division (divided regions). In this manner, the region defined by adjacent droplets among a plurality of droplets of the curable composition IM is a region demarcated by the Voronoi boundary of the Voronoi diagram, where each of the plurality of droplets is designated as a generation point. Bubbles (defects) generated in the film of the curable composition IM tend to generate on the boundary lines 803 of the individual droplets, away from the curable composition IM. Therefore, in the Voronoi diagram, the intersection point of the boundary lines 803 is designated as node 804, and the line connecting node 804 (node) is designated as a link (boundary line 803), thereby producing the pattern shown in 8c. Note that node 804 is not limited to the intersection point of the boundary lines 803, but can be designated to include the boundary line 803. That is, node 804 can be designated on the boundary line 803.

[0078] 8d shows a graph generated by combining the graphs shown in 8b and 8c. The graph shown in 8d includes the nodes and links of the graphs shown in 8b and 8c. Furthermore, in the graph shown in 8d, link 805, which connects to link 802 of the graph shown in 8b, intersects with link 806, which connects to link (boundary line 803) of the graph shown in 8c, and a new node 807 is added at each of the intersection points (partially).

[0079] In this manner, in step S703, the patterns shown in 8b, 8c, and 8d are generated based on the droplet configuration pattern 801 of the curable composition IM shown in 8a. These patterns are information (second information) indicating the relative positions of adjacent droplets among a plurality of droplets of the curable composition IM. In this embodiment, the patterns shown in 8b, 8c, and 8d generated from the configuration pattern 801 shown in 8a are used as input to a graph neural network.

[0080] Referring back to Figure 7, in step S704, feature values ​​are assigned to the graph that will be used as input to the graph neural network, i.e., the graph generated in step S703.

[0081] Here, referring to FIG9, a procedure for assigning feature quantities to a pattern that will be used as input to a graphical neural network will be described. 9a shows pattern 901 generated in step S703. For example, information about the position and volume of droplets of the curable component IM, information about the shape (density, tilt, etc.) of the pattern of the mold M, information about the shape (steps, etc.) of the substrate S, and information about the volatilization of the curable component IM are used as feature quantities assigned to pattern 901. When feature quantities are assigned to (reflect) patterns, different patterns are used for different types of feature quantities. For example, in 9b, the position (coordinates) of droplets of the curable component IM is reflected in pattern 902, the density of the pattern of the mold M is reflected in pattern 903, and the steps of the substrate S are reflected in pattern 904.

[0082] Referring back to Figure 7, in step S705, feature values ​​are assigned to the graph that will be used as learning data for the graph neural network.

[0083] Here, referring to Figures 10A and 10B, the procedure for generating learning data from measurement data will be described. Figure 10A shows an example of the measurement data included in the data group (list) acquired in step S702. The measurement data shown in Figure 10A includes information about the location (site) and size of a defect 1002 appearing in the injection region 1001 of the substrate S. Figure 10B shows learning data including information indicating the correspondence between the defect 1002 in the measurement data shown in Figure 10A and the droplets of the curable component IM that caused the defect 1002. In the learning data shown in Figure 10B, there is a configuration pattern 1004 that generates droplets of the curable component IM and a link 1005 connecting each adjacent droplet of the curable component IM. In addition, each link 1005 in the learning data shown in Figure 10B is associated with defects 1006 and 1007 included in the measurement data. Defects 1006 and 1007 occur when adjacent droplets of the curable component IM do not merge with each other. Therefore, the probability (degree) of merging of adjacent droplets of the curable component IM is used as a feature quantity of the learning data. For example, similar to link 1005, if defects 1006 and 1007 do not appear near the link, the probability of merging of droplets of curable component IM present at both ends of link 1005 is high. On the other hand, similar to link 1008, if defects 1006 and 1007 have already appeared near the link, the probability of merging of droplets of curable component IM present at both ends of link 1008 is low. In this way, the probability of merging of droplets of curable component IM is assigned as a feature quantity to the link, serving as an example of the learning data. Note that the location and size of defects, the size of the area surrounded by the link, etc., can also be used as feature quantities of the learning data.

[0084] In graph neural networks, each node in the graph typically has a feature quantity. Therefore, for convenience, it is also effective to reallocate the feature quantities assigned (applied) to the links (e.g., the probability of droplet merging of the curable component IM) to the feature quantities of the nodes existing at the two ends of the link.

[0085] In step S706, a learning model is set. Figure 11 is a view showing an example of a graph neural network set as a learning model. The graph neural network shown in Figure 11 is formed by layers including an input layer 11010, two intermediate layers 11020 and 11030, and an output layer 11040. Each layer includes graphs as elements for different feature quantities. Weights 1101, 1102, and 1103 between graphs are associated between layers. Weights 1101, 1102, and 1103 are represented, for example, as matrices. The graph neural network has a convolutional effect, where the feature quantities of corresponding nodes in the previous layer and the feature quantities of nodes adjacent to the corresponding node are used as inputs (input parameters) to the next layer. Since the graph neural network shown in Figure 11 includes two intermediate layers 11020 and 11030, learning can be performed by considering the feature quantities of the two nodes preceding a given node.

[0086] In step S707, the learning model set in step S706 is executed. More specifically, in step S704, a graph of feature quantities is assigned as input parameters and set for the input layer 11010 of the graph neural network shown in FIG11. Furthermore, in step S705, a graph of feature quantities is assigned as learning data and set for learning data 11050. During learning, a loss 1104 representing the error between the output layer 11040 and the learning data 11050 is calculated, and the weights are updated in the direction 1105 from the output layer 11040 toward the input layer 11010 to reduce the loss 1104 as the error.

[0087] In step S708, it is determined whether learning has been performed on all measurement data included in the data group (list) obtained in step S702. If learning has not been performed on all measurement data, that is, if there are measurement data for which learning has not been completed, the program proceeds to step S703 and executes steps S703 to S707 (learning procedure). On the other hand, if learning has been performed on all measurement data, the program proceeds to step S709.

[0088] In step S709, the learned model that has been learned is output (i.e., the learned model is generated).

[0089] As described above, by executing the procedure shown in FIG7, a learning model of a graph neural network can be generated, which includes measurement data that has learned the configuration pattern of droplets corresponding to the curable component IM. In this embodiment, the generated learning model becomes a learning model that includes the feature quantities of adjacent droplets of the curable component IM and the feature quantities of droplets farther away than the adjacent droplets.

[0090] Referring to Figure 12, a procedure will be described that uses a learning model generated in the process shown in Figure 7 to predict the behavior of droplets of curable composition IM disposed on substrate S. Here, the behavior of droplets of curable composition IM refers to the behavior of droplets of curable composition IM in the process of forming a film of curable composition IM in the space between substrate S and mold M.

[0091] In step S1201, the conditions (program conditions) required for the process of forming a film of curable composition IM in the space between the substrate S and the mold M are set. As described above, the program conditions include the configuration of the pattern, the shape of the pattern of the mold M, the target value of the thickness of the film of curable composition IM to be formed on the substrate S, and the depth of the pattern (groove) in the pattern area MP of the mold M.

[0092] In step S1202, the graphs included in each layer of the graph neural network are generated. The specific procedure for generating the graphs is similar to that in step S703, and will not be repeated here.

[0093] In step S1203, feature values ​​are assigned to the graph that will be used as input to the graph neural network, i.e., the graph generated in step S1202. The specific procedure for assigning feature values ​​to the graph is similar to that in step S704, and will not be repeated here.

[0094] In step S1204, the learning model is set. Here, the learning model generated in the program shown in Figure 7 is set.

[0095] In step S1205, using the learning model set in step S1204, the behavior of the process in which droplets of curable composition IM form a film of curable composition IM in the space between substrate S and mold M is as expected.

[0096] Here, referring to FIG11, the prediction (inference) procedure for the behavior of droplets of the curable component IM in step S1205 will be described. As described above, in this embodiment, when predicting the behavior of droplets of the curable component IM, the learning model generated in the procedure shown in FIG7 is used. In this learning model, each of the weights 1101, 1102, and 1103 between layers, represented by matrices, has been updated. First, a graph of feature quantities assigned in step S1203 is set as an input parameter for input layer 11010. In the prediction procedure, the feature quantities in the graph are updated in direction 1106 from input layer 11010 toward output layer 11040. Due to the effect of convolution processing as a graph convolutional network performed between layers, the feature quantities of adjacent droplets of the curable component IM in the previous layer are reflected in the subsequent layer.

[0097] Referring back to Figure 12, in step S1206, the behavior of the droplets of the curable component IM predicted in step S1205 is output as a prediction result. For example, as a prediction result of the behavior of the droplets of the curable component IM, the degree of merging of adjacent droplets among a plurality of droplets of the curable component IM on the substrate is displayed on the display unit 409.

[0098] Referring to Figures 13A and 13B, an example of the result predicted from the input parameters in this embodiment will be described. Figure 13A shows the configuration pattern of droplets of the curable component IM as input parameters. Referring to Figure 13A, the density of droplets 1302 of the curable component IM is low in region 1303 of the injection region 1301 of the substrate S. Figure 13B shows the result (prediction result) of predicting the configuration pattern of droplets of the curable component IM shown in Figure 13A in step S1205. In this embodiment, the merging state of adjacent droplets of the curable component IM as a characteristic quantity is predicted. For example, as shown in Figure 13B, for link 1305 indicated by the solid line, the probability of merging of adjacent droplets of the curable component IM has been predicted to be high. On the other hand, for link 1306 indicated by the dashed line, the probability of merging of adjacent droplets of the curable component IM has been predicted to be low. Here, the prediction of the merging state of adjacent droplets of the curable component IM is used as a characteristic quantity, but the location and size of defects, the size of the area surrounded by the link, etc. can also be treated as learning data.

[0099] As described above, according to this embodiment, in the process of predicting the behavior of droplets of curable composition IM disposed on substrate S, machine learning is used instead of physical calculations to predict the behavior of droplets of curable composition IM. Therefore, a technique can be provided that can predict the complex behavior considering the interactions of multiple droplets of curable composition IM even with a small computational load.

[0100] The use of graph neural networks as learning models in machine learning has been described. However, neural network models can also be used as learning models as shown in Figure 14. Figure 14 is a view illustrating an example of a neural network.

[0101] The neural network route comprises an input layer 14010, one or more intermediate (hidden) layers 14020 and 14030, and an output layer 14040. Each layer includes neurons 1401 as elements, and weights 1402, 1403, and 1404 connect the layers. As in graph neural networks, the weights 1402, 1403, and 1404 between the layers are updated in the neural network. For example, weights 1402, 1403, and 1404 are updated in a direction 1406 from the output layer 14040 toward the input layer 14010. At this time, the weights 1402, 1403, and 1404 are updated to reduce the loss 1405 of the error between the learning data 14050 and the output layer 14040 as output data.

[0102] Referring to Figures 15A and 15B, the input data used for prediction using a neural network will be described. Figure 15A shows a configuration pattern 1502 of droplets of curable composition IM in the injection region 1501 of the substrate S. Figure 15B shows data generated as input data for the neural network based on the configuration pattern 1502 shown in Figure 15A. Here, image data 1503 indicating the relationship between adjacent droplets of curable composition IM is generated as input data. Furthermore, the density of droplets of curable composition IM included in each pixel (region) of image data 1503 is used as information indicating the relationship between adjacent droplets of curable composition IM. In Figure 15B, the pixel value (color) of each pixel of image data 1503 changes according to the density of droplets of curable composition IM. More specifically, a black pixel value is set for pixels 1504 with a high density of droplets of curable composition IM, and a white pixel value is set for pixels 1505 with a low density of droplets of curable composition IM.

[0103] Referring to Figures 16A and 16B, learning data used for learning using a neural network will be described. Figure 16A shows measurement data of the indentation region 1601 of the substrate S, and shows the location and size of each defect 1602 appearing in the film of the curable composition IM formed on the indentation region 1601. Figure 16B shows data generated as learning data for the neural network based on the measurement data shown in Figure 16A. Here, image data 1603 indicating the location of defects that have appeared in the film of the curable composition IM is generated as learning data. In Figure 16B, the pixel value (color) of each pixel in the image data 1603 changes according to the presence / absence of the defect. More specifically, a black pixel value is set for the pixel 1604 corresponding to the location where a defect exists, and a white pixel value is set for the pixel 1605 corresponding to the location where no defect exists.

[0104] The neural network shown in Figure 14 is learned using the input and learning data generated as described above. By using a model of the learned neural network, such as in a graphical neural network, the complex behavior taking into account the interaction of multiple droplets of the curable component IM disposed on the substrate S can be predicted.

[0105] In this embodiment, the behavior of droplets of curable composition IM in forming a film made from a cured product of curable composition IM by distributing droplets of curable composition IM on a substrate S and contacting a mold M with the droplets has been described. However, this embodiment is not limited to the process of forming a film of curable composition IM by contacting the mold M with the droplets of curable composition IM. For example, this embodiment is also applicable to the case of forming a film of curable composition IM by merging adjacent droplets of curable composition IM disposed on the substrate S. Even when it is not necessary to contact the droplets of curable composition IM on the substrate S with the mold M as described above, the behavior of droplets of curable composition IM can be predicted while using the density of droplets of curable composition IM, the shape of the substrate S, the film thickness of curable composition IM, etc., as characteristic quantities.

[0106] Embodiments of the present invention can also be implemented by a computer of a system or device, which reads and executes computer-executable instructions (e.g., one or more programs) recorded on a storage medium (more comprehensively referred to as a "non-transitory computer-readable storage medium") to perform the functions of one or more embodiments described above, and / or the computer includes one or more circuits (e.g., application-specific integrated circuits (ASICs)) for performing the functions of one or more embodiments described above, and embodiments of the present invention can also be implemented by a method performed by a computer of a system or device, which performs the functions of one or more embodiments described above by, for example, reading and executing computer-executable instructions from a storage medium, and / or the computer controls one or more circuits to perform the functions of one or more embodiments described above. The computer may include one or more processors (e.g., a central processing unit (CPU), a microprocessor unit (MPU)) and may include a network of separate computers or separate processors to read and execute computer-executable instructions. The computer-executable instructions may, for example, be provided to the computer from a network or storage medium. Storage media may include, for example, one or more of the following: hard disk, random access memory (RAM), read-only memory (ROM), storage for distributed computing systems, optical discs (such as CDs, DVDs or Blu-ray discs (BD)™), flash memory devices, memory cards, etc.

[0107] The film forming apparatus IMP, which includes a prediction server 303 (information processing device), controls the process of forming a film of a curable composition from a plurality of droplets of a curable composition disposed on a first member based on the prediction of the behavior of droplets of a curable composition by the prediction server 303.

[0108] The article manufacturing method according to this embodiment includes the steps of determining the conditions for a procedure in which a plurality of droplets of a curable composition disposed on a first member form a film of the curable composition while repeating the above-described prediction method (simulation), and the step of executing the procedure according to the conditions. The patterned mold has been described so far, but the present invention is also applicable to the patterned substrate.

[0109] Figures 17A to 17F show more specific examples of the method for manufacturing articles. As shown in Figure 17A, a substrate such as a silicon wafer is prepared, on which a processed material, such as an insulator, is formed on its surface. Next, an imprinting material is coated onto the surface of the processed material using an inkjet printing method or the like. Here, the imprinting material is shown as a plurality of droplets coated onto the substrate.

[0110] As shown in Figure 17B, one side of a mold with protrusions and grooves for imprinting is formed on a substrate and faces the imprinting material on the substrate. As shown in Figure 17C, the substrate coated with imprinting material is brought into contact with the mold, and pressure is applied. The gap between the mold and the treated material is filled with imprinting material. In this state, when light, which serves as curing energy, is irradiated through the mold, the imprinting material cures.

[0111] As shown in Figure 17D, after the imprinting material has cured, the mold is removed from the substrate. A pattern of the cured product of the imprinting material is then formed on the substrate. In the pattern of the cured product, the grooves of the mold correspond to the protrusions of the cured product, and the protrusions of the mold correspond to the grooves of the cured product. That is, the pattern of the protrusions and grooves of the mold is transferred onto the imprinting material.

[0112] As shown in Figure 17E, when etching is performed using a pattern of the cured product as an etch resist mask, a thin portion of the cured product that is absent or remains on the surface of the treated material is removed to form a groove. As shown in Figure 17F, when the pattern of the cured product is removed, an article having grooves formed in the surface of the treated material can be obtained. Here, the pattern of the cured product is removed; however, for example, this pattern can be used as a film for insulating layers contained in semiconductor elements, etc., and is not removed after processing; in other words, as a constituent component of the article.

[0113] Although the invention has been described with reference to exemplary embodiments, it should be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims should be given the broadest interpretation in order to cover all such modifications and equivalent structures and functions.

[0114] IMP: Membrane Forming Equipment S:Substrate M: Mold CS: Pressure Control Space IM: Curable Components MP: Pattern Area 102: Substrate holding unit 103: Position Measurement Unit 104: Base 105: Substrate driving mechanism 106: Alignment Measurement System 107: Curing Unit 108: Distributor 110: Control Unit 111: Optical components 112: Image Capture Unit 121: Mold Holding Unit 122: Mold drive mechanism 123: Deformation Mechanism 125: Window components 130: Supporting structure 140: Mold conveying mechanism 150: Mold Cleaner 151: Sensor 152: Sensor 300: Prediction System 301: Measuring equipment 302: Data Collection Server 303: Prediction Server 304: Internet 401: System Bus 407: Communication Unit 408: Input Unit 409: Display Unit 501: Graphics 502: Weight 503: Graphics 5010: Input Layer 5020: Intermediate Layer 5030: Intermediate Layer 5040: Output Layer 601: Graphics 602: Graphics 603: Graphics 604: Weight 605: Weight h10: Node h11: Node h12: Node h13: Node h20: Node h21: Node h22: Node h23: Node h30: Node h31: Node h32: Node h33: Node 801: Configure Pattern 802: Link 803: Boundary Line 804: Node 805: Link 806: Link 807: Node 901: Graphics 902: Graphics 903: Graphics 904: Graphics 1001: Injection Zone 1002: Defect 1004: Configure Pattern 1005: Link 1006: Defect 1007: Defect 1008: Link 1101: Weight 1102: Weight 1103: Weight 1104: Loss 1105: Direction 1106: Direction 11010: Input Layer 11020: Intermediate Layer 11030: Intermediate Layer 11040: Output Layer 11050: Learning Materials 1301: Injection Zone 1302: Droplet 1303: Area 1305: Link 1306: Link 1401: Neuron 1402: Weight 1403: Weight 1404: Weight 1405: Loss 1406: Direction 14010: Input Layer 14020: Intermediate Layer 14030: Intermediate Layer 14040: Output Layer 14050: Learning Materials 1501: Injection Zone 1502: Configuration Pattern 1503: Video Footage 1504: pixels 1505 pixels 1601: Injection Zone 1602: Defect 1603: Video footage 1604: pixels 1605: pixels

Claims

1. A prediction method for predicting the behavior of droplets of a curable composition in a process in which a film of the curable composition is formed from a plurality of droplets of the curable composition disposed on a first member, the method comprising: The behavior of the droplet is predicted using a learning model, wherein the input of the learning model includes first information indicating the position of the droplet on the first component where the curable component will be disposed and second information indicating the relative positional relationship between adjacent droplets among the plurality of droplets.

2. The method as described in claim 1, wherein the second information is represented by a graph formed by a node and the links connecting the node.

3. The method as described in claim 2, wherein in the graph, the position corresponding to each of the plurality of droplets is designated as the node, and the line connecting adjacent nodes is designated as the link.

4. The method as described in claim 3, wherein the position includes the center position of each of the plurality of droplets.

5. The method as described in claim 2, wherein in the graph, the position of the region defined by adjacent droplets among the plurality of droplets is designated as the node, and the line connecting adjacent nodes is designated as the link.

6. The method as described in claim 5, wherein the region is defined by the Voronoi boundary of the Voronoi diagram, and each of the plurality of droplets is designated as a generation point.

7. The method as described in claim 5, wherein the location includes the centroid location of the region.

8. The method as described in claim 5, wherein the location includes the Voronoi boundary of the Voronoi diagram, and each of the plurality of droplets is designated as a generation point.

9. The method of claim 2, wherein in the graph, the position corresponding to each of the plurality of droplets, the position in the region defined by adjacent droplets among the plurality of droplets, and the position where the Voronoi boundary of the Voronoi graph intersects are set as nodes, wherein each of the plurality of droplets is set as a generation point, and the line connecting adjacent nodes is set as the link.

10. The method of claim 2, wherein in the graph, at least one of the node and the link holds one of information relating to the position and volume of the droplet and information relating to the shape of the first component as a characteristic quantity.

11. The method as described in claim 1, further comprising: The learning model is generated while using at least one of the first information and the second information as input and using the predictive behavior of the droplet as learning data.

12. The method of claim 1, wherein in the prediction, the degree of merging of adjacent droplets among the plurality of droplets is predicted as the behavior of the droplet.

13. The method of claim 1, wherein the method includes the step of bringing the curable composition disposed on the first member and the second member into contact with each other, thereby forming a film of the curable composition in the space between the first member and the second member.

14. The method of claim 13, wherein the input of the learning model includes at least one of information indicating the volume of the droplet, information about the evaporation of the droplet, information about the shape of the first component, and information about the shape of the pattern disposed on the second component.

15. The method as described in claim 1, wherein the learning model uses a graph neural network.

16. The method as described in claim 1, wherein the learning model uses a neural network.

17. An information processing apparatus for predicting the behavior of droplets of a curable composition in a process of forming a film of the curable composition from a plurality of droplets of the curable composition disposed on a first member, wherein the apparatus uses a learning model to predict the behavior of the droplets, and the input of the learning model includes information indicating the position of the droplet on the first member where the curable composition will be disposed and second information indicating the relative positional relationship between adjacent droplets among the plurality of droplets.

18. A film forming apparatus comprising the information processing apparatus of claim 17, wherein a process for forming a film of the curable composition from a plurality of droplets of the curable composition disposed on a first member is controlled based on a prediction of the behavior of droplets of the curable composition through the information processing apparatus.

19. A method for manufacturing an article, comprising: While repeating the prediction method defined in request 1, the conditions for a procedure to form a film of the curable composition from a plurality of droplets of the curable composition disposed on the first member are determined, and the procedure is executed according to the conditions.

20. A non-transitory storage medium storing a program for causing a computer to execute the prediction method defined in request item 1.

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