Simulation method, simulation device, film formation device, article manufacturing method, and non-transitory storage medium

Abstract

The present application provides a simulation method that predicts behavior of a curable component in a process of bringing a plurality of droplets of the curable component disposed on a first member into contact with a second member and forming a film of the curable component in a space between the first member and the second member, the method including, for each of the plurality of droplets of the curable component, obtaining, based on whether the droplet merges with an adjacent droplet, an evaluation value for evaluating a relationship related to a degree of merging with the adjacent droplet, and displaying the evaluation value obtained in the obtaining step together with information indicating a state of the droplet corresponding to the evaluation value. A simulation device, a film forming device, an article manufacturing method, and a non-transitory storage medium are also provided.

Description

Technical Field

[0001] This invention relates to simulation methods, simulation equipment, film-forming equipment, article manufacturing methods, and storage media. Background Technology

[0002] A film-forming technology is provided that forms a film from a cured product of a curable component on a substrate by arranging a curable component on a substrate, contacting the curable component with a mold, and curing the curable component. This film-forming technology is applied to imprinting and planarization techniques. In imprinting, a patterned mold is used to transfer a patterned mold pattern onto a curable component on a substrate by contacting and curing the curable component on the substrate with the pattern of the mold. In planarization, a film with a flat upper surface is formed by using a mold with a flat surface by contacting and curing the curable component on the substrate with the flat surface.

[0003] A curable component is arranged as droplets on a substrate, and then a mold is pressed against the droplets. This diffuses the droplets of curable component onto the substrate, forming a film of the curable component. It is important to form a film of the curable component with uniform thickness and without air bubbles. To achieve this, the arrangement of the droplets, the method and conditions for pressing the mold against the curable component, etc., must be adjusted. Achieving this adjustment operation through repeated trials using equipment requires significant time and cost. To address this issue, it is desirable to develop a simulator that supports this adjustment operation.

[0004] Japanese Patent No. 5599356 discloses a simulation method for predicting the wet expansion and aggregation (droplet merging) of multiple droplets arranged on a pattern forming surface, and a method for generating a droplet arrangement pattern using this prediction. Japanese Patent No. 5599356 also discloses calculating the droplet height distribution relative to the generated droplet arrangement pattern and adjusting the droplet arrangement so that the droplet height distribution falls within a predetermined range.

[0005] On the other hand, during the embossing process, it is necessary to control the amount of air bubbles confined between the droplets of the curable component. This is because if a large number of air bubbles are confined between the droplets of the curable component, the droplets will not expand even after extrusion, leading to defects (abnormalities) due to unfilling.

[0006] However, the amount of gas confined between the droplets of the curable component is determined by complex interactions, including the interaction between the mold and the droplets, as well as droplet merging. Therefore, simply adjusting the droplet arrangement to ensure that the height distribution of the curable component droplets falls within a predetermined range cannot maintain the amount of gas confined between the droplets at or below a predetermined level. Summary of the Invention

[0007] This invention provides a technique that facilitates the detection of abnormalities in the behavior of curable components during the formation of films of curable components.

[0008] According to a first aspect of the invention, a simulation method is provided for predicting the behavior of a curable component during the process of contacting a plurality of droplets of a curable component disposed on a first member with a second member and forming a film of the curable component in the space between the first member and the second member. The method includes, for each of the plurality of droplets of the curable component, obtaining an evaluation value for assessing a relationship related to the degree of merging with adjacent droplets based on whether the droplet merges with adjacent droplets, and displaying the evaluation value obtained in the obtaining step together with information indicating the state of the droplet corresponding to the evaluation value.

[0009] According to a second aspect of the invention, a simulation apparatus is provided that predicts the behavior of a curable component during the process of bringing a plurality of droplets of a curable component disposed on a first member into contact with a second member and forming a film of the curable component in the space between the first member and the second member, wherein, for each of the plurality of droplets of the curable component, an evaluation value is obtained based on whether the droplet merges with an adjacent droplet to assess the degree of merging with the adjacent droplets, and the evaluation value is displayed together with information indicating the state of the droplet corresponding to the evaluation value.

[0010] According to a third aspect of the invention, a film-forming apparatus including the above-described simulation device is provided, wherein a process for contacting a plurality of droplets of the curable component disposed on a first member with a second member and forming a film of the curable component in the space between the first member and the second member is controlled based on a prediction of the behavior of the curable component performed by the simulation device.

[0011] According to a fourth aspect of the present invention, a method for manufacturing an article is provided, comprising, while repeating the above-described simulation method, determining conditions for a process of contacting a plurality of droplets of a curable component disposed on a first component with a second component and forming a film of the curable component in the space between the first and second components, and performing the process according to the conditions.

[0012] According to a fifth aspect of the invention, a non-transitory storage medium is provided that stores a program for causing a computer to execute the above-described simulation method.

[0013] Other aspects of the invention will become apparent from the following description of exemplary embodiments, with reference to the accompanying drawings. Attached Figure Description

[0014] Figure 1 This is a schematic diagram illustrating the arrangement of the film-forming apparatus and the simulation apparatus according to an embodiment of the present invention.

[0015] Figure 2 This is a flowchart used to describe the simulation method according to the first embodiment.

[0016] Figure 3 This is a view illustrating the concept of droplet composition of a curable component.

[0017] Figure 4 It is a view used to describe the process of determining whether adjacent droplet components merge with each other.

[0018] Figure 5 It shows through Figure 1 The image shows an example view of a simulation device used to calculate the behavior of droplets of a curable component.

[0019] Figure 6 This is a diagram showing the composition of a droplet of curable components defined by 18 angles.

[0020] Figure 7 This is a view showing an example of an image displayed on the monitor.

[0021] Figure 8 This is a view showing an example of another image displayed on the monitor.

[0022] Figure 9 This is a view showing an example of another image displayed on the monitor.

[0023] Figure 10 This is a flowchart used to describe the simulation method according to the second embodiment.

[0024] Figure 11 It is a view used to describe the link structure.

[0025] Figure 12 This is a view showing an example of an image displayed on the monitor.

[0026] Figure 13 This is a view showing an example of another image displayed on the monitor.

[0027] Figure 14 This is a view showing an example of another image displayed on the monitor.

[0028] Figure 15 This is a flowchart used to describe the simulation method according to the third embodiment.

[0029] Figure 16A and Figure 16B It is a view used to describe the existence / non-existence of a closed region.

[0030] Figure 17 It is a view used to describe the existence / non-existence of a closed region.

[0031] Figure 18A and Figure 18B This is a view used to describe the method for calculating the amount of bubbles contained within a closed region.

[0032] Figure 19 This is a view showing an example of an image displayed on the monitor.

[0033] Figure 20 This is a view showing an example of another image displayed on the monitor.

[0034] Figure 21 It is a graph used to describe the method of detecting abnormal behavior of curable components.

[0035] Figure 22 This is a view showing an example of another image displayed on the monitor.

[0036] Figures 23A to 23F It is a view used to describe the method of making an item. Detailed Implementation

[0037] In the following, embodiments will be described in detail with reference to the accompanying drawings. It should be noted that the following embodiments are not intended to limit the scope of the claimed invention. Several features are described in the embodiments, but the invention is not limited to requiring all such features, and multiple such features can be suitably combined. Furthermore, in the drawings, the same reference numerals indicate the same or similar configurations, and redundant descriptions thereof are omitted.

[0038] Figure 1 This is a schematic diagram illustrating the arrangement of a film-forming apparatus IMP and a simulation device 1 according to an embodiment of the present invention. The film-forming apparatus IMP performs a process of contacting a plurality of droplets of a curable component IM disposed on a substrate S with a mold M and forming a film of the curable component IM in the space between the substrate S and the mold M. The film-forming apparatus IMP can be configured as, for example, an imprinting apparatus or a planarization apparatus. The substrate S and the mold M are interchangeable, and by contacting a plurality of droplets of the curable component IM disposed on the mold M with the substrate S, a film of the curable component IM can be formed in the space between the mold M and the substrate S. Therefore, the film-forming apparatus IMP is entirely an apparatus for performing a process of contacting a plurality of droplets of the curable component IM disposed on a first member with a second member and forming a film of the curable component IM in the space between the first member and the second member. This embodiment is described by assuming the first member is the substrate S and the second member is the mold M. However, the first member can be assumed to be the mold M, and the second member can be assumed to be the substrate S. In this case, the substrate S and the mold M are interchangeable in the following description.

[0039] An imprinting apparatus uses a patterned mold M to transfer the pattern of the mold M onto a curable component IM on a substrate S. The imprinting apparatus uses a mold M having a patterned area PR. As part of the imprinting process, the apparatus brings the curable component IM on the substrate S into contact with the patterned area PR of the mold M, fills the space between the mold M and the area where the pattern on the substrate S will be formed with the curable component IM, and then cures the curable component IM. This transfers the pattern of the patterned area PR of the mold M onto the curable component IM on the substrate S. For example, the imprinting apparatus forms a pattern made of the cured product of the curable component IM in each of a plurality of injection areas on the substrate S.

[0040] As a planarization process, a mold M with a flat surface is used. The planarization equipment brings the curable component IM on the substrate S into contact with the flat surface of the mold M and cures the curable component IM, thereby forming a film with a flat upper surface. If a mold M with a size that covers 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.

[0041] As a curable component, a material that cures by receiving curing energy is used. The curing energy can be electromagnetic waves or heat. Electromagnetic waves include light selected from a wavelength range of, for example, 10 nm (inclusive) to 1 mm (inclusive), and more specifically, infrared light, visible light, or ultraviolet light. The curable component is a component that cures by light irradiation or heating. A photocurable component that cures by light irradiation contains at least a polymerizable compound and a photopolymerization initiator, and may also contain a non-polymerizable compound or solvent as needed. The non-polymerizable compound is at least one material selected from sensitizers, hydrogen donors, internal release agents, surfactants, antioxidants, and polymer components. The viscosity of the curable component (viscosity at 25°C) is, for example, from 1 mPa·s (inclusive) to 100 mPa·s (inclusive).

[0042] Materials used as substrates include, for example, glass, ceramics, metals, semiconductors, and resins. Depending on the requirements, components made of a different material from the substrate can be disposed on the surface of the substrate. Substrates include, for example, silicon wafers, compound semiconductor wafers, or quartz glass.

[0043] In the specification and accompanying drawings, directions will be indicated in the XYZ coordinate system, where the direction parallel to the surface of substrate S is defined as the XY plane. The directions of the X-axis, Y-axis, and Z-axis parallel to 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 regarding the X-axis, Y-axis, and Z-axis refers to control or drive regarding the directions parallel to the X-axis, parallel to the Y-axis, and parallel to the Z-axis, respectively. Furthermore, control or drive regarding the θX-axis, θY-axis, and θZ-axis refers to control or drive regarding rotation about an axis parallel to the X-axis, rotation about an axis parallel to the Y-axis, and rotation about an axis parallel to the Z-axis, respectively. Additionally, position is information specified based on coordinates on the X-axis, Y-axis, and Z-axis, and orientation is information specified by values ​​on the θX-axis, θY-axis, and θZ-axis. Positioning refers to controlling position and / or orientation.

[0044] The film deposition apparatus IMP includes a substrate holder SH that holds a substrate S, a substrate drive mechanism SD that moves the substrate S by driving the substrate holder SH, and a base SB that supports the substrate drive mechanism SD. Furthermore, the film deposition apparatus IMP includes a mold holder MH that holds a mold M, and a mold drive mechanism MD that moves the mold M by driving the mold holder MH.

[0045] A substrate driving mechanism SD and a mold driving mechanism MD form a relative movement mechanism that moves at least one of a substrate S and a mold M to adjust the relative position between the substrate S and the mold M. Adjusting the relative position between the substrate S and the mold M via the relative movement mechanism includes driving to bring the curable component IM on the substrate S into contact with the mold M, and driving to separate the mold M from the cured curable component IM on the substrate S. Furthermore, adjusting the relative position between the substrate S and the mold M via the relative movement mechanism includes positioning between the substrate S and the mold M. The substrate driving mechanism SD is configured to drive the substrate S relative to multiple 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 driving mechanism MD is configured to drive the mold M relative to multiple 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).

[0046] The film-forming apparatus IMP includes a curing unit CU for curing a curable component IM, which fills the space between a substrate S and a mold M with the curable component IM. For example, the curing unit CU cures the curable component IM on the substrate S by applying curing energy to the curable component IM via the mold M.

[0047] The film-forming apparatus IMP includes a transmission member TR for forming a space SP on the rear side of the mold M (the opposite side of the surface opposite the substrate S). The transmission member TR is made of a material that transmits curing energy from the curing unit CU and can apply the curing energy to the substrate S.

[0048] The film-forming apparatus IMP includes a pressure control unit PC, which controls the deformation of the mold M in the Z-axis direction by controlling the pressure of the space SP. For example, when the pressure control unit PC increases the pressure of the space SP to above atmospheric pressure, the mold M deforms towards the substrate S in a convex shape.

[0049] The film-forming apparatus IMP includes a distributor DSP for arranging, supplying, or distributing a curable component IM on a substrate S. However, the curable component IM can be supplied (loaded) to the film-forming apparatus IMP via a substrate S disposed thereon by another device. In this case, the film-forming apparatus IMP does not need to include a distributor DSP.

[0050] The film-forming equipment IMP may include an alignment mirror AS for measuring the positional offset (alignment error) between the substrate S (or the injection area of ​​the substrate S) and the mold M.

[0051] The simulation device 1 performs calculations to predict the behavior of the curable component IM during the process executed by the film-forming device IMP. More specifically, the simulation device 1 performs calculations to predict the behavior of the curable component IM during the process of bringing multiple droplets of the curable component IM arranged on the substrate S into contact with the mold M and forming a film of the curable component IM in the space between the substrate S and the mold M.

[0052] For example, the analog device 1 can be formed by incorporating the simulation program 21 into a general-purpose or special-purpose computer. It should be noted that the analog device 1 can be formed from a PLD (programmable logic device) such as an FPGA (Field-Programmable Gate Array). Alternatively, the analog device 1 can be formed from an ASIC (Application-Specific Integrated Circuit).

[0053] In this embodiment, the simulation device 1 is formed by storing the simulation program 21 in the memory 20 of a computer that includes a processor 10, a memory 20, a display 30, and an input device 40. The memory 20 may be a semiconductor memory, a disk such as a hard disk, or another form of memory. The simulation program 21 may be stored in a computer-readable storage medium or provided to the simulation device 1 via a communication facility such as a telecommunications network.

[0054] The simulation method and apparatus according to the invention relate to the process of forming a film of a curable component in the space between a substrate and a mold, for example, simulating the behavior of the curable component during an imprinting process. More specifically, the simulation method and apparatus according to the invention predict the expansion of droplets of the curable component on the substrate (including interactions between droplets) at any given time and visually display it. Furthermore, the simulation method and apparatus according to the invention detect anomalies (anomalies in droplet expansion) caused by air bubbles confined between droplets from the merging state and changes in the merging state of the droplets of the curable component on the substrate, and visually display them. Thus, the expansion behavior (state) of the droplets of the curable component on the substrate can be visually inspected, and anomalies in droplet expansion can be anticipated in advance. By adjusting the droplet arrangement based on the above information, defects caused by infill can be suppressed.

[0055] The simulation method performed by simulation device 1 in each embodiment will now be described in more detail.

[0056] <First Embodiment>

[0057] Figure 2 This is a flowchart describing a simulation method according to a first embodiment. The simulation method includes steps S001, S002, S003, S004, S005, S006, S007, S008, and S009. The simulation device 1 can be understood as a collection of hardware components that perform the various steps of the simulation method according to the first embodiment.

[0058] Step S001 is the step of setting the conditions required for simulation (simulation conditions). Step S002 is the step of setting the initial state of the curable component IM based on the simulation conditions set in step S001. Steps S001 and S002 can be understood as a single step obtained by combining steps S001 and S002, for example, as a preparation step. Step S003 is the step of updating (calculating) the position of the mold M (the distance between the substrate S and the mold M) by calculating the movement of the mold M. Step S004 is the step of calculating the behavior (flow) of the droplets pressed and expanded by the mold M for each of the multiple droplets of the curable component IM based on the position of the mold M updated in step S003. Step S005 is the step of determining whether adjacent droplets of the multiple droplets of the curable component IM merge with each other based on the droplet behavior calculated in step S004. Step S006 is the step of calculating the merging information of each of the multiple droplets of the curable component IM based on the determination in step S004 regarding whether adjacent droplets merge with each other. Step S007 is a step of determining whether an anomaly exists in the behavior of the curable component IM at the corresponding time based on the merged information calculated in step S006 and its temporal changes (that is, detecting anomalies in the behavior of the curable component IM). Step S008 is a step of determining whether the time in the calculation (simulation) has reached the end time. If the time in the calculation has not reached the end time, the time advances to the next time, and the process moves to step S003; otherwise, the process moves to step S009. Step S009 is a step of displaying at least one of the merged information calculated in step S006 and the anomaly information indicating the presence or absence of anomalies in the behavior of the curable component determined in step S007, together with information indicating the state of multiple droplets of the curable component IM (the behavior of the curable component IM).

[0059] Each step of the simulation method according to the first embodiment will now be described in detail.

[0060] In step S001, various parameters are set to the conditions required for simulation. These parameters include the arrangement of droplets of the curable component IM on the substrate S, the volume of each droplet, the physical properties of the curable component IM, information regarding the surface roughness of the mold M (e.g., information about the pattern of the patterned region PR), and information regarding the surface roughness of the substrate S. Parameters also include the time curve of the force applied to the mold M via the mold drive mechanism MD, and the curve of the pressure applied to the space SP (mold M) via the pressure control unit PC.

[0061] In step S002, the initial state (droplet state at the start of the simulation) of each of the plurality of droplets of the curable component IM is set. The initial state includes the profile (shape) and height of each droplet as it wets and expands on the substrate S. The initial state can be calculated by assuming a static equilibrium state using the physical properties of the curable component IM. Alternatively, the initial state can be calculated based on the dynamic wetting and expansion behavior by performing an overall fluid simulation based on the time elapsed since the droplets from the curable component IM were placed on the substrate S and the physical properties of the curable component IM.

[0062] In the simulation method according to this embodiment, each droplet of the curable component IM is modeled as a droplet element DRP, such as Figure 3 As shown. Figure 3 This is a diagram illustrating the concept of droplet element DRP for curable component IM. (Reference) Figure 3 DRP i This represents the i-th droplet element in the computation region. In the following description, the subscript i indicates the number of droplet elements in the DRP.

[0063] A representative point is set within the droplet element of the curable component IM. The coordinates of the representative point are represented by Ci(x0, y0). The representative point of the droplet element of the curable component IM can be set at the centroid of the droplet or at a point (position) different from the centroid of the droplet, but it must be set within the outline of the droplet. Then, the distance from the representative point of the droplet element of the curable component IM to the point on the outline (periphery) of the droplet element at an angle θ (the angle formed by the baseline and the line connecting the representative point and the point on the outline of the droplet) is represented as the radius r(θ). For each angle θ, the radius r(θ) has a different value. Information indicating whether each point on the outline of the droplet element merges with an adjacent droplet element (intrudes into the adjacent droplet element) is stored together. The position (radius r(θ)) of the point on the outline that merges with an adjacent droplet element is fixed at this time. Figure 3 As shown by the shaded lines, the region with a fixed radius r(θ) and a fixed angle θ is set as a fixed region FIX. i On the other hand, such as Figure 3 As shown by the solid lines, the region with a radius r(θ) and a non-fixed angle θ is defined as the free region FRE. i In the initial state of the droplet of the curable component IM, all angles θ belong to the free region.

[0064] When the simulation method according to this embodiment is implemented as an actual program, a finite number of dividing angles θ are considered to be processed (that is, in order to define the outline of the droplet, a finite number of points are set on the outline of the droplet). Figure 6This is a view showing droplet elements of a curable component IM defined (divided) by 18 angles θ (θ1 to θ18). Here, the angles θ can be set by dividing 360° equally, or they can be set to arbitrary angles. When obtaining a profile between adjacent points on a profile represented by a finite number of angles, any interpolation can be applied. For example, adjacent points on the profile can be connected by lines, or higher-order interpolation can be applied.

[0065] In step S003, the motion of the mold M is calculated and the position of the mold M is updated. The motion of the mold M is calculated by dynamic calculation, taking into account the forces generated when droplets of the curable component IM or liquid films in which droplets merge together are crushed, the forces caused by the flow of gas in the space SP between the mold M and the substrate S, the load applied to the mold M, the effect of the elastic deformation of the mold M, etc.

[0066] In step S004, the behavior of the droplet element DRP, pressed and expanded by the mold M, is calculated. Step S004 includes determining whether the droplet element DRP contacts the mold M. If the droplet element DRP obtained in step S002... i height h drp,i With droplet element DRP i The distance h between the mold M and the substrate S at the representative point (x0, y0) i By comparing the results and satisfying the following expression (1), the droplet element DRP is determined. i Contact mold M.

[0067] h drp,i ≤h i ...(1)

[0068] On the other hand, if expression (1) is not satisfied, then the droplet element DRP is determined. i The mold M is not in contact at the current time in the calculation. In this case, the behavior of the droplet element DRPi is not calculated.

[0069] Regarding the droplet element DRP that was identified as being in contact with mold M i The behavior of being pressed and expanded by the movement of the mold M is calculated. In this step, the volume of the droplet of the curable component IM is preserved (maintained). Therefore, droplet element DRP can be used. i Volume V i The distance h between the droplet element position and the current time i The droplet element DRP at the current time is represented by the following expression. i area S new :

[0070]

[0071] In step S005, it is determined whether adjacent droplet elements merge with each other. Since the profile of the droplet elements was calculated in step S004, points on the profile belonging to the free region FRE at angle θ fall within the adjacent droplet elements (within the profile). In this case, the radius r(θ) at angle θ is fixed (that is, the distance from the representative point to the point on the profile corresponding to the merged portion of the droplet is fixed). In other words, angle θ is included in the fixed region FIX, and after this point, the droplet elements of the curable component IM do not expand (flow) in the direction of angle θ. In step S005, for all pairs of adjacent droplet elements, it is determined whether the droplets merge with each other as described above.

[0072] Reference Figure 4 Describes the process of determining whether adjacent droplet elements merge, i.e., whether points on the droplet profile lie within the profiles of adjacent droplets. This is achieved through droplet element observation (DRP). i Considering the DRP element belonging to the droplet category i Free region FRE i Point P on the contour along the angular direction. And the droplet element DRP. i Adjacent droplet elements are set as droplet element DRPs. j And then obtain the connection point P and the droplet element DRP. j Representative point C j (Center) line segment PC j The length of the line segment PC is also obtained. j The angle θ formed with the baseline of the droplet element j And then obtain the angle θ j The radius QC of the droplet element DRPj at that location j The length of QC. If the radius QC is... j Length and line segment PC j The lengths are compared, and the radius QC j The length of line segment PC j If the length is long, then the droplet element DRP is determined. i Point P on the outline is located in the adjacent droplet element DRP. j Within the outline, that is, the droplet elements merge with each other. On the other hand, if the radius QC j The length of line segment PC j If the length is short, then the droplet element DRP is determined. i Point P on the outline is not located in an adjacent droplet element DRP. j Within the outline, the droplet elements do not merge with each other. It should be noted that... Figure 4 DRP of droplet elements is shown i Point P on the outline greatly intrudes into the adjacent droplet element DRP.j The state within. This emphasizes the characteristics of this embodiment. In actual calculations, by making the time interval sufficiently short, the droplet element DRP i Point P on the outline invades the adjacent droplet element DRP j The amount of intrusion within can be reduced to a negligible level.

[0073] Figure 5 This is a diagram illustrating an example of calculating the behavior (extended) of droplets of the curable component IM using a simulation device 1 implementing the simulation method according to this embodiment. The distance between the mold M and the substrate S is oriented towards... Figure 5 The center is shorter and farther away. Figure 5 The center is longer. (Reference) Figure 5 Obviously, the complex merging state of droplets can be represented by the arrangement of droplets of the curable component IM on the substrate S.

[0074] In step S006, merging information is calculated based on the determination of whether adjacent droplet elements have merged with each other. Merging information refers to an evaluation value used to assess the relationship related to the degree of merging of adjacent droplets. For example, in this embodiment, information indicating the portion of the profile of each droplet of curable component IM that contacts the profile of another droplet is used as merging information. More specifically, the ratio of the portion contacting another droplet to the length of the profile of the droplet of curable component IM, i.e., the ratio of the portion contacting the profile of an adjacent droplet to the entire circumference of the droplet profile, is used as merging information. At this time, the profile of the droplet of curable component IM can be divided into multiple angles, and the ratio of the angles contacting another droplet can be used as merging information.

[0075] refer to Figure 6 This describes the merging ratio of the profile lengths of adjacent droplets relative to the curable component IM, i.e., an overview of the merging information in this embodiment. Figure 6 In the diagram, reference numeral 601 denotes the outline of the target droplet element, and reference numeral 602 denotes the outline of the droplet element adjacent to the target droplet element. The outline 601 of the target droplet element is sampled at multiple points 603, and for each of the multiple points 603, it is determined whether point 603 contacts the outline 602 of an adjacent droplet element. For example, among the multiple points 603, point 604 is determined to be the point that contacts the outline 602 of an adjacent droplet element. Finally, the ratio of the number of points 604 that contact the outline 602 of an adjacent droplet element to the total number of sampling points 603 of the outline 601 of the target droplet element is used as merged information.

[0076] In step S009, the merging information obtained as described above, together with information indicating the state (expansion state) of the droplets of the curable component IM corresponding to the merging information, is displayed on the display 30. Figure 7This is a view showing an example of an image including the merged information displayed on the display 30 in step S009. Figure 7 In the middle, the merging information is relative to the droplet elements DRP arranged in the injection region ST of the substrate S. i The distribution is displayed in color. In this embodiment, for each droplet element DRP i Droplet element DRP i The color in the region changes according to the ratio of the merged portion to the outline length of the droplet.

[0077] Consider a scenario where, when the mold M comes into contact with the curable component IM on the substrate S, the mold M deforms toward the substrate S in a convex shape. In this case, droplet elements DRP arranged at the center of the injection region ST... i DRP droplet elements arranged on the outside of the injection area ST i Sequential compression and expansion of droplet elements DRP i Therefore, the droplet element DRP is arranged at the center of the injection region ST. i DRP droplets are often placed outside the injection zone ST. i It exhibits a higher merger rate with adjacent droplets. Figure 7 In the process, for each droplet element, DRP i Droplet element DRP i The density within a region varies depending on the merging ratio with neighboring droplets. Droplet elements with higher merging ratios with neighboring droplets (DRP) i The areas of the droplets are displayed in a darker color. More specifically, the areas of the droplet elements are displayed in a brighter color according to the order of droplet elements DRP1, DRP2, and DRP3, that is, according to their distance from the center of the injection area ST. Like droplet element DRP4, if a droplet element does not contact an adjacent droplet, its area is displayed in white. It should be noted that by displaying droplet elements DRP in different colors... i Regions and droplet elements DRP i The outline is used to distinguish them from each other (distinguishable), and the boundary with adjacent droplets can also be checked.

[0078] In this embodiment, the case where the density in the droplet region corresponding to the merging information changes according to the size of the merging information has been described, but the invention is not limited thereto. For example, the hue in the droplet region corresponding to the merging information can be changed according to the size of the merging information. Furthermore, by displaying a general example of the relationship between the color representing the size of the merging information and the size of the merging information indicated by the color (in this embodiment, the merging ratio with adjacent droplets), the merging information can be grasped numerically. Therefore, for each of the multiple droplets of the curable component IM, the contact state of the droplets as the expanded state of the droplets can be visually grasped.

[0079] In step S007, based on the merging information calculated in step S006 and its temporal changes, it is determined whether or not anomalies exist in the behavior of the curable component IM at the corresponding time (that is, anomalies in the behavior of the curable component IM are detected). Typically, as contact progresses between the curable component IM on the substrate S and the mold M, the merging ratio with adjacent droplets increases from the droplet element DRP arranged near the center of the injection region ST. i The droplet elements DRP begin to increase and move towards the periphery of the injection area ST. i Gradually increase. On the other hand, if the behavior of the curable component IM becomes abnormal, then the droplet element DRP arranged near the center of the injection area ST... i The DRP exists in the droplet compared to the surrounding droplet elements. i Droplet elements DRP with a smaller coalescence ratio with adjacent droplets i .

[0080] Figure 8 This is an example view showing an image, including merged information, displayed on the display 30 in step S009 when the behavior of the curable component IM has become abnormal. Figure 8 In the middle, the merging information is relative to the droplet elements DRP arranged in the injection region ST of the substrate S. i The distribution is displayed in color. In this embodiment, for each droplet element DRP i Droplet element DRP i The color in the region changes according to the ratio of the merged portion to the length of the droplet's outline. Figure 8 Among them, droplet elements with a higher merging ratio with adjacent droplets are DRP. i The area is displayed in a darker color.

[0081] Typically, droplet elements DRP are arranged near the center of the injection region ST. i It has a higher merging ratio with adjacent droplets, and its area is arranged with the center of the droplet element far away from the injection area ST. iCompared to displaying it in a darker color. However, in Figure 8 In the middle, droplet elements DRP are arranged near the center of the injection region ST. i The area of ​​droplet element DRP1 is displayed in a brighter color than the area of ​​the surrounding droplet element DRP2. More specifically, the area of ​​droplet element DRP2, located outside droplet element DRP1 within the injection area ST, is displayed in a darker color than the area of ​​droplet element DRP1. Thus, it is clear that the behavior of droplet element DRP1 is significantly abnormal.

[0082] The following describes an example of a method for detecting abnormal behavior of a curable component IM. This is a method for searching for and detecting droplets that are abnormal, wherein the droplet is surrounded by droplets whose entire profile is merged with adjacent droplets and includes a portion of the profile that is not merged with adjacent droplets. More specifically, droplets with a lower merging ratio with adjacent droplets compared to surrounding droplets are detected as abnormal droplets. In this embodiment, the presence / absence of an anomaly is determined by following a process including (1), (2), and (3) below. It should be noted that in the state where the entire profile is not merged with adjacent droplets, the droplet merging information is represented by 0; in the state where the entire profile is merged with adjacent droplets, the droplet merging information is represented by 1; and in the state where a portion of the profile is merged with adjacent droplets, the droplet merging information is represented by a value between 0 and 1.

[0083] (1) From all droplets, extract a subset of droplets whose contours do not merge with adjacent droplets, i.e., droplets whose merging information is not 1, and consider the extracted droplets to be included in droplet group DG1 (e.g., Figure 8 The droplet element shown is DRP1.

[0084] (2) From all droplets included in droplet group DG1, extract droplets whose representative points fall within a predetermined distance D from the representative points of droplets included in droplet group DG1, and consider the extracted droplets to be included in droplet group DG2 (e.g., Figure 8 The droplet element shown is DRP2). Figure 8 In the figure, reference numeral 801 indicates the range of distance D from the droplet element DRP1, i.e., the droplet extraction range.

[0085] (3) For each droplet included in all droplets in droplet group DG1, if all droplets included in each droplet group DG2 are in a state where their entire outline is merged with adjacent droplets (merging information is 1), an anomaly is determined to have occurred. Furthermore, if the droplets included in each droplet group DG2 have greater merging information than the droplets included in droplet group DG1, an anomaly is determined to have occurred.

[0086] In step S009, the abnormal behavior of the curable component IM detected as described above is displayed on the display 30 together with abnormal information indicating the presence / absence of the abnormal behavior of the curable component IM and information indicating the state (expansion state) of the droplets of the curable component IM. Figure 9 This is a view showing an example of an image including the abnormal information displayed on the display 30 in step S009. Figure 9 In China, for Figure 8 Each droplet element DRP shown i The system determines whether an anomaly has occurred, and the area of ​​the droplet element DRP1 identified as anomalous is displayed in black. Alternatively, the droplet element DRP1 identified as anomalous can be displayed in a different color than the droplets identified as normal (not anomalous) (e.g., droplet element DRP2). In this way, by displaying the droplets identified as anomalous and those identified as normal in different colors to distinguish them from each other, the presence / absence of an anomaly can be visually assessed. Alternatively, the droplets identified as anomalous and those identified as normal can be displayed in different modes. For example, the droplets identified as anomalous may flash, while the droplets identified as normal may not flash.

[0087] The calculation steps, including S003, S004, S005, S006, and S007, are performed at multiple preset times. For example, multiple times are arbitrarily set within the time period from the time when the mold M begins to descend from its initial position until the mold M contacts multiple droplets. The multiple droplets are crushed to expand and merge with each other to eventually form a film, and the curable component should be cured. Typically, multiple times are set at predetermined time intervals.

[0088] In step S008, it is determined whether the calculated time has reached the end time. As described above, if the calculated time has not yet reached the end time, the time advances to the next time step, and the process moves to step S003; otherwise, the process moves to step S009. In the example, in step S008, the current time is advanced by a specified time step to set a new time. Then, if the new time has reached the end time, the process moves to step S009.

[0089] As described above, in step S009, the display is shown on the display 30. Figure 7 The image shown Figure 8 The image shown and Figure 9 At least one of the images shown. In step S009, for example, based on a user request, the image can be switched and displayed. Figure 7 The image shown Figure 8 The image shown and Figure 9 The image shown, or can be displayed Figure 7 The image shown Figure 8 The image shown and Figure 9 Some or all of the images shown.

[0090] According to this embodiment, the presence / absence of anomalies in the behavior of each of a plurality of droplets of the curable component IM disposed on the substrate S can be determined, particularly in droplet expansion, and can be visually identified. Therefore, a technique can be provided that facilitates the detection of anomalies in the behavior of the curable component IM during the formation of a film of the curable component IM in a film-forming apparatus (IMP). Furthermore, by repeatedly adjusting the arrangement pattern of the droplets of the curable component IM using the simulation method according to this embodiment and the resulting conditions, the conditions for the process of forming a film of the curable component IM can be easily set, while reducing anomalies in the process.

[0091] <Second Embodiment>

[0092] Figure 10 This is a flowchart describing a simulation method according to a second embodiment. The simulation method includes steps S101, S102, S103, S104, S105, S106, S107, S108, and S109. The simulation device 1 can be understood as a collection of hardware components that perform the various steps of the simulation method according to the second embodiment.

[0093] Step S101 is the step of setting the conditions required for the simulation (simulation conditions). Step S102 is the step of generating a link structure connecting adjacent droplets based on the droplet arrangement information of the curable component IM set in step S101. Steps S101 and S102 can be understood as a single step obtained by combining steps S101 and S102, for example, as a preparation step. Step S103 is the step of updating the position of the mold M by calculating the movement of the mold M. Step S104 is the step of calculating the behavior of the droplets pressed and expanded by the mold M for each of the multiple droplets of the curable component IM based on the position of the mold M updated in step S103. Step S105 is the step of determining whether each link of the link structure generated in step S102 is closed, that is, determining whether the link is open or closed. Step S106 is the step of calculating the merging information of each of the multiple droplets of the curable component IM based on the determination in step S105 regarding whether each link of the link structure is closed. Step S107 is a step of determining whether an anomaly exists in the behavior of the curable component IM at the corresponding time based on the merged information calculated in step S106 and its temporal changes (that is, detecting anomalies in the behavior of the curable component IM). Step S108 is a step of determining whether the time in the calculation (simulation) has reached the end time. If the time in the calculation has not reached the end time, the time advances to the next time, and the process moves to step S103; otherwise, the process moves to step S109. Step S109 is a step of displaying at least one of the merged information calculated in step S106 and the anomaly information indicating the presence or absence of anomalies in the behavior of the curable component determined in step S107, together with information indicating the state of multiple droplets of the curable component IM (the behavior of the curable component IM).

[0094] Each step of the simulation method according to the second embodiment will now be described in detail. It should be noted that steps S101, S103, and S104 are respectively similar to... Figure 2 Steps S001, S003, and S004 are shown, and their detailed descriptions will be omitted here.

[0095] In step S102, a link structure connecting adjacent droplets is generated based on the droplet arrangement information of the curable component IM. (Reference) Figure 11 This will describe the link structure. For example... Figure 11 As shown, each droplet of the curable component IM is modeled as a droplet element DRP. (Reference) Figure 11A node ND is generated at the representative point C of the droplet element DRP, and links are generated by connecting adjacent nodes. More specifically, links are generated between nodes in droplet elements near the portion where the solidifiable component IM merges, and are defined as line segments connecting two nodes. If the two droplet elements forming a link merge, the link is called a closed link (LNC). If the two droplet elements forming a link do not merge, the link is called an open link (LNO). Note that when describing a link without distinguishing between closed and open links, the link is called a link (LN). Links are generated such that they always intersect each other at nodes and never intersect each other outside of nodes (that is, links are generated only between adjacent droplet elements). For example, methods such as the Deloney partitioning method are used to generate this link structure.

[0096] In step S105, for all links LN, the open / closed nature of the link is determined. In this embodiment, within each link LN, if the droplet elements forming the link LN do not merge with each other, the link is determined to be an open link LNO. If the droplet elements forming the link LN merge with each other, the link LN is determined to be a closed link LNC. (See reference...) Figure 4 To determine whether adjacent droplet elements have merged, a process can be used to determine whether a point on the droplet's profile lies inside the profile of an adjacent droplet. More specifically, as... Figure 4 As shown, if the radius QC j Length and line segment PC j The lengths are compared, and the radius QC j The length of line segment PC j If the length of the link LN is long, then the link LN is considered closed. On the other hand, if the radius QC is... j Length and line segment PC j The lengths are compared, and the radius QC j The length of line segment PC j If the length is short, then the link LN is determined to be open.

[0097] In step S106, merging information is calculated using the determination results regarding the open / closed nature of links LN. Merging information refers to an evaluation value used to assess the relationship with the degree of merging of adjacent droplets. For example, in this embodiment, information indicating the number of closed links in the links of each droplet of the curable component IM is used as merging information. More specifically, the ratio of closed links LNC to links LN generated for the droplet element DRP is used as merging information.

[0098] In step S109, the merging information obtained as described above, together with information indicating the state (expansion state) of the droplets of the curable component IM corresponding to the merging information, is displayed on the display 30. Figure 12 This is a view showing an example of an image including the merged information displayed on the display 30 in step S109. Figure 12 In the middle, the merging information is relative to the droplet elements DRP arranged in the injection region ST of the substrate S. i The distribution is shown in color. Furthermore, in Figure 12 In the process, for each droplet element, DRP i At the node located in the droplet element DRP i In the link LN, solid lines represent closed links LNC, and dashed lines represent open links LNO. In this embodiment, for each droplet element DRP... i The droplet element DRP is changed according to the ratio of closed-link LNC. i The color in the area.

[0099] Consider a scenario where, when the mold M comes into contact with the curable component IM on the substrate S, the mold M deforms toward the substrate S in a convex shape. In this case, droplet elements DRP arranged at the center of the injection region ST... i DRP droplet elements arranged on the outside of the injection area ST i Droplet element DRP i They are sequentially squeezed and expanded. Therefore, the droplet element DRP arranged at the center of the injection region ST... i DRP droplets are often placed outside the injection zone ST. i It has a higher ratio of closed-link LNCs. In Figure 12 In the process, for each droplet element, DRP i The droplet element DRP is changed according to the ratio of closed-link LNC. i The density in the region. Droplet element DRP with a high ratio of closed-linked LNCs. i The areas of the droplet elements are displayed in a darker color. More specifically, in the order of droplet elements DRP1, DRP2, and DRP3, that is, in order of distance from the center of the injection area ST, the areas of the droplet elements are displayed in a brighter color. Like droplet element DRP4, if a droplet element does not contact an adjacent droplet, that is, if the ratio of the closed link LNC is 0, its area is displayed in white. It should be noted that by displaying droplet elements DRP in different colors... i Regions and droplet elements DRP i The outline is used to distinguish them from each other (distinguishable), and the boundary with adjacent droplets can also be checked.

[0100] In this embodiment, the case where the density in the region of the droplet corresponding to the merging information changes according to the size of the merging information has been described, but the invention is not limited thereto. For example, the hue in the region of the droplet corresponding to the merging information can be changed according to the size of the merging information. Furthermore, by showing a general example of the relationship between the color representing the size of the merging information and the size of the merging information indicated by the color (in this embodiment, the ratio of the closed link LNC), the merging information can be grasped numerically. Therefore, for each of the multiple droplets of the curable component IM, the contact state of the droplet as the expansion state of the droplet can be visually grasped. Furthermore, since in Figure 12 In the diagram, solid lines represent closed links (LNC) and dashed lines represent open links (LNO), thus allowing for a visual understanding of whether droplets merge or not.

[0101] In step S107, based on the merged information calculated in step S106 and its temporal changes, it is determined whether there are any anomalies in the behavior of the curable component IM at the corresponding time (that is, anomalies in the behavior of the curable component IM are detected). Typically, as contact progresses between the curable component IM on the substrate S and the mold M, the ratio of the closed-link LNC increases from the droplet element DRP arranged near the center of the injection region ST. i It begins to increase, and moves towards the droplet elements DRP arranged around the injection area ST. i Gradually increase. On the other hand, if anomalies have already occurred in the behavior of the curable component IM, then the droplet element DRP arranged near the center of the injection area ST... i DRP containing droplet elements i It has higher density than the surrounding droplet elements DRP i A lower ratio of closed-link LNCs.

[0102] Figure 13 This is an example view showing an image, including merged information, displayed on the display 30 in step S109 when the behavior of the curable component IM becomes abnormal. Figure 13 In the middle, the merging information is relative to the droplet elements DRP arranged in the injection region ST of the substrate S. i The distribution is displayed in color. In this embodiment, for each droplet element DRP i The droplet element DRP is changed according to the ratio of closed-link LNC. i The color in the area. Figure 13 In the droplet element DRP, a high ratio of closed-linked LNCs is observed. i The area is displayed in a darker color.

[0103] Typically, droplet elements DRP are arranged near the center of the injection zone ST. iIt has a higher ratio of closed-loop LNCs, and its region is arranged with droplet steps DRPs that are far from the injection region ST center. i Compared to displaying it in a darker color. However, in Figure 13 In the middle, droplet elements DRP are arranged near the center of the injection region ST. i The area of ​​the droplet element DRP1 is displayed in a brighter color than the area of ​​the surrounding droplet element DRP2. More specifically, the area of ​​droplet element DRP2, located outside droplet element DRP1 within the injection area ST, is displayed in a darker color than the area of ​​droplet element DRP1. This clearly indicates that the behavior of droplet element DRP1 has become abnormal.

[0104] The following describes an example of a method for detecting abnormal behavior of a curable component IM. This is a method for searching for droplets surrounded by all closed-link LNs (Linked Links N) and including open-linked LNOs within the linked LNs, and detecting such droplets as those in which anomalies have occurred. In this embodiment, the presence / absence of an anomaly is determined (anomaly detection) by following a process comprising (1), (2), and (3) below. It should be noted that the merging information of droplets where all linked LNs are open-linked LNOs is indicated by 0, the merging information of droplets where all linked LNs are closed-linked LNCs is indicated by 1, and the merging information of droplets where some linked LNs are closed-linked LNCs is indicated by a value between 0 and 1 based on the ratio of closed-linked LNCs.

[0105] (1) From all droplets, extract droplets that include open-link LNO, i.e., droplets where the merged information is not 1, and consider the extracted droplets to be included in droplet group DG1 (e.g., Figure 13 The droplet element shown is DRP1.

[0106] (2) From all droplets included in droplet group DG1, extract droplets whose representative points fall within a preset distance D from the representative points of the droplets included in droplet group DG1, and consider the extracted droplets to be included in droplet group DG2 (e.g., Figure 13 The droplet element shown is DRP2). Figure 13 In the figure, reference numeral 1301 indicates the range of distance D from droplet element DRP1, i.e., the droplet extraction range.

[0107] (3) An anomaly is determined to have occurred if the node is located at all links LNs of all droplets included in each droplet group DG2 and all links LNCs are closed links (merging information is 1). Furthermore, an anomaly is determined to have occurred if the droplets included in each droplet group DG2 have greater merging information than the droplets included in droplet group DG1.

[0108] In step S109, the abnormal behavior of the curable component IM detected as described above is displayed on the display 30 together with information indicating the presence / absence of the abnormal behavior of the curable component IM and the state (expansion state) of the droplets of the curable component IM. Figure 14 This is a view showing an example of an image including the abnormal information displayed on the display 30 in step S109. Figure 14 In China, for Figure 13 Each droplet element DRP shown i To determine if an anomaly has occurred, the area of ​​droplet element DRP1 identified as anomalous is displayed in black. Alternatively, droplet element DRP1 identified as anomalous is displayed in a different color than droplets identified as normal (not anomalous) (e.g., droplet element DRP2). In this way, by displaying droplets identified as anomalous and droplets identified as normal in different colors to distinguish them from each other, the presence / absence of an anomaly can be visually assessed. Alternatively, droplets identified as anomalous and droplets identified as normal can be displayed in different display modes. For example, droplets identified as anomalous may flash, while droplets identified as normal may not flash. Note that in Figure 14 In the diagram, since closed links (LNC) are represented by solid lines and open links (LNO) are represented by dashed lines, it is possible to visually determine whether droplets in the parts where anomalies have occurred are merging or not.

[0109] The calculation steps, including S103, S104, S105, S106, and S107, are performed at multiple preset times. For example, multiple times are arbitrarily set within a period from the time when the mold M begins to descend from its initial position until the time when the mold M contacts multiple droplets. The multiple droplets are crushed to expand and merge with each other to eventually form a film, and the curable component should be cured. Typically, multiple times are set at predetermined time intervals.

[0110] In step S108, it is determined whether the calculated time has reached the end time. As described above, if the calculated time has not yet reached the end time, the time advances to the next time step, and the process moves to step S103; otherwise, the process moves to step S109. In the example, in step S108, the current time is advanced by a specified time step, thereby setting a new time. Then, if the new time has reached the end time, the process moves to step S109.

[0111] As described above, in step S109, the display is shown on the display 30. Figure 12 The image shown Figure 13 The image shown and Figure 14 At least one of the images shown. In step S109, for example, based on a user request, the image can be switched and displayed. Figure 12The image shown Figure 13 The image shown and Figure 14 The image shown, or can be displayed Figure 12 The image shown Figure 13 The image shown and Figure 14 Some or all of the graphics in the image shown.

[0112] According to this embodiment, the presence / absence of anomalies in the behavior of each of a plurality of droplets of the curable component IM disposed on the substrate S can be determined, particularly in droplet expansion, and can be visually identified. Therefore, a technique can be provided that facilitates the detection of anomalies in the behavior of the curable component IM during the formation of a film of the curable component IM in a film-forming apparatus (IMP). Furthermore, by repeatedly adjusting the arrangement pattern of the droplets of the curable component IM using the simulation method according to this embodiment and the resulting conditions, the conditions for the process of forming a film of the curable component IM can be easily set, while reducing anomalies in the process.

[0113] <Third Embodiment>

[0114] Figure 15 This is a flowchart describing a simulation method according to a third embodiment. The simulation method includes steps S201, S202, S203, S204, S205, S206, S207, S208, S209, and S210. The simulation device 1 can be understood as a collection of hardware components that perform the various steps of the simulation method according to the third embodiment.

[0115] Step S201 is the step of setting the conditions required for the simulation (simulation conditions). Step S202 is the step of generating a link structure connecting adjacent droplets based on the droplet arrangement information of the curable component IM set in step S201. Steps S201 and S202 can be understood as a single step obtained by combining steps S201 and S202, for example, as a preparation step. Step S203 is the step of updating the position of the mold M by calculating the movement of the mold M. Step S204 is the step of calculating the behavior of the droplets pressed and expanded by the mold M for each of the multiple droplets of the curable component IM based on the position of the mold M updated in step S203. Step S205 is the step of determining whether each link of the link structure generated in step S202 is closed, that is, determining the open / closed nature of the link. In step S206, the presence / absence of a closed region formed by adjacent droplets when the pressed and expanded droplets merge with each other is determined. Step S207 is a step of calculating the merging information of each droplet among the multiple droplets of the curable component IM based on the determination results in step S205 and step S206. Step S208 is a step of determining whether there is an anomaly in the behavior of the curable component IM at the corresponding time (that is, detecting anomalies in the behavior of the curable component IM) based on the merging information calculated in step S207 and its temporal changes. Step S209 is a step of determining whether the time in the calculation (simulation) has reached the end time. If the time in the calculation has not reached the end time, the time advances to the next time and the process moves to step S203; otherwise, the process moves to step S210. Step S210 is a step of displaying at least one of the merging information calculated in step S207 and the anomaly information indicating the presence / absence of anomalies in the behavior of the curable component determined in step S208, together with information indicating the state of the multiple droplets of the curable component IM (the behavior of the curable component IM).

[0116] Each step of the simulation method according to the third embodiment will now be described in detail. It should be noted that steps S201, S202, S203, S204, and S205 are respectively similar to... Figure 10 The detailed descriptions of S101, S102, S103, S104, and S105 shown are omitted here. Each droplet of the curable component IM is modeled as a droplet element DRP.

[0117] In step S206, it is determined whether a closed region formed by adjacent droplets exists. The existence or non-existence of a closed region is determined by referring to the determination in step S205 regarding whether each link of the linked structure is closed and whether adjacent closed links are connected to form a closed pattern (loop).

[0118] refer to Figure 16A and Figure 16B This will provide a more specific description of the determination of the existence / non-existence of closed regions. Figure 16A This is a view showing the extended state of a droplet element at a given time, and Figure 16B It shows from Figure 16A The shown view represents the expanded state of a droplet element after a given time period. Figure 16A and Figure 16B In this context, the LN link connects adjacent droplet elements generated in step S202.

[0119] exist Figure 16A The link connecting representative point C1 of droplet element DRP1 and representative point C3 of droplet element DRP3, as shown in the figure, is determined to be an open link LNO. 13 Similarly, the link connecting representative point C2 of droplet element DRP2 and representative point C3 of droplet element DRP3 was determined to be an open link LNO. 23 Similarly, the link connecting the representative point C1 of droplet element DRP1 and the representative point C2 of droplet element DRP2 is determined to be an open link LNO. 12 .like Figure 16B As shown, after a given time period, these links are identified as closed links (LNCs). 13 Linking LNC 23 and link LNC 12 (That is, droplet elements DRP1, DRP2, and DRP3 merge with each other). For example... Figure 16B As shown, if the closed link LNC exists, then the existence / non-existence of the closed region is determined.

[0120] Next, the method for determining the existence / non-existence of a closed region will be described. First, based on the determination of the open / closed nature of the links, among each link that has been transformed from an open link to a closed link, the closed link in the target region is selected as the starting point. Then, at the closed link used as the starting point, it is determined whether the adjacent links are closed links. If the adjacent link is a closed link, it is selected as the starting point. Then, using the adjacent closed link as the starting point, it is determined whether its adjacent links are closed links. By repeating this process, if a closed figure is formed by the links selected as closed links, a closed region is determined to exist. It should be noted that if multiple adjacent closed links exist when selecting adjacent closed links, the closed region can be appropriately extracted by continuing to select the adjacent closed link with the largest (or smallest) angle to the closed link used as the starting point.

[0121] refer to Figure 16B This will describe in more detail the method for determining the presence / absence of closed regions. First, select the newly identified closed links (LNCs). 12 This serves as a link used as a starting point. Then, a closed link (LNC) is formed through attention.12 Starting from the target node, search for a closed link among adjacent links in one of the nodes (droplet elements DRP1 and DRP3). Here, for the node of droplet element DRP1, the closed link LNC is... 14 and LNC 13 It is a candidate. Note that the closed-link LNC... 14 This is a closed link corresponding to the link connecting representative point C1 of droplet element DRP1 and representative point C4 of droplet element DRP4. Then, the closed link LNC... 12 and closed link LNC 14 The angle θ between 14 With closed link LNC 12 and closed link LNC 13 The angle θ between 13 The comparisons are made, and the closing link with the larger angle is selected as the closing link to be used as the next starting point. Here, the angle θ 13 Greater than angle θ 14 Therefore, choose closed-link LNC. 13 This serves as the starting point for the next closed link. By repeating the process described above, when using the closed link LNC as the starting point... 23 When selecting adjacent closed links, the already selected links LNC 12 It was selected again. Therefore, a closed region was determined to have been formed. Figure 17 The diagram shows a closed region formed by five droplet elements: DRP1, DRP2, DRP3, DRP4, and DRP5. Similarly, in... Figure 17 As in Figure 16, the presence or absence of a closed region formed by a large number of droplet elements can be determined by repeatedly selecting adjacent closed links.

[0122] In step S207, merging information is calculated using the determination results regarding the opening / closing of links LN and the determination results regarding the presence / absence of closed regions. Merging information refers to an evaluation value used to assess the relationship with the degree of merging of adjacent droplets. In this embodiment, the amount of bubbles contained in the closed region formed by multiple adjacent closed links is used as merging information.

[0123] Figure 18A and Figure 18B This is a view describing a method for calculating the amount of bubbles contained within a closed region. In this embodiment, as merged information, the amount V of bubbles contained within the closed region formed by droplet elements DRP1, DRP2, and DRP3 is calculated. bub . Figure 18A The state of substrate S as viewed from above is shown, and Figure 18B It shows when along Figure 18A The state of substrate S when viewed from the side, as shown by line 1801.

[0124] First, such as Figure 18A As shown, calculate the bubble area S when viewed from above. bub As expressed in equation (3), the area S of the closed region defined by the links forming the closed region. close and the area S of droplet elements DRP1, DRP2, and DRP3 included in the closed region. drp The difference between them yields the bubble area S. bub :

[0125] S bub =S close -S drp ...(3)

[0126] refer to Figure 18B The amount of bubbles V bub It is the amount of air bubbles trapped between the mold M and the substrate S, and is obtained by the following equation (4). Here, h is the distance (height) between the mold M and the substrate S.

[0127] V bub =S bub ×h ...(4)

[0128] It should be noted that in equation (4), the volume of the bubble is calculated as the amount of bubble contained in the closed region, but the invention is not limited thereto. For example, the amount of bubble contained in the closed region can be calculated as the number of gas molecules n contained in the bubble, as expressed by equation (5) below. bub Here, R is the gas constant, and T is the temperature.

[0129]

[0130] In this way, the number of gas molecules contained in the bubble is determined as a quantity proportional to the product of the gas pressure and the bubble volume. It should be noted that the gas pressure can be calculated, for example, as the force exerted on the bubble when it is compressed by the mold M.

[0131] In step S210, the merging information obtained as described above, together with information indicating the state (expansion state) of the droplets of the curable component IM corresponding to the merging information, is displayed on the display 30. Figure 19 This is a view showing an example of an image including the merged information displayed on the display 30 in step S210. Figure 19 In the middle, as merging information, relative to the droplet element DRP arranged in the injection region ST of the substrate S. iThe distribution shows the amount of bubbles calculated by equation (4) or (5). More specifically, the amount of bubbles is displayed by a bubble chart display, where the size of circle 1901 varies according to the amount (size) of the bubbles. For example, as Figure 20 As shown, this displays the droplet element DRP. i Furthermore, the size of the circle 2001, which indicates the amount of bubbles contained within the closed region, changes according to the amount of bubbles. Thus, the amount (and distribution) of bubbles contained within the closed region can be visually assessed.

[0132] In this embodiment, the case where the size of the circle representing the bubble changes according to the amount (size) of the bubble has been described, but the invention is not limited thereto. For example, the hue in the closed region corresponding to the amount of bubble can be changed according to the amount of bubble.

[0133] In step S208, based on the merged information and its temporal changes calculated in step S207, it is determined whether there is an anomaly in the behavior of the curable component IM at the corresponding time (that is, anomalies in the behavior of the curable component IM are detected).

[0134] The following describes an example of a method for detecting abnormal behavior of the curable component IM. In this embodiment, the presence / absence of an anomaly is determined by following a process including (1) and (2) below (anomaly detection).

[0135] (1) As Figure 21 As shown, a graph is generated showing the amount of bubbles contained within the closed region. Figure 21 In the diagram, the vertical axis represents the number of bubbles contained within a closed region, and the horizontal axis represents the number of closed regions, each containing bubbles.

[0136] (2) In Figure 21 In the graph shown, a threshold for the amount of bubbles is set, and bubbles exceeding this threshold are identified as abnormal. Then, droplets forming closed regions including these abnormal bubbles are also identified as abnormal. It should be noted that the threshold is set based on the filling time of the mold M with the curable component IM. For example, if the filling time is long, the amount of bubbles absorbed during filling will increase. Therefore, a large threshold is set. On the other hand, if the filling time is short, the amount of bubbles absorbed during filling will decrease. Therefore, a small threshold is set.

[0137] In step S210, the amount of bubbles that are determined to be abnormal as described above is displayed on the display 30 as abnormal information indicating the presence or absence of abnormalities in the behavior of the curable component IM. Figure 22 This is a view showing an example of an image including the abnormal information displayed on the display 30 in step S210. Figure 22In the process, only bubbles identified as anomalous are displayed as round, with their size varying according to the number of bubbles. This allows for visual inspection of only bubbles identified as anomalous, making it easy to control each droplet element in the DRP (Discharge-Related Processing) analysis. i The abnormal portions within the bubble are shown. It should be noted that in this embodiment, only the bubbles identified as abnormal are displayed; however, information indicating the state (expansion state) of the droplets indicating the curable component IM can also be displayed. This allows for a visual assessment of the abnormal portions (droplets). Furthermore, the bubbles identified as abnormal can be made to flash to distinguish them from other bubbles.

[0138] The calculation steps, including S203, S204, S205, S206, S207, and S208, are performed at multiple preset times. For example, multiple times are arbitrarily set within the time period from when the mold M begins to descend from its initial position until the mold M contacts multiple droplets. The multiple droplets are crushed to expand and merge with each other to eventually form a film, and the curable component should be cured. Typically, multiple times are set at predetermined time intervals.

[0139] In step S209, it is determined whether the calculated time has reached the end time. As described above, if the calculated time has not yet reached the end time, the time advances to the next time step, and the process moves to step S203; otherwise, the process moves to step S210. In the example, in step S209, the current time advances by a specified time step, thereby setting a new time. Then, if the new time has reached the end time, the process moves to step S210.

[0140] As described above, in step S210, the display is shown on the display 30. Figure 19 The image shown Figure 20 The image shown and Figure 22 At least one of the images shown. In step S210, for example, based on a user request, the image can be switched and displayed. Figure 19 The image shown Figure 20 The image shown and Figure 22 The image shown, or can be displayed Figure 19 The image shown Figure 20 The image shown and Figure 22 Some or all of the images shown.

[0141] According to this embodiment, the presence / absence of anomalies in the behavior of each of a plurality of droplets of the curable component IM disposed on the substrate S can be determined, particularly in droplet expansion, and can be visually identified. Therefore, a technique can be provided that facilitates the detection of anomalies in the behavior of the curable component IM during the formation of a film of the curable component IM in a film-forming apparatus (IMP). Furthermore, by repeatedly adjusting the arrangement pattern of the droplets of the curable component IM using the simulation method according to this embodiment and the resulting conditions, the conditions for the process of forming a film of the curable component IM can be easily set, while reducing anomalies in the process.

[0142] Embodiments of the present invention can also be implemented by a computer that reads and executes computer-executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be more fully referred to as a "non-transitory computer-readable storage medium") to perform the functions of one or more embodiments of the above embodiments and / or includes one or more circuits (e.g., application-specific integrated circuits (ASICs)) for performing the functions of one or more embodiments of the above embodiments, and by methods executed by the computer of the system or device, for example, by reading and executing computer-executable instructions from a storage medium to perform the functions of one or more embodiments of the above embodiments and / or controlling one or more circuits to perform the functions of one or more embodiments of the above embodiments. 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 individual computers or individual processors to read and execute computer-executable instructions. The computer-executable instructions may be provided to the computer, for example, from a network or a storage medium. The storage medium may include, for example, a hard disk, random access memory (RAM), read-only memory (ROM), the memory of a distributed computing system, an optical disk (such as an optical disc (CD), a digital versatile optical disc (DVD), or a Blu-ray disc (BD)). TM One or more of the following: flash memory devices and memory cards.

[0143] Other embodiments

[0144] The embodiments of the present invention can also be implemented by providing software (programs) that perform the functions of the above embodiments to a system or device via a network or various storage media, and the computer or central processing unit (CPU) or microprocessor unit (MPU) of the system or device reads out and executes the program.

[0145] The film-forming apparatus IMP, including the simulation device 1, controls the process of bringing a curable component arranged on a first component into contact with a second component and forming a curable component film based on predictions of the behavior of the curable component performed by the simulation device 1.

[0146] The article manufacturing method according to the invention includes the steps of determining, while repeating the above-described simulation method, conditions for a process in which a curable component disposed on a first component contacts a second component to form a curable component film, and the step of performing the process according to the conditions. So far, patterns in which the mold includes a pattern have been described, but the invention is also applicable to patterns in which the substrate includes a pattern.

[0147] Figures 23A to 23F A more specific example of a method for manufacturing an article is shown. For example... Figure 23A As shown, a substrate, such as a silicon wafer, is prepared, wherein a processing material, such as an insulator, is formed on its surface. Next, an imprinting material (a curable component) is applied to the surface of the processing material using a method such as inkjet printing. The state in which the imprinting material is applied to the substrate as multiple droplets is shown here.

[0148] like Figure 23B As shown, the side of the die used for embossing, having a raised and recessed pattern, is formed on the substrate and faces the embossing material on the substrate. For example... Figure 23C As shown, a substrate on which an imprinting material is applied contacts a mold, and pressure is applied. The gap between the mold and the processing material is filled by the imprinting material. In this state, when the imprinting material is irradiated with light, which serves as curing energy, through the mold, the imprinting material is cured.

[0149] like Figure 23D As shown, after the imprinting material is cured, the mold is demolded from the substrate. Therefore, the pattern of the cured product of the imprinting material is 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.

[0150] like Figure 23E As shown, when using a pattern of cured product as an etch resist mask for etching, the areas on the surface of the treated material where the cured product is absent or still relatively thin are removed to form grooves. For example... Figure 23F As shown, when the pattern of a cured product is removed, an article with grooves formed in the surface of the processed material is obtained. The pattern of the cured material is removed here; however, for example, the pattern may be used as an insulating film between layers included in a semiconductor element (in other words, as a component of the article) and is not removed after processing.

[0151] 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 appended claims should be given the broadest interpretation to cover all such variations and equivalent structures and functions.

Claims

1. A simulation method for predicting the behavior of a curable component during the process of bringing a plurality of droplets of a curable component disposed on a first component into contact with a second component and forming a film of the curable component in a space between the first component and the second component, the simulation method comprising: Obtain merging information, which is information related to the degree of merging between each droplet of the curable component and its adjacent droplets, and The merging information obtained in the acquisition step will be displayed together with information indicating the expansion state of the plurality of droplets, and In the obtaining step, for each of the multiple droplets of the curable component, the ratio of the portion of the outline that contacts the adjacent droplet to the total circumference of the droplet outline is obtained as the merging information.

2. A simulation method for predicting the behavior of a curable component during the process of bringing a plurality of droplets of a curable component disposed on a first component into contact with a second component and forming a film of the curable component in a space between the first component and the second component, the simulation method comprising: Obtain merging information, which is information related to the degree of merging between each droplet of the curable component and its adjacent droplets, and The merging information obtained in the acquisition step will be displayed together with information indicating the expansion state of the plurality of droplets, and For each link created by setting a node at each of the multiple droplets of the curable component and connecting the nodes, if the droplets forming the link merge with each other, the link is determined to be a closed link. In the obtaining step, for each of the multiple droplets of the curable component, the ratio of the closed link to the link of the droplet is obtained as the merging information.

3. The simulation method according to claim 2, wherein In the display step, the ratio obtained in the acquisition step is displayed in color.

4. A simulation method for predicting the behavior of a curable component during the process of bringing a plurality of droplets of a curable component disposed on a first component into contact with a second component and forming a film of the curable component in a space between the first component and the second component, the simulation method comprising: Obtain merging information, which is information related to the degree of merging between each droplet of the curable component and its adjacent droplets, and The merging information obtained in the acquisition step will be displayed together with information indicating the expansion state of the multiple droplets. For each link created by setting a node at each of the multiple droplets of the curable component and connecting the nodes, if the droplets forming the link merge with each other, the link is determined to be a closed link. In the obtaining step, the amount of bubbles contained in the closed region formed by multiple adjacent closed links is obtained as the merging information.

5. The simulation method according to claim 4, wherein In the display step, the amount of bubbles obtained in the acquisition step is displayed as a circle.

6. The simulation method according to claim 1 or 4, further comprising: Based on the merged information obtained in the obtaining step, it is determined whether there are or no anomalies in the behavior of the curable components during the process.

7. The simulation method according to claim 6 further includes: Information indicating the presence or absence of anomalies in the behavior of the curable components determined in the determination step will be displayed together with information indicating the expansion state of the plurality of droplets.

8. The simulation method according to claim 7, wherein In the determination step, if an anomaly is determined in the behavior of the curable component during the process, the droplets from a plurality of droplets of the curable component that have exhibited the anomaly are designated.

9. The simulation method according to claim 8, further comprising: Display the droplets that have shown abnormalities as specified in the determination step, so that they can be distinguished from droplets that have not shown abnormalities.

10. The simulation method according to claim 9, wherein When the droplets are displayed in a distinguishable manner, the droplets that have shown abnormalities and the droplets that have not shown abnormalities, as specified in the determination step, are displayed in different colors.

11. The simulation method according to claim 9, wherein When the droplets are displayed in a distinguishable manner, the droplets that have exhibited abnormal flickering are identified in the determination step.

12. A simulation apparatus that predicts the behavior of a curable component during the process of bringing a plurality of droplets of a curable component disposed on a first component into contact with a second component and forming a film of the curable component in the space between the first component and the second component, wherein, Obtain merging information, which is information related to the degree of merging between each droplet of the curable component and its adjacent droplets, and The merging information is displayed together with information indicating the expansion state of the multiple droplets. Specifically, for each of the multiple droplets of the curable component, the ratio of the portion of the outline that contacts the adjacent droplet to the total circumference of the droplet outline is obtained as the merging information.

13. A simulation apparatus that predicts the behavior of a curable component during the process of bringing a plurality of droplets of a curable component disposed on a first component into contact with a second component and forming a film of the curable component in the space between the first component and the second component, wherein, Obtain merging information, which is information related to the degree of merging between each droplet of the curable component and its adjacent droplets, and The merging information, along with information indicating the expansion state of the multiple droplets, is displayed. For each link created by setting a node at each of the multiple droplets of the curable component and connecting the nodes, if the droplets forming the link merge with each other, the link is determined to be a closed link. The amount of bubbles contained in the closed region formed by multiple adjacent closed links is obtained as the merging information.

14. A film-forming apparatus comprising the simulation apparatus as defined in claim 12 or 13, wherein Based on predictions of the behavior of the curable component performed by the simulation device, the process of controlling multiple droplets of the curable component arranged on the first component to contact the second component and form a film of the curable component in the space between the first and second components is controlled.

15. A method for manufacturing an article, comprising: While repeating the simulation method defined in any one of claims 1 to 11, the conditions for the process of contacting a plurality of droplets of the curable component disposed on the first member with the second member and forming a film of the curable component in the space between the first member and the second member are determined, and The process is executed according to the stated conditions.

16. A non-transitory storage medium storing a program for causing a computer to perform the simulation method defined in any one of claims 1 to 11.

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