Generation method for arrangement pattern of droplets, information processing device, program, and manufacturing method of article

Abstract

To generate an arrangement pattern of droplets for reducing occurrence of an abnormality, which may occur in a film of a curable composition on a substrate, with computational complexity less than the prior arts in processing for forming the film.SOLUTION: A generation method for an arrangement pattern of droplets is used for processing using a plurality of droplets of a curable composition arranged on a substrate to form a film of the curable composition on the substrate. The generation method includes the steps of: determining a droplet subjected to operation from an initial arrangement pattern; operating each of the droplets determined in the determination step to generate a plurality of arrangement pattern candidates; acquiring an evaluation value of each of the plurality of arrangement pattern candidates; comparing the evaluation values of the plurality of arrangement pattern candidates to select any arrangement pattern candidate from among the plurality of arrangement pattern candidates; and repeating updating processing on the basis of the arrangement pattern candidate selected in the selection step.SELECTED DRAWING: Figure 6

Description

[Technical field]

[0001] The present invention relates to a method for generating a droplet arrangement pattern, an information processing device, a program, and a method for manufacturing an article. [Background technology]

[0002] There is a film forming method in which a curable composition is placed on a substrate, the curable composition is brought into contact with a mold, and the curable composition is cured to form a film made of a cured product of the curable composition on the substrate. Such a film forming method can be applied to an imprinting method, a planarization method, and the like. In the imprinting method, a mold having a pattern is used to transfer the pattern of the mold to the curable composition on the substrate.

[0003] The curable composition is placed in the form of droplets on the substrate. A mold is then pressed against the droplets of the curable composition on the substrate. This causes the droplets to spread and form a film of the curable composition. In such a process, it is important to form a film of the curable composition with a uniform thickness and without any air bubbles in the film.

[0004] The droplet arrangement pattern needs to be adjusted depending on the pattern formed on the mold and the target film thickness. For this reason, in the imprinting apparatus, a droplet arrangement pattern suitable for the mold and imprinting conditions is calculated, and the curable composition is arranged on the substrate according to the droplet arrangement pattern.

[0005] Regarding a method for calculating the droplet arrangement pattern, Patent Document 1 proposes a method for dividing a mold into local regions and calculating the droplet arrangement pattern from pattern density information for each divided region. Patent Document 2 proposes a method for changing the calculation method of the droplet arrangement pattern for each local region. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] US Patent Application Publication No. 2004 / 0065976 [Patent Document 2] JP 2022-182991 A Summary of the Invention [Problem to be solved by the invention]

[0007] The method of calculating the droplet arrangement pattern described in Patent Documents 1 and 2 divides the pattern formed on the mold into similar regions and calculates the droplet arrangement pattern for each divided region, but does not consider the boundaries between the regions. For this reason, at the boundaries between the regions, the thickness of the film may become uneven, or defects may occur due to large bubbles in the film. In addition, the regions formed on the mold include the circuit pattern region, the region of the mark portion used for alignment, and the peripheral region of the mold, and abnormalities may occur at the boundaries between the respective regions due to the above-mentioned boundaries. Hereinafter, the droplet arrangement pattern along the boundaries between different regions is referred to as a discontinuous arrangement pattern.

[0008] At the boundaries between regions decomposed according to the surface state of the above mold, the interactions between droplets are different compared to regions where the droplet pattern is continuous. The interactions between droplets can be calculated by physical simulations such as fluid simulations. However, in the method of generating the droplet arrangement pattern, it is necessary to repeatedly calculate the interactions between droplets. In such repeated calculations, it is not practical to use physical simulations with a large amount of calculations because it requires a huge amount of calculation time.

[0009] Therefore, an exemplary object of the present invention is to generate a droplet arrangement pattern that reduces the occurrence of abnormalities that may occur in a film on a substrate with a smaller amount of calculation than conventional methods in a process for forming a film of a curable composition. [Means for solving the problem]

[0010] In order to achieve the above object, one embodiment of the present invention is a method for generating a droplet arrangement pattern used in a process of forming a film of a curable composition on a substrate using multiple droplets of the curable composition arranged on the substrate, the method comprising the steps of: determining droplets to be operated on from an initial arrangement pattern; generating multiple arrangement pattern candidates by performing operations on each droplet determined in the determining step; acquiring evaluation values ​​for each of the multiple arrangement pattern candidates; selecting one of the arrangement pattern candidates from the multiple arrangement pattern candidates by comparing the evaluation values ​​of the multiple arrangement pattern candidates; and repeating an update process based on the arrangement pattern candidate selected in the selecting step. Effect of the Invention

[0011] According to the present invention, for example, in a process for forming a film of a curable composition, a droplet arrangement pattern that reduces the occurrence of abnormalities that may occur in the film on a substrate can be generated with a smaller amount of calculation than in the past. [Brief description of the drawings]

[0012] [Figure 1] FIG. 2 is a diagram illustrating a configuration of an imprint apparatus IMP. [Diagram 2] 1A to 1C are diagrams showing how an imprint material placed on a substrate spreads. [Diagram 3] 1 is a schematic diagram illustrating a configuration of a system for generating an arrangement pattern of droplets IM. [Figure 4] FIG. 1 is a schematic diagram illustrating the hardware configuration of a calculation server that generates an arrangement pattern of droplets IM. [Diagram 5] FIG. 13 illustrates an anomaly that can occur in an area where the droplet pattern is discontinuous. [Figure 6] FIG. 11 is a flow diagram showing an example of a droplet arrangement pattern generation process in a calculation server. [Figure 7] FIG. 13 is a diagram illustrating an adjustment region. [Figure 8]11A to 11C are diagrams illustrating an example of a method for automatically determining a droplet to be operated. [Figure 9] 13A to 13C are diagrams illustrating a method for determining a droplet to be operated on depending on the size of an abnormality. [Figure 10] 13A and 13B are diagrams illustrating a method for determining a droplet to be manipulated based on the amount of improvement effect when comparing before and after manipulation of the droplet. [Figure 11] FIG. 13 is a diagram illustrating an operation. [Figure 12] FIG. 13 is a diagram for explaining the evaluation method performed in step S607. [Figure 13] FIG. 11 is a diagram illustrating step S610. [Figure 14] FIG. 11 is a diagram for explaining a method of determining an additional update. [Figure 15] 1A to 1C are diagrams for explaining a method for manufacturing an article. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] Hereinafter, the embodiments will be described in detail with reference to the attached drawings. Note that the following embodiments do not limit the invention according to the claims. Although the embodiments describe a number of features, not all of these features are essential to the invention, and the features may be combined in any manner. Furthermore, in the attached drawings, the same reference numbers are used for the same or similar configurations, and duplicated descriptions are omitted.

[0014] Fig. 1 is a diagram showing the configuration of an imprint apparatus IMP. Fig. 1(A) is a schematic diagram showing an example of the configuration of the imprint apparatus IMP according to one embodiment. The imprint apparatus IMP performs an imprint process in which droplets IM of an imprint material on a substrate S are brought into contact with a pattern region MP of a mold M to harden the imprint material, and then the hardened imprint material is separated (peeled off) from the mold M. A pattern is formed on the substrate S by this imprint process.

[0015] As the imprint material, a curable composition (sometimes called an uncured resin) that is cured by applying energy for curing is used. As the energy for curing, electromagnetic waves, heat, etc. can be used. The electromagnetic waves can be, for example, light having a wavelength selected from the range of 10 nm to 1 mm, such as infrared rays, visible light, and ultraviolet rays. The curable composition can be a composition that is cured by irradiation with light or by heating. Among these, the photocurable composition that is cured by irradiation with light contains at least a polymerizable compound and a photopolymerization initiator, and may further contain a non-polymerizable compound or a solvent as necessary. The non-polymerizable compound is at least one selected from the group consisting of a sensitizer, a hydrogen donor, an internal mold release agent, a surfactant, an antioxidant, and a polymer component. The imprint material can be arranged on the substrate in the form of droplets, or in the form of islands or a film formed by connecting a plurality of droplets. The viscosity of the imprint material (at 25° C.) can be, for example, 1 mPa·s to 100 mPa·s. Examples of the material of the substrate include glass, ceramics, metal, semiconductor, and resin. If necessary, a member made of a material different from that of the substrate may be provided on the surface of the substrate. The substrate may be, for example, a silicon wafer, a compound semiconductor wafer, or quartz glass.

[0016] In this specification and the drawings, directions are indicated in an XYZ coordinate system with the horizontal plane as the XY plane. The substrate S is placed on the substrate holder 102 so that its surface is parallel to the horizontal plane (XY plane). The directions parallel to the X-axis, Y-axis, and Z-axis in the XYZ coordinate system are the X direction, Y direction, and Z direction, respectively, and the rotation around the X-axis, the Y axis, and the Z axis are θX, θY, and θZ, respectively. Control or drive regarding the X-axis, Y-axis, and Z-axis means control or drive regarding the direction parallel to the X-axis, the direction parallel to the Y axis, and the direction parallel to the Z axis, respectively. Furthermore, control or drive regarding the θX-axis, θY-axis, and θZ-axis means control or drive regarding the rotation around an axis parallel to the X-axis, the rotation around an axis parallel to the Y axis, and the rotation around an axis parallel to the Z axis, respectively. Furthermore, the position is information that can be specified based on the coordinates of the X-axis, Y-axis, and Z-axis, and the attitude is information that can be specified by the values ​​of the θX-axis, θY-axis, and θZ-axis. Positioning means controlling the position and / or the orientation. Alignment may include controlling the position and / or the orientation of at least one of the substrate and the mold.

[0017] The imprint apparatus IMP may include a substrate holding unit 102 that holds the substrate S, a substrate driving mechanism 105 that drives the substrate holding unit 102 to drive the substrate S, a base 104 that supports the substrate holding unit 102, and a position measurement unit 103 that measures the position of the substrate holding unit 102. The substrate driving mechanism 105 may include a motor such as a linear motor. The imprint apparatus IMP may include a sensor 151 that detects a substrate driving force (alignment load) required for the substrate driving mechanism 105 to drive the substrate S (substrate holding unit 102) during alignment. The substrate driving force in alignment performed in a state in which the imprint material on the substrate S is in contact with the pattern region MP of the mold M corresponds to, for example, a shear force acting between the substrate S and the mold M. The shear force is a force that mainly acts in the planar direction of the substrate S and the mold M. The substrate driving force during alignment is correlated with, for example, the magnitude of the current supplied to the motor of the substrate driving mechanism 105 during alignment, and the sensor 151 can detect the substrate driving force based on the magnitude of the current. The sensor 151 is an example of a sensor that measures the influence (shear force) on the mold M during pattern formation. A drive request (command value) that the control unit 110, which will be described later, issues to the substrate driving mechanism 105 is called a stage control value.

[0018] The imprint apparatus IMP may include a mold holding section 121 that holds a mold (mold) M, a mold driving mechanism 122 that drives the mold M by driving the mold holding section 121, and a support structure 130 that supports the mold driving mechanism 122. The mold driving mechanism 122 may include a motor such as a voice coil motor. The imprint apparatus IMP may include a sensor 152 that detects a release force (separation load) and / or a pressing force. The release force is a force required to separate the mold M from the cured product of the imprint material IM on the substrate S. The pressing force is a force with which the mold M is pressed to bring the mold M into contact with the imprint material IM on the substrate S. The release force and the pressing force are forces that mainly act in a direction perpendicular to the planar direction of the substrate S and the mold M. The release force and the pressing force are correlated to, for example, the magnitude of a current supplied to the motor of the mold driving mechanism 122, and the sensor 152 can detect the separation force and the pressing force based on the magnitude of the current. The sensor 152 is an example of a sensor that measures the influence (mold release force and / or pressing force) that the mold M receives in forming a pattern. In addition, a drive request (command value) that the control unit 110, which will be described later, issues to the mold driving mechanism 122 is also called a stage control value.

[0019] The substrate driving mechanism 105 and the mold driving mechanism 122 constitute a driving mechanism for adjusting the relative position and the relative attitude of the substrate S and the mold M. The adjustment of the relative position of the substrate S and the mold M by the driving mechanism includes driving for contact of the mold with the imprint material on the substrate S and separation of the mold from the hardened imprint material (pattern of the hardened material). The substrate driving mechanism 105 can be configured to drive the substrate S about a plurality of axes (e.g., three axes of the X axis, the Y axis, and the θZ axis, preferably six axes of the X axis, the Y axis, the Z axis, the θX axis, the θY axis, and the θZ axis). The mold driving mechanism 122 can be configured to drive the mold M about a plurality of axes (e.g., three axes of the Z axis, the θX axis, and the θY axis, preferably six axes of the X axis, the Y axis, the Z axis, the θX axis, the θY axis, and the θZ axis).

[0020] The imprint apparatus IMP may include a mold transport mechanism 140 that transports the mold M, and a mold cleaner 150. The mold transport mechanism 140 may be configured to, for example, transport the mold M to the mold holding unit 121, or transport the mold M from the mold holding unit 121 to an original plate stocker (not shown) or the mold cleaner 150. The mold cleaner 150 cleans the mold M with ultraviolet light, a chemical solution, or the like.

[0021] The mold holding part 121 may include a window member 125 that forms a pressure-controlled space CS on the back surface of the mold M (the surface opposite to the pattern area MP in which a pattern to be transferred to the substrate S is formed). FIG. 1(B) is a schematic diagram showing the mold holding part 121 and its periphery. The imprint apparatus IMP may include a deformation mechanism 123 that controls the pressure in the pressure-controlled space CS (hereinafter referred to as cavity pressure) to deform the pattern area MP of the mold M into a convex shape toward the substrate S, as shown diagrammatically in FIG. 1(B).

[0022] The imprint apparatus IMP may also include an alignment measuring instrument 106, a curing unit 107, an imaging unit 112, and an optical member 111. The alignment measuring instrument 106 measures the relative position between the alignment marks of the substrate S and the mold M by illuminating the alignment marks and imaging the images. The imprint apparatus IMP includes multiple alignment measuring instruments 106, and can simultaneously observe multiple alignment marks formed in the shot area of ​​the substrate S and the mold M. For example, the imprint apparatus IMP includes four alignment measuring instruments 106 that observe the alignment marks formed in the shot area of ​​the substrate S and the four corners of the mold M. The alignment measuring instruments 106 may also be positioned by a driving mechanism (not shown) according to the position of the alignment mark to be observed. Hereinafter, an image captured by the alignment measuring instrument is referred to as an alignment image, and an alignment mark position measured by the alignment measuring instrument is referred to as an alignment measurement value. An example of an alignment image observed by an alignment measurement instrument is an image obtained by capturing reflected light from alignment marks on the substrate and mold. Alternatively, an image obtained by capturing an image generated by moire fringes of alignment marks on the substrate and mold may be used.

[0023] The shot area is a partitioned area where a pattern is to be formed. The shot area means, for example, an area having a size equivalent to the pattern area MP of the mold M, that is, a partitioned area (molding area) on the substrate that is molded by the mold M in one imprint cycle.

[0024] The curing unit 107 irradiates the imprint material IM with energy (for example, light such as ultraviolet light) via the optical member 111, thereby curing the imprint material.

[0025] The imaging section 112 captures images of the substrate S, the mold M, and the imprint material IM through the optical member 111 and the window member 125. Hereinafter, the image captured by the imaging section 112 will be referred to as a spread image.

[0026] The imprint apparatus IMP may include a dispenser 108 that places droplets IM of the imprint material on the substrate S. The dispenser 108 ejects the imprint material IM so that the imprint material IM is placed on the substrate S according to, for example, a placement pattern that indicates the placement of the imprint material.

[0027] The imprint apparatus IMP may include a control unit 110 that controls the substrate driving mechanism 105, the mold driving mechanism 122, the deformation mechanism 123, the mold transport mechanism 140, the mold cleaner 150, the alignment measuring instrument 106, the curing unit 107, the imaging unit 112, the dispenser 108, etc. The control unit 110 may be configured by a PLD (abbreviation of Programmable Logic Device) such as an FPGA (abbreviation of Field Programmable Gate Array), an ASIC (abbreviation of Application Specific Integrated Circuit), a general-purpose computer with a program embedded therein, or a combination of all or part of these 113, for example.

[0028] FIG. 2 is a diagram showing how the imprint material arranged on the substrate spreads. Specifically, the process of the mold M being pressed against the imprint material, in which the droplets IM of the imprint material spread, is shown in six diagrams, FIGS. 2(A) to (F), in stages. FIG. 2(A) shows the state immediately after the droplets IM are arranged on the substrate S, in which each droplet IM is small and each imprint material is separated. After that, the droplets IM are pressed by the mold M, and gradually spread as shown in FIGS. 2(B) and (C). Then, by continuing to press the mold M, the droplets IM spread until they come into contact with each other as shown in FIG. 2(D), and the intervals between the droplets IM become smaller as shown in FIG. 2(E), and finally, as shown in FIG. 2(F), the droplets IM spread over the entire mold M.

[0029] In the process of the droplets IM spreading, as shown in FIG. 2(E), air bubbles 201 are formed between the droplets IM, the mold M, and the substrate S. If the droplets IM are cured in a state in which the air bubbles 201 are present, the portions of the air bubbles 201 will become defects. For this reason, in order to improve the productivity of the imprint apparatus IMP, it is important to make the air bubbles 201 smaller so that they disappear in a short time. In this embodiment, a means is provided for generating an arrangement pattern of the droplets IM of a curable composition, taking into consideration the size of the air bubbles 201.

[0030] 3 is a schematic diagram illustrating the configuration of a system 300 that generates an arrangement pattern of droplets IM. The system 300 includes an imprint apparatus IMP, a measurement apparatus 301, a data collection server 302, a simulation server 303, and a calculation server 304. The components of the system 300 are connected to each other via a network 305 so as to be able to communicate with each other.

[0031] The measuring device 301 is a device that inspects the state of the substrate S that has been processed by the imprint device IMP. The measurement results obtained by the measuring device 301 are accumulated in a data collection server 302 via a network.

[0032] The simulation server 303 includes a simulator that executes calculations to predict the behavior of the imprint material IM in a process executed in the imprint apparatus IMP. Specifically, the simulator executes calculations to predict the behavior of the imprint material IM in a process in which a plurality of droplets of the imprint material IM arranged on the substrate S are brought into contact with the mold M to form a film of the imprint material IM in the space between the substrate S and the mold M. By simulating the imprint process, the simulator can generate prediction result data similar to the measurement result data measured by the measuring device 301. The prediction result data generated by the simulation server 303 is accumulated in the data collection server 302 via the network 305.

[0033] The data collection server 302 accumulates the measurement result data. The data collection server 302 receives the measurement result data from the measuring device 301 or the prediction result data from the simulation server 303 via the network 305. The data collection server 302 also transmits the measurement data to the calculation server 304 via the network 305.

[0034] A program for generating an arrangement pattern of droplets IM may be installed in the calculation server 304. Data and the like required for processing by the calculation server 304 are transmitted from the data collection server 302 via the network 305.

[0035] The imprint apparatus IMP receives an arrangement pattern of droplets IM from the calculation server 304 via a network 305. The imprint apparatus IMP arranges droplets IM on the substrate S in accordance with the received arrangement pattern of droplets IM.

[0036] FIG. 4 is a schematic diagram illustrating a hardware configuration of a calculation server 304 that generates an arrangement pattern of droplets IM. Each component of the calculation server 304 functions according to a program. In the example of FIG. 4, a CPU 402 is a processing device that performs calculations related to the generation of a droplet arrangement pattern according to a program and controls each component connected to a system bus 401. A ROM 403 is a memory dedicated to reading data, and stores programs and data. A RAM 404 is a memory for reading and writing data, and is used for saving programs and data. The RAM 404 is also used for temporarily saving data such as the results of calculations by the CPU 402.

[0037] The HDD 405 is also used as a temporary storage area for the operating system (OS) program of the information processing device, as well as for programs and data. The HDD 405 is slower in data input / output than the RAM 404, but is capable of storing large amounts of data. It is desirable that the HDD 405 is a non-volatile storage device that can store data as permanent data so that the data can be referenced for a long period of time. In FIG. 4, a magnetic storage device (HDD) is configured as the storage device, but it may also be a device that reads and writes data by loading external media such as CDs, DVDs, and memory cards.

[0038] The GPU 406 is an arithmetic processing device, and can perform more parallel calculation processing than the CPU 402. The GPU 406 shares with the CPU the calculations related to the generation of droplet arrangement patterns. The communication device 407 is connected to the network 305 and performs data communication using a communication protocol such as TCP / IP, and is used when communicating with other information processing devices.

[0039] The input unit 408 is a device for inputting characters and data to the information processing device, and corresponds to various keyboards, mice, etc. The display unit 409 is a device for displaying information necessary for operating the information processing device, processing results, etc., and corresponds to a CRT or liquid crystal monitor, etc. The display unit 409 may have the function of the input unit 408, such as a touch panel.

[0040] FIG. 5 is a diagram illustrating anomalies that can occur in areas where the droplet pattern becomes discontinuous. Specifically, this figure explains abnormalities that may occur in the state of the surface of the mold M, in other words, in the area where the droplet pattern is discontinuous, such as the boundary between areas divided according to type. FIG. 5(A) is a diagram illustrating the mold M and the patterns formed on the mold M. The types of the surface of the mold M include a circuit pattern 501 intended to form a semiconductor circuit pattern, a mark 502 used for alignment purposes, and a blank area 503 where no pattern is formed. In addition, an area such as a shot peripheral area 504 located on the periphery (outer periphery) of the mold M can also be a boundary. The shot peripheral area 504 is an area where the pattern of the mold M is not formed, and is an area within a range specified in advance.

[0041] 5(B) shows an example of dividing the surface of the mold M into regions according to the type of the surface. The regions may be a first region 505 corresponding to a circuit pattern 501, a second region 507 corresponding to a mark 502, a third region 506 corresponding to a blank region 503, and a fourth region 508 corresponding to a shot periphery 504.

[0042] FIG. 5(C) is a diagram for explaining the boundaries between regions when the mold M is divided according to the type of the surface. Here, the boundaries between the regions correspond to the boundaries between the regions shown in FIG. 5(B). FIG. 5(C) shows a boundary region 509, which is the boundary between the first region 505 and the third region 506, as an example of a boundary. In FIG. 5(C), the arrangement pattern of the droplets IM to be arranged on the substrate S is superimposed on the pattern formed on the mold M shown in FIG. 5(A). In the first region 505 corresponding to the circuit pattern 501 and the third region 506 corresponding to the blank region 503, the arrangement pattern of the droplets IM according to the type of the surface of the mold M is continuously arranged in each region. Specifically, the arrangement pattern of the droplets IM is dense in the first region 505 corresponding to the circuit pattern 501. On the other hand, the arrangement pattern of the droplets IM is sparse in the third region 506 corresponding to the blank region 503.

[0043] The arrangement pattern of the droplets IM differs for each divided region in this way. Therefore, the arrangement pattern of the droplets included in the boundary region 509 is not continuous, and the distance between the droplets IM in the boundary region 509 and the adjacent droplets IM is not uniform, so the arrangement pattern of the droplets IM may be discontinuous. In other words, the boundary region 509 can be said to be a region that includes the boundary between regions where the droplet arrangement is continuous.

[0044] FIG. 5(D) shows the distribution of defects as a result of measuring the substrate S with the measuring device 301 after imprinting with the imprinting device IMP. FIG. 5(D) shows defects 511 measured by the measuring device 301 superimposed on the pattern formed on the mold M shown in FIG. 5(A). It can be seen that defects ER occur at the boundary between the regions when the mold M is divided, as in the boundary region 509. For ease of understanding, the boundary region 509 is also shown in this figure. Note that, as an example, the region is divided according to the pattern formed on the surface of the mold M, but it is also possible to target regions divided according to other factors, such as the region of the substrate S or the distribution of the target film thickness.

[0045] 6 is a flow diagram showing an example of a process for generating an arrangement pattern of droplets IM in the calculation server 304. Specifically, this diagram shows a flow of a process for updating the arrangement pattern of droplets IM to an arrangement pattern that reduces the occurrence of abnormalities in an area where the arrangement pattern of droplets IM becomes discontinuous, such as near a boundary when the mold M is divided into areas. Each operation (step) shown in this flowchart can be executed under the control of the CPU of the calculation server 304.

[0046] In step S601, imprint conditions can be set, such as density information of the mold M, the depth of the groove in the pattern region of the mold M, a target film thickness, etc. Note that the density information of the mold M and the depth of the groove in the pattern region of the mold M can be acquired in advance from design information of the mold M.

[0047] In step S602, an initial arrangement pattern of droplets IM to be updated is set. In step S603, an adjustment region to be updated is determined from the arrangement pattern. FIG. 7 is a diagram illustrating an example of an adjustment region. The adjustment region may be a region including a boundary between different patterns shown in region 701, a region corresponding to a mark and its periphery shown in region 702, or a region corresponding to the outer periphery of the mold M shown in region 703. The adjustment region may be manually specified by a user based on a pattern formed on the mold M, or may be automatically determined based on information on the mold M. For example, the adjustment region is determined based on design information on the mold M to determine a region where the droplet pattern is discontinuous as described above, and the region where the droplet pattern is discontinuous is determined as the adjustment region.

[0048] In step S604, the droplet IM to be actually operated is determined from among the droplets IM to be placed in the adjustment area determined in step S603. All droplets IM included in the adjustment area may be treated as the operation target. On the other hand, in order to shorten the calculation time, it may be possible to narrow down the droplets IM to be operated. Furthermore, the droplet IM to be operated may be determined manually by the user by referring to the droplet arrangement information. Note that the operation of the droplet here refers to making some kind of change to the droplet, including changing (moving) the droplet arrangement position, adding a droplet, deleting a droplet, and changing the volume of the droplet.

[0049] FIG. 8 is a diagram for explaining an example of a method for automatically determining a droplet to be operated. FIG. 8 shows an arrangement pattern of droplets IM and an abnormal ER when imprinting is performed using the arrangement pattern. FIG. 8(A) is a schematic diagram showing an example of an arrangement pattern of droplets IM and an abnormal ER when imprinting is performed using the arrangement pattern. The abnormal ER may be a defect measured by the measurement device 301 in FIG. 3. This defect may include the location and size of the defect as information. The abnormal ER may also be a defect predicted by the simulation server 303 shown in FIG. 3. The abnormal ER may be an air bubble in a film formed on a substrate, a difference from a target film thickness, seepage or non-filling of the imprint material, etc. When automatically determining a droplet to be operated, for example, the determination is made based on the position of an abnormal ER that has occurred in the result of measuring a film on a substrate imprinted using an arrangement pattern of droplets IM by the measurement device 301. Alternatively, the determination may be made based on the position of an abnormal ER that has occurred in the result predicted by the simulation server 303.

[0050] Fig. 8(B) is a diagram for explaining a first example of a method for determining droplets IM to be operated on. In Fig. 8(B), there is a possible method for determining droplets 803 (four droplets in this case) shown in black and included in an area 802 that is a predetermined distance 801 away from the anomaly as the operation target.

[0051] FIG. 8C is a diagram for explaining a second example of a method for determining a droplet IM to be operated. The straight line 804 in FIG. 8C represents a Delaunay diagram. The Delaunay diagram is composed of links that connect the centers of adjacent droplets IM with a straight line 804. As a method for determining a droplet IM to be operated, a method using the number of links from the adjacent link 805 that is closest to the abnormality ER is possible. Specifically, the number of links on the path is determined when tracing adjacent links from the adjacent link 805. In FIG. 8C, the adjacent link 805 is set as the first link, and the droplets IM located at both ends of the links 806 up to the second link are set as the operation targets. With this method, the droplet IM illustrated in black, including the droplet 807 as the operation target, is determined as the operation target.

[0052] FIG. 8(D) is a diagram for explaining a third example of a method for determining a droplet to be operated. The Voronoi region 808 in FIG. 8(D) is a region formed by a Voronoi diagram. The Voronoi diagram is calculated by dividing a plurality of points (nuclear points) arranged at any position in a certain metric space according to which other points in the same metric space are closer to each other. In this specification, each divided region (unit cell) is called a Voronoi region. For example, the location included in the Voronoi region 808 is the droplet to which the droplet IM is closest. As a method for determining the droplet IM to be operated, there is a method for determining the number of Voronoi regions adjacent to the Voronoi region 809 including the abnormal ER. Specifically, when tracing the adjacent Voronoi regions, the number of Voronoi regions on the path is used to determine the droplet IM. In FIG. 8(D), the Voronoi region 809 including the abnormal ER is set as the first region, and the droplet IM illustrated in black that is included in the Voronoi regions adjacent to the first two droplets is set as the operation target. By this operation, the droplet IM, which is shown in black and includes the droplet 811, is determined as the operation target.

[0053] As described above, there are several methods for determining the droplet IM to be operated. When reducing the calculation processing, the first example method in which the IM to be operated is determined using the distance D from the abnormality is effective. When dealing with an abnormality caused by the amount of gas, the second example method in which the IM to be operated is determined from the number of links in the Delaunay diagram is effective. When dealing with an abnormality such as an abnormality in the film thickness of the droplet or an abnormality such as non-filling or seepage around the shot, the third example method in which the IM to be operated is determined from the number of Voronoi diagram regions is effective. In this way, it is effective to change (select) the method for determining the droplet IM to be operated depending on the type of abnormality to be improved. In other words, it is effective to determine the method to be used to determine the droplet to be operated depending on the type of abnormality.

[0054] Fig. 9 is a diagram for explaining a method for determining a droplet to be operated on depending on the size of the abnormality. In Fig. 9, a droplet IM is placed in an adjustment area 901. ER1 to ER4 in Fig. 9 are abnormalities ER included in the adjustment area, and the size of the triangular icon representing the abnormality is changed depending on the size of the abnormality. The sizes of the abnormalities included in Fig. 9 are ranked as follows: ER1>ER4>ER3>ER2

[0055] When determining the droplet IM to be operated, it may be determined based on the order of the size of the abnormality ER. Specifically, first, a list of the order of the size of the abnormality ER is generated. Then, the droplet IM in the vicinity of the abnormality ER with a higher size in the order list is set as the operation target. For example, in FIG. 9, based on the order list, an operation is performed on the droplet IM1 located near the abnormality ER1 with a higher order than a predetermined order and the droplet IM4 located near the abnormality ER4. On the other hand, the droplet IM3 located near the abnormality ER3 with a lower order than the predetermined order and the droplet IM2 located near the abnormality ER2 are not set as the operation target. In this way, when determining the droplet IM to be operated based on the order list of the abnormality ER based on the size of the abnormality ER, the droplet in the upper order in the order list, that is, the droplet in the vicinity of the abnormality with a size equal to or larger than the threshold value, can be set as the operation target. At this time, for example, an abnormality smaller than a predetermined size may be excluded from the droplet IM to be operated.

[0056] FIG. 10 is a diagram for explaining a method for determining a droplet IM to be operated on based on the amount of improvement effect when comparing before and after the operation of the droplet IM. Here, the amount of improvement effect represents the degree of improvement of the abnormality when comparing before and after the operation of the droplet IM. FIG. 10(A) shows the result of performing the droplet operation described below on the arrangement pattern of the droplet IM shown in FIG. 9. Here, by moving the droplet that was at IM4 before the operation to IM4' through the operation, the abnormality ER4 in FIG. 9 changes to abnormality ER4' in FIG. 10(A), and the magnitude of the abnormality becomes smaller.

[0057] Fig. 10(B) is a diagram for explaining the improvement effect amount DIF when an operation is performed on a droplet IM included in the adjustment area 901. DIF1 to DIF4 in this figure are changes in the abnormality included in the adjustment area 901, and the size of the square icon representing the amount of change is changed according to the magnitude of the improvement effect of the abnormality. For example, the improvement effect amount when the abnormality ER4 in Fig. 9 is improved to the abnormality ER4' in Fig. 10(A) is represented by DIF4. The magnitudes of the improvement effect amounts included in Fig. 10(B) are in the following order: DIF4>DIF1>DIF3>DIF2

[0058] When determining the droplet to be operated, it may be determined based on the order of the improvement effect amount DIF. Specifically, first, a ranking list of abnormalities ER based on the improvement effect amount DIF is generated. Then, the droplet in the vicinity of the abnormality ER with the higher improvement effect amount DIF in the ranking list is set as the operation target. For example, in FIG. 10(B), an operation is performed on the droplet IM4 located near DIF4, which is higher than a predetermined order, and the droplet IM1 located near DIF1, based on the ranking list. On the other hand, the droplet IM3 located near DIF3, which is lower than the predetermined order, and the droplet IM2 located near DIF2 are not set as the operation target. In this way, when determining the droplet to be operated based on the ranking list of abnormalities ER based on the improvement effect amount DIF, the droplet IM located near the higher order in the order of the improvement effect amount of the abnormality, that is, the droplet IM located near the abnormality whose improvement effect amount is equal to or greater than a threshold value, may be set as the operation target. At this time, for example, the vicinity area of ​​the improvement effect amount smaller than a predetermined improvement effect amount may be excluded from the droplet IM to be operated.

[0059] The update frequency of the ranking list used when determining the droplets to be operated on can be changed. Specifically, the one determined when step S604 is executed for the first time may continue to be used, or the ranking list may be updated at a predetermined frequency (e.g., after a predetermined number of times or after a predetermined time) while step S604 is repeatedly executed. By reducing the update frequency of the ranking list, the processing time can be shortened. On the other hand, by increasing the update frequency of the ranking list, the accuracy can be improved.

[0060] In step S605 in FIG. 6, the type of operation to be performed on the droplet to be operated is determined. FIG. 11 is a diagram for explaining the operation. FIG. 11(A) shows the droplet IM before the operation. A grid 1101 defines the position where the droplet can be placed, and the droplet can be placed at the intersection of the grid 1101. (B1) to (B8) in FIG. 11 show the movement operation of the droplet IM. In FIG. 11(B1), the droplet IM is moved to a position where it can be placed upward to become the droplet 1102, in comparison with the droplet IM in FIG. 11(A) before the operation. Similarly, FIG. 11(B2) shows the movement operation in the upper left direction. FIG. 11(B3) shows the movement operation in the left direction. FIG. 11(B4) shows the movement operation in the lower left direction. FIG. 11(B5) shows the movement operation in the lower direction. FIG. 11(B6) shows the movement operation in the lower right direction. FIG. 11(B7) shows the movement operation in the right direction. FIG. 11(B8) shows a movement operation in the upper right direction.

[0061] As described above, eight directions of movement are possible. It is also possible to limit the direction of movement to four directions, such as up, down, left, and right. When the abnormality is large, it is possible to reduce the calculation time by limiting the direction of movement. The size of the movement may be one grid, or it may be a number equal to the number of grids.

[0062] Fig. 11 (C1) shows the operation of adding a droplet IM. In the addition operation, the droplet IM before the operation is not changed, and a droplet is added to an adjacent grid. In Fig. 11 (C1), a droplet 1103 is added to the grid in the upward direction. Droplets can be added in the upward direction, upper left direction, left direction, lower left direction, downward direction, lower right direction, right direction, and upper right direction, just like the movement operations from (B1) to (B8).

[0063] Fig. 11(C2) shows the operation of deleting the droplet IM. In the deletion operation, the droplet IM before the operation in Fig. 11(A) can be changed to a state where there is no droplet, as shown in Fig. 11(C2) IM'.

[0064] 11(D1) and 11(D2) show the operation of changing the volume of a droplet IM. In FIG. 11(D1), an operation of increasing the amount of the droplet is performed on the droplet IM in FIG. 11(A), and the amount of the droplet changes (increases) in the droplet 1104. In FIG. 11(D2), an operation of decreasing the amount of the droplet is performed on the droplet IM in FIG. 11(A), and the amount of the droplet changes (decreases) in the droplet 1105. The amount of the droplet when manipulating the volume of the droplet can be specified as an arbitrary value. As an operation of changing the amount of the droplet, for example, in an operation of increasing or decreasing the amount of the droplet, operations of different amounts can be used as separate operations.

[0065] All of these types of droplet operations may be performed. However, if there are many types of droplet operation amounts to be handled, the calculation time increases, so it is effective to select an appropriate droplet operation. When the degree of abnormality is large, droplet movement operations, addition operations, and deletion operations are effective. On the other hand, when the degree of abnormality is small, operations that manipulate the droplet amount are effective. Furthermore, whether or not the droplet amount can be manipulated may depend on the performance of the dispenser 108 in FIG. 1.

[0066] 6, in step S606, a plurality of candidates for droplet arrangement patterns are generated by performing an operation on the droplets IM. Specifically, in step S606, the operation determined in step S605 is performed on each droplet to be operated on, thereby generating a plurality of candidates for the arrangement pattern.

[0067] In step S607, the droplet arrangement pattern candidates generated by the operation performed in step S606 are evaluated. Specifically, the evaluation is performed by obtaining an evaluation value for each of the multiple droplet arrangement pattern candidates generated in step S606.

[0068] Fig. 12 is a diagram for explaining the evaluation method performed in step S607. An adjustment region 1201 in Fig. 12(A) is the adjustment region determined in step S603.

[0069] The droplet IM displayed in Fig. 12(A) is the droplet arrangement pattern updated by performing step S606. Fig. 12(B) shows the result of a simulation performed using the arrangement pattern of Fig. 12(A) updated by the operation. Here, an example will be described in which the amount of gas volume generated in the film 1202 is used as a feature of the evaluation value. This gas amount can be predicted by the simulator of the simulation server 303. The following (Equation 1) can be used as the evaluation value.

number

[0070] Moreover, the following (Equation 2) can also be used as the evaluation value.

number

[0071] where n i represents the amount of gas 1203 contained in the adjustment region 1201 as shown in FIG. mean represents the average amount of gas contained in the adjustment region 1201. In (Equation 2), the square error of the amount of gas contained in the adjustment region is used as the evaluation value.

[0072] In Fig. 12(C), the distance between droplets is used as a feature value for the arrangement pattern in Fig. 12(A) updated by operation. The distance between droplets can be obtained by creating the above-mentioned Delaunay diagram and finding the distance between the links 1204 that make up the Delaunay diagram. As with (Equation 1), the maximum or minimum value of the distance between droplets included in the adjustment region 1201 can be used as the evaluation value. Also, as with (Equation 2), the squared error of the distance between droplets included in the adjustment region 1201 can be used as the evaluation value.

[0073] In Fig. 12(D), the film thickness is used as a feature value for the arrangement pattern of Fig. 12(A) updated by the operation. The film thickness of this droplet can be obtained by creating the Voronoi diagram described above and dividing the Voronoi area 1205 of each droplet by the volume of each droplet. As with (Equation 1), the evaluation value can be the maximum or minimum film thickness of the droplets included in the adjustment region 1201. As with (Equation 2), the evaluation value can be the square error of the film thickness for each droplet included in the adjustment region 1.

[0074] FIG. 12(E) uses the unfilled amount or seepage amount of droplets as a feature amount for the arrangement pattern of FIG. 12(A) updated by operation. In FIG. 12(E), the boundary 1207 of the shot area and the liquid film 1206 are displayed overlapping each other. In a range 1208 located near the boundary 1207 and inside the shot area, the droplets do not reach the boundary 1207 and are unfilled. Here, the range 1208 represents the degree of unfilling. In a range 1209 located near the boundary 1207 and outside the shot, the droplets exceed the boundary 1207 and seep out to the outside of the shot. Here, the range 1209 represents the degree of seepage. As in (Equation 1), the unfilled amount or seepage amount, or the maximum value of both, included in the adjustment area 1201 can be used as the evaluation value. As an evaluation value, similarly to (Equation 2), the square error of the unfilled amount or the seeped amount, or both, for each droplet included in the adjustment region 1201 can be used.

[0075] In this way, several feature quantities can be used to calculate the evaluation value. When adjusting defects caused by gas volume, it is effective to switch the feature quantity depending on the type of abnormality, such as using the gas volume as the feature quantity.

[0076] In step S608, the type of remaining operations is confirmed. Specifically, if there are any operations determined in step S605 that have not been executed (Yes), the unexecuted operations are executed on the target droplet, and steps S606 to S608 are repeated until there are no unexecuted operations. On the other hand, if execution of all the operations determined in step S605 has been completed (No), the process proceeds to step S609.

[0077] In step S609, it is confirmed whether there are any droplets on which an operation has not been performed. Specifically, if there are any droplets on which an operation has not been performed (Yes) among the droplets to be operated on determined in step S604, steps S605 to S609 are repeated until there are no more droplets on which an operation has not been performed.

[0078] In step S610, a better droplet arrangement pattern is selected from a plurality of arrangement pattern candidates obtained by the droplet manipulation executed in the adjustment area. Specifically, the evaluation values ​​of the plurality of arrangement pattern candidates are compared to select one of the plurality of arrangement pattern candidates.

[0079] Fig. 13 is a diagram for explaining step S610. Specifically, it is a diagram for explaining a method for selecting an arrangement pattern to be used in the next step S611 from a plurality of droplet arrangement pattern candidates. Fig. 13(A) shows the droplet arrangement pattern before operation in the adjustment area 1301. ER1 in Fig. 13(A) represents an abnormality, and the size of the triangular icon shown in the figure is changed according to the size of the abnormality.

[0080] FIG. 13(B1) to FIG. 13(B4) are diagrams showing the results of performing each operation with the droplet IMB as the droplet operation target. FIG. 13(B1) shows the case where the droplet IMB is moved upward, FIG. 13(B2) shows the case where the droplet IMB is moved leftward, FIG. 13(B3) shows the case where the droplet IMB is moved downward, and FIG. 13(B4) shows the case where the droplet IMB is moved rightward. In FIG. 13(B1) to FIG. 13(B4), the position of the droplet IMB before movement is shown by a dashed line, and the positions of the droplets IMB1 to IMB4 after movement are shown by black circles. In FIG. 13(B1) to FIG. 13(B4), it can be seen that the location and size of the abnormality change due to the droplet movement operation. Similarly, Fig. 13(C1) to Fig. 13(C4) show the case where an operation is performed on droplet IMC, the positions of droplets IMC1 to IMC4 after movement are indicated by black circles, and the result of the occurrence of an abnormality is shown. Fig. 13(D1) to Fig. 13(D4) show the case where an operation is performed on droplet IMD, the positions of droplets IMD1 to IMD4 after movement are indicated by black circles, and the result of the occurrence of an abnormality is shown.

[0081] In determining the arrangement pattern in step S610, the best arrangement pattern is selected from the candidate droplet arrangement patterns shown in Fig. 13 (B1) to Fig. 13 (D4). The method of selecting the arrangement pattern is preferably to calculate an evaluation value for each of the arrangement patterns in Fig. 13 (B1) to Fig. 13 (D4), compare them, and select the one with the best evaluation. However, multiple patterns with evaluation values ​​above or below a threshold may also be selected. Here, whether the evaluation value is above or below the threshold is determined according to the type of evaluation value.

[0082] In Fig. 13, the evaluation value used is the smallest square error (evaluation value L) of the amount of gas surrounded by the droplets shown in (Equation 2). When comparing the results of applying (Equation 2) to each arrangement pattern, the abnormal ERC3 included in (C3) in Fig. 13 is small, and the evaluation value L in the arrangement pattern of Fig. 13 (C3) is the smallest. Therefore, from among the multiple arrangement pattern candidates shown in Fig. 13, the arrangement pattern of (C3) is selected as the best arrangement pattern.

[0083] In step S611, a decision is made as to whether or not to add or update the arrangement pattern. FIG. 14 is a diagram for explaining a method of deciding whether or not to add or update. The vertical axis of FIG. 14 represents the evaluation value L of the arrangement pattern selected in step S610, and the horizontal axis represents the number of times the arrangement pattern has been added or updated. FIG. 14 represents the evaluation value L0 for the initial arrangement pattern. The evaluation value L1 in FIG. 14 represents the evaluation value L1 of the arrangement pattern selected in step S610. In FIG. 14, it can be confirmed that the evaluation value L1 has been improved compared with the evaluation value L0. In step S611, if there is an improvement in the evaluation value, it is determined that further improvement effects are expected and that the arrangement pattern should be added or updated (Yes). When the arrangement pattern is added or updated, the arrangement pattern selected in step S610 is replaced with the initial pattern, and steps S604 to S611 are repeatedly executed until the addition or update is no longer necessary. In this specification, steps S604 to S611, which are performed using the arrangement pattern selected in step S610 instead of the initial arrangement pattern, are referred to as an update process. If it is determined in step S611 of the first update process that additional update is to be performed, in the second update process, steps S604 to S611 are performed using the arrangement pattern selected in step S610 of the first update process.

[0084] In this way, by performing the update process using the arrangement pattern selected in step S610, an arrangement pattern with a smaller evaluation value L can be obtained. In step S611, if a predetermined condition is satisfied, it is determined that no additional update is to be performed (No). That is, the update process is repeated until the predetermined condition is satisfied. Specifically, in FIG. 14, the evaluation value LN has not changed from the previous evaluation value LN-1. In this way, even if the droplet arrangement pattern is updated, if the evaluation value does not improve, that is, if there is no improvement, it is determined in step S611 that no additional update of the arrangement pattern is to be performed (No).

[0085] In the above, whether to perform additional update of the droplet arrangement is determined based on whether the evaluation value of the droplet arrangement pattern has improved. On the other hand, as a method of determining whether to perform additional update, it is also possible to determine not to perform additional update of the droplets when the evaluation value L reaches a threshold value, when the number of times the update process has been executed reaches a predetermined number of times, or when the execution time of the update process reaches a predetermined number of hours.

[0086] In addition, in step S604 in the update process, a smaller number of droplets may be determined as operation targets than in the previously performed step S604. Specifically, for example, a smaller number of droplets may be determined as operation targets than in the previously performed step S604 by changing the threshold value of the abnormality ranking list used when determining the operation target droplets IM. Alternatively, the number of operation target droplets may be reduced by updating the ranking list itself, or by performing both. By reducing the number of operation target droplets IM, it is possible to shorten the calculation time.

[0087] In step S612, a final arrangement pattern is determined, where the arrangement pattern of droplets when the condition for not performing additional update of the droplet arrangement is met in step S611 is determined as the final arrangement pattern.

[0088] The imprinting apparatus, imprinting method, and information processing device to which the present invention is applied have been described above. The present invention is expected to realize, with a small amount of calculation, a means for generating a droplet arrangement pattern that reduces abnormalities that may occur in areas where the droplet pattern is discontinuous, such as the boundaries between areas decomposed according to the contents of the mold.

[0089] In the above embodiment, the calculation server 304 is an independent device, but the imprint apparatus IMP or the simulation server 303 may have the function of the calculation server 304, or these may be one device.

[0090] Although the present embodiment illustrates an imprint apparatus that presses a mold against droplets, the present invention can also be used in a film forming apparatus that forms a liquid film by arranging droplets without pressing a mold.

[0091] <Embodiment of the article manufacturing method> The pattern of the cured product formed by the imprinting apparatus using the droplet arrangement pattern generated by the above-mentioned method is used permanently on at least a part of various articles, or temporarily when manufacturing various articles. The articles are electric circuit elements, optical elements, MEMS, recording elements, sensors, or molds. Examples of the electric circuit elements include volatile or non-volatile semiconductor memories such as DRAM, SRAM, flash memory, and MRAM, and semiconductor elements such as LSI, CCD, image sensors, and FPGA. Examples of the molds include molds for imprinting.

[0092] The pattern of the cured product is used as it is as at least a part of a component of the article, or is used temporarily as a resist mask, which is removed after etching or ion implantation in a substrate processing step.

[0093] Next, a specific method for manufacturing the article will be described. As shown in Fig. 15(A), a substrate 1z such as a silicon wafer having a workpiece 2z such as an insulator formed on its surface is prepared, and then a composition 3z is applied to the surface of the workpiece 2z by an inkjet method or the like. Here, a state in which the composition 3z in the form of multiple droplets is applied onto the substrate is shown.

[0094] As shown in Fig. 15(B), the imprinting mold 4z is placed facing the composition 3z on the substrate with the side on which the concave-convex pattern is formed. As shown in Fig. 15(C), the substrate 1z to which the composition 3z is applied is brought into contact with the mold 4z, and pressure is applied. The composition 3z fills the gap between the mold 4z and the workpiece 2z. When light is irradiated through the mold 4z in this state as energy for curing, the composition 3z is cured.

[0095] As shown in Fig. 15(D), after the composition 3z is cured, the mold 4z and the substrate 1z are separated, and a pattern of the cured product of the composition 3z is formed on the substrate 1z. In this cured product pattern, the concave portions of the mold correspond to the convex portions of the cured product, and the convex portions of the mold correspond to the concave portions of the cured product, that is, the concave-convex pattern of the mold 4z is transferred to the composition 3z.

[0096] As shown in FIG. 15(E), when etching is performed using the pattern of the cured material as an etching-resistant mask, the portion of the surface of the workpiece 2z where there is no cured material or where only a thin portion remains is removed, forming a groove 5z. As shown in FIG. 15(F), when the pattern of the cured material is removed, an article having grooves 5z formed on the surface of the workpiece 2z can be obtained. Here, the pattern of the cured material is removed, but it may be used as an interlayer insulating film included in a semiconductor element or the like, that is, a component of an article, without being removed after processing. Note that, although an example of using a mold for transferring a circuit pattern with a concave-convex pattern has been described as the mold 4z, a mold (flat template) having a flat portion without a concave-convex pattern may also be used.

[0097] <Other embodiments> The present invention can also be realized by a process in which a program for implementing one or more of the functions of the above-described embodiments is supplied to a system or device via a network or a storage medium, and one or more processors in a computer of the system or device read and execute the program. The present invention can also be realized by a circuit (e.g., ASIC) for implementing one or more of the functions.

[0098] The disclosure of the present embodiment includes the following methods and configurations.

[0099] (Method 1) 1. A method for generating an arrangement pattern of droplets used in a process for forming a film of a curable composition on a substrate using a plurality of droplets of the curable composition arranged on the substrate, the method comprising the steps of: determining a droplet to be operated from an initial arrangement pattern; generating a plurality of arrangement pattern candidates by performing an operation on each of the droplets determined in the determining step; acquiring an evaluation value for each of the plurality of arrangement pattern candidates; selecting one of the arrangement pattern candidates from the plurality of arrangement pattern candidates by comparing evaluation values ​​of the plurality of arrangement pattern candidates; and repeating an update process based on the arrangement pattern candidates selected in the selection process.

[0100] (Method 2) The generation method described in Method 1, characterized in that the update process is performed by repeating the steps from determining the droplet to be operated using the selected arrangement pattern instead of the initial arrangement pattern to selecting the arrangement pattern.

[0101] (Method 3) The generating method according to method 1 or 2, characterized in that the update process is repeated until a predetermined condition is satisfied.

[0102] (Method 4) The generation method according to Method 3, characterized in that the specified condition is any one of the following: there is no longer any improvement in the evaluation value, the number of times the update process has been executed has reached a specified number of iterations, the execution time of the update process has reached a specified number of hours, and the evaluation value of the arrangement pattern candidate has reached a threshold value.

[0103] (Method 5) A generation method described in any one of methods 2 to 4, characterized in that in the update process, the step of determining the droplets to be operated on determines a smaller number of droplets to be operated on than in the previous step of determining the droplets to be operated on.

[0104] (Method 6) The method for generating a droplet according to any one of methods 1 to 5, characterized in that the step of determining the droplet to be operated is based on the position of an abnormality that occurs in the measurement results of the film on the substrate formed using the initial arrangement pattern, or in the results of predicting the process of forming a film on the substrate by simulation using the initial arrangement pattern.

[0105] (Method 7) The generation method described in Method 6, characterized in that the step of determining the droplet to be operated on comprises determining as the droplet to be operated on the initial arrangement pattern, the droplet located a predetermined distance from the anomaly where the degree of improvement in the anomaly is greater than a threshold value when comparing before and after the operation.

[0106] (Method 8) The generation method described in Method 6 or 7, characterized in that the step of determining the droplet to be operated on determines the droplet to be operated on using the distance from the position of the anomaly, or the number of links in a Delaunay diagram generated based on the droplet arrangement pattern, or the number of Voronoi regions in a Voronoi diagram generated based on the droplet arrangement pattern.

[0107] (Method 9) The generating method described in Method 8, wherein the step of determining the droplet to be operated on determines a method to be used for determining the droplet to be operated on depending on the type of the abnormality.

[0108] (Method 10) A method for generating droplets described in any one of Methods 6 to 9, characterized in that the step of determining the droplets to be operated on generates a ranking list of abnormalities based on the magnitude of the abnormality or the degree of improvement of the abnormality, and selects droplets that are located near abnormalities in the ranking list that have a higher ranking than a predetermined ranking as the droplets to be operated on.

[0109] (Method 11) Method according to method 10, characterized in that the frequency of updating the ranking list can be changed.

[0110] (Method 12) The method for generating a film described in any one of Methods 6 to 11, characterized in that the abnormalities include air bubbles present in the film measured by a measuring device that measures the state of the film formed on the substrate or predicted by a simulator, a difference from the target film thickness, and seepage and non-filling of the curable composition.

[0111] (Method 13) The method for generating a droplet according to any one of methods 1 to 12, characterized in that the step of determining the droplet to be operated is performed from a region of the initial arrangement pattern that includes a boundary between areas where the droplet arrangements are continuous, a region corresponding to a mark used to align the mold and the substrate and its surroundings, or a region corresponding to the outer periphery of the mold.

[0112] (Method 14) A method for generating a droplet according to any one of methods 1 to 13, characterized in that the operation on the droplet includes one or more of moving the droplet, adding the droplet, deleting the droplet, and changing the volume of the droplet.

[0113] (Method 15) A generation method according to any one of Methods 1 to 14, characterized in that the evaluation value of the arrangement pattern candidate is a value using any one of the maximum value, minimum value, and squared error of the feature amount of the arrangement pattern.

[0114] (Method 16) The method for generating a film according to the method 15, characterized in that the feature of the arrangement pattern is any one of the amount of gas present in the film, the film thickness, the amount of the droplets seeping out, and the unfilled amount of the curable composition.

[0115] (Configuration 1) 1. An information processing apparatus for generating an arrangement pattern of droplets, the arrangement pattern being used in a process for forming a film of a curable composition on a substrate using a plurality of droplets of the curable composition arranged on the substrate, the apparatus comprising: A droplet to be operated is determined from the initial arrangement pattern; generating a plurality of candidate arrangement patterns by performing an operation on each of the determined droplets; obtaining an evaluation value for each of the plurality of arrangement pattern candidates; selecting one of the arrangement pattern candidates from among the plurality of arrangement pattern candidates by comparing evaluation values ​​of the plurality of arrangement pattern candidates; The information processing apparatus is characterized in that an update process is repeated based on the selected arrangement pattern candidate.

[0116] (program) A program for causing a computer to execute any one of the generating methods according to methods 1 to 16.

[0117] (Production method of the article) Mold the curable composition on the substrate using the droplet arrangement pattern produced by any one of the production methods described in methods 1 to 16; treating the substrate on which the curable composition has been molded in the above step; producing an article from the processed substrate; A method for producing an article, comprising the steps of: [Explanation of symbols]

[0118] 300 Systems IMP Imprinting Equipment 301 Measuring Equipment 302 Data Collection Server 303 Simulation Server 304 Calculation Server 305 Network

Claims

1. 1. A method for generating an arrangement pattern of droplets used in a process for forming a film of a curable composition on a substrate using a plurality of droplets of the curable composition arranged on the substrate, the method comprising the steps of: determining a droplet to be operated from an initial arrangement pattern; generating a plurality of arrangement pattern candidates by performing an operation on each of the droplets determined in the determining step; acquiring an evaluation value for each of the plurality of arrangement pattern candidates; selecting one of the arrangement pattern candidates from among the plurality of arrangement pattern candidates by comparing evaluation values ​​of the plurality of arrangement pattern candidates; and repeating an update process based on the arrangement pattern candidates selected in the selection process.

2. The generation method described in claim 1, characterized in that the update process is performed by repeating the steps from determining the droplet to be operated using the selected arrangement pattern instead of the initial arrangement pattern to selecting the arrangement pattern.

3. 2. The method according to claim 1, wherein the update process is repeated until a predetermined condition is satisfied.

4. The generation method according to claim 3, characterized in that the specified condition is any one of the following: there is no longer any improvement in the evaluation value, the number of times the update process has been executed has reached a specified number of iterations, the execution time of the update process has reached a specified number of hours, and the evaluation value of the arrangement pattern candidate has reached a threshold value.

5. The generation method according to claim 2, characterized in that in the update process, the step of determining the droplets to be operated on determines a smaller number of droplets to be operated on than in the previous step of determining the droplets to be operated on.

6. The generation method described in claim 1, characterized in that the process of determining the droplet to be operated is determined based on the position of an abnormality that occurs in the measurement results of the film on the substrate formed using the initial arrangement pattern, or in the results of predicting the process of forming a film on the substrate by simulation using the initial arrangement pattern.

7. The generation method described in claim 6, characterized in that the process of determining the droplet to be operated on determines as the droplet to be operated on the initial arrangement pattern a droplet located a predetermined distance from an anomaly where the degree of improvement of the anomaly is greater than a threshold value when comparing before and after the operation is performed on the initial arrangement pattern.

8. The method of generating the droplet to be operated on, characterized in that the process of determining the droplet to be operated on determines the droplet to be operated on using the distance from the position of the anomaly, or the number of links in a Delaunay diagram generated based on the droplet arrangement pattern, or the number of Voronoi regions in a Voronoi diagram generated based on the droplet arrangement pattern.

9. The generating method according to claim 8 , wherein the step of determining the droplet to be operated on determines a method to be used for determining the droplet to be operated on depending on a type of the abnormality.

10. The generation method described in claim 6, characterized in that the process of determining the droplet to be operated on generates a ranking list of abnormalities based on the magnitude of the abnormality or the degree of improvement of the abnormality, and selects droplets that are located near abnormalities in the ranking list that have a higher ranking than a predetermined ranking as the droplet to be operated on.

11. The method of claim 10, wherein the frequency with which the ranking list is updated can be changed.

12. The method of claim 6, characterized in that the abnormalities include air bubbles present in the film measured by a measuring device that measures the state of the film formed on the substrate or predicted by a simulator, a difference from a target film thickness, and seepage and non-filling of the curable composition.

13. The method of generating a liquid droplet according to claim 1, characterized in that the step of determining the liquid droplet to be operated on determines the liquid droplet to be operated on from a region of the initial arrangement pattern that includes a boundary between areas where the droplet arrangements are continuous, a region corresponding to a mark used for aligning the mold and the substrate and its surroundings, or a region corresponding to the outer periphery of the mold.

14. The method of claim 1 , wherein the operations on the droplets include one or more of moving the droplets, adding the droplets, deleting the droplets, and changing a volume of the droplets.

15. 2. The method according to claim 1, wherein the evaluation value of the arrangement pattern candidate is a value using any one of a maximum value, a minimum value, and a square error of a feature amount of the arrangement pattern.

16. The method according to claim 15, characterized in that the feature of the arrangement pattern is any one of the amount of gas present in the film, the film thickness, the amount of the droplets seeping out, and the amount of the curable composition not filled.

17. 1. An information processing apparatus for generating an arrangement pattern of droplets, the arrangement pattern being used in a process for forming a film of a curable composition on a substrate using a plurality of droplets of the curable composition arranged on the substrate, the apparatus comprising: A droplet to be operated is determined from the initial arrangement pattern; generating a plurality of candidate arrangement patterns by performing an operation on each of the determined droplets; obtaining an evaluation value for each of the plurality of arrangement pattern candidates; selecting one of the arrangement pattern candidates from among the plurality of arrangement pattern candidates by comparing evaluation values ​​of the plurality of arrangement pattern candidates; The information processing apparatus is characterized in that an update process is repeated based on the selected arrangement pattern candidate.

18. A program causing a computer to execute the generating method according to any one of claims 1 to 16.

19. shaping the curable composition on the substrate using the droplet arrangement pattern produced by the production method according to any one of claims 1 to 16; treating the substrate on which the curable composition has been molded in the above step; producing an article from the processed substrate; A method for producing an article, comprising the steps of:

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