Information processing method, exposure method, exposure apparatus, method for manufacturing articles, program, and information processing apparatus.

Abstract

To provide a technology useful for highly precisely obtaining an array of regions on a substrate.SOLUTION: A method for obtaining an array of a plurality of regions on a substrate includes: acquiring position measurement data by measuring a mark assigned to a sample region of a plurality regions on the substrate; and estimating a position of a non-measured region of the plurality of regions except for the sample region by using a regression model for estimating the array from the position measurement data. The regression model is a nonparametric regression model.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a method for determining an arrangement of a plurality of regions on a substrate, an exposure method, an exposure apparatus, an article manufacturing method, a program, and an information processing apparatus. [Background technology]

[0002] The exposure device transfers 10 or more layers of patterns (circuit patterns) onto the substrate in an overlapping manner, but if the overlapping accuracy of the patterns between the layers is not good, problems may occur with the circuit characteristics. In such cases, the chip will not meet the desired characteristics, resulting in a defective chip and a reduced yield. Therefore, it is necessary to precisely align each of the multiple areas to be exposed on the substrate with the original pattern.

[0003] In an exposure apparatus, alignment marks arranged in each region on a substrate are detected, and each region on the substrate is aligned with the pattern on the original based on position information of the alignment marks and position information of the pattern on the original. Ideally, the most accurate alignment is possible by detecting alignment marks in all regions on the substrate, but this is not realistic from the viewpoint of productivity. Therefore, the global alignment method is currently the mainstream method for aligning a substrate and an original (see Patent Document 1).

[0004] In the global alignment method, it is assumed that the relative position of each area on the substrate can be expressed by a function model of the position coordinates of the area, and the positions of alignment marks arranged only in a plurality of sample areas (4 to 16) on the substrate are measured. Next, parameters of the function model are estimated using regression analysis-like statistical calculation processing from the assumed function model and the measurement results of the alignment mark positions. Then, alignment is performed by calculating the position coordinates of each area in the stage coordinate system (arrangement of areas on the substrate) using the parameters and the function model. In the global alignment method, a polynomial model with the stage coordinates as a variable is generally used, and scaling, rotation, uniform offset, etc., which are first-order polynomials of the stage coordinates, are mainly used (see Patent Document 2). In addition, a technology using a regression model that also considers high-order components of the array of areas on the substrate as parameters has also been proposed (see Patent Document 3). [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Publication No. 62-84516 [Patent Document 2] Japanese Patent Application Publication No. 6-349705 [Patent Document 3] Patent No. 3230271 Summary of the Invention [Problem to be solved by the invention]

[0006] As devices become finer and more highly integrated, there is a demand for improved alignment accuracy, and so it is necessary to increase the degree of freedom of the polynomial order of the function model by using higher-order components. However, if there are fewer measurement points for measuring the positions of alignment marks in a substrate compared to the degrees of freedom of the function model, overfitting occurs, and the correction error in the unmeasured regions increases. On the other hand, if the number of measurement points for measuring the positions of alignment marks is increased to suppress overfitting, the measurement time increases and productivity decreases. Since there is a trade-off between these two, there is a demand for a technology that can predict with high accuracy the arrangement of regions on a substrate that contain higher-order components, using a function model with fewer measurement points and a high degree of freedom.

[0007] The present invention has been made in consideration of the problems with the conventional techniques, and has an exemplary object to provide a technique that is advantageous for determining the arrangement of regions on a substrate with high accuracy. [Means for solving the problem]

[0008] In order to achieve the above-mentioned object, a method as one aspect of the present invention is a method for determining an arrangement of a plurality of regions on a substrate, comprising the steps of measuring a mark assigned to a sample region among the plurality of regions on the substrate to obtain position measurement data, and estimating the position of a non-measurement region among the plurality of regions excluding the sample region using a regression model for estimating the arrangement from the position measurement data, wherein the regression model is a non-parametric regression model.

[0009] Further objects or other aspects of the present invention will become apparent from the following description of the embodiments with reference to the accompanying drawings. Effect of the Invention

[0010] According to the present invention, for example, it is possible to provide a technique that is advantageous for determining the arrangement of regions on a substrate with high accuracy. [Brief description of the drawings]

[0011] [Figure 1] 1 is a schematic diagram showing a configuration of an exposure apparatus according to one aspect of the present invention. [Diagram 2] 2 is a schematic diagram showing the configuration of an alignment optical system of the exposure apparatus shown in FIG. [Diagram 3] 2 is a flowchart for explaining an exposure process in the exposure apparatus shown in FIG. [Figure 4] FIG. 2 is a diagram showing an arrangement of shot areas on a substrate. [Diagram 5] FIG. 11 is a diagram showing the results of a comparison between this embodiment and the prior art. [Figure 6] FIG. 11 is a diagram showing the results of a comparison between this embodiment and the prior art. [Figure 7] FIG. 11 is a diagram showing an example of a screen displayed as a user interface. [Figure 8] FIG. 11 is a diagram showing an example of a screen displayed as a user interface. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] 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.

[0013] 1 is a schematic diagram showing the configuration of an exposure apparatus 1 according to one aspect of the present invention. The exposure apparatus 1 is a lithography apparatus used in the manufacturing process of devices such as semiconductor elements. In this embodiment, the exposure apparatus 1 projects a pattern of an original 2 (reticle or mask) onto a substrate 4 via a projection optical system 3 to expose the substrate 4 to light.

[0014] 1, the exposure apparatus 1 has a projection optical system 3 that projects (reduced projection) a pattern formed on an original 2, and a chuck 5 that holds a substrate 4 on which a base pattern and alignment marks have been formed in a previous process. The exposure apparatus 1 also has a substrate stage 6 that holds the chuck 5 and positions the substrate 4 at a predetermined position, an alignment optical system 7 that measures the position of an alignment mark provided on the substrate 4, a control unit CN, a storage unit SU, and a display unit DP.

[0015] The control unit CN is composed of, for example, a computer (information processing device) including a CPU, memory, etc., and performs overall control of each unit of the exposure apparatus 1 in accordance with a program stored in the storage unit SU, etc. In this embodiment, the control unit CN functions as a processing unit that determines the arrangement (shot arrangement, area arrangement) of multiple shot areas (multiple areas on the substrate) on the substrate, in addition to controlling the exposure process that exposes the substrate 4 via the original 2.

[0016] The storage unit SU stores programs and various information (data) required to control each part of the exposure apparatus 1 and perform an exposure process for exposing the substrate 4. The storage unit SU also stores programs and various information (data) required for the control unit CN to determine a shot arrangement.

[0017] The display unit DP is a display device for displaying various types of information related to the exposure apparatus 1. In this embodiment, the display unit DP includes a touch panel, displays various user interfaces (screens), and accepts operations from the user.

[0018] 2 is a schematic diagram showing the configuration of the alignment optical system 7. The alignment optical system 7 has a function of optically detecting marks assigned to each shot area of ​​the substrate 4 and acquiring position measurement data. In this embodiment, the alignment optical system 7 includes a light source 8, a beam splitter 9, lenses 10 and 13, and a sensor 14.

[0019] Light from the light source 8 is reflected by the beam splitter 9 and passes through a lens 10 to illuminate an alignment mark 11 or 12 provided on the substrate 4. The light diffracted by the alignment mark 11 or 12 passes through the lens 10, the beam splitter 9, and a lens 13 and is received by a sensor 14.

[0020] The exposure process in the exposure apparatus 1 will be described with reference to Fig. 3. Here, the process from aligning the substrate 4 to exposing it will be described.

[0021] In S301, the substrate 4 is loaded into the exposure apparatus 1. The substrate 4 loaded into the exposure apparatus 1 is held by a chuck 5.

[0022] In S302, pre-alignment is performed. Specifically, alignment marks 11 for pre-alignment provided on the substrate 4 are detected by the alignment optical system 7 to roughly determine the position of the substrate 4. At this time, detection of the alignment marks 11 is performed for a plurality of shot areas of the substrate 4 to determine the overall shift and first-order linear components (magnification and rotation) of the substrate 4.

[0023] In S303, fine alignment is performed. Specifically, first, based on the result of the pre-alignment, the substrate stage 6 is driven to a position where the alignment mark 12 for fine alignment provided on the substrate 4 can be detected by the alignment optical system 7. Then, the alignment mark 12 provided in a sample shot area among the multiple shot areas on the substrate 4 is detected by the alignment optical system 7, and position measurement data of the alignment mark 12 is obtained.

[0024] In S304, the shift and first-order linear components (magnification and rotation) of the entire substrate 4 are precisely obtained based on the position measurement data (alignment mark information of the sample shot area) of the alignment mark 12 obtained in S303. In this embodiment, the alignment mark information of the non-sample shot area is estimated from the alignment mark information of the sample shot area obtained by fire alignment. In other words, the position measurement data (position of the non-measurement area excluding the sample area) of the shot area other than the sample shot area, that is, the non-sample shot area where the alignment mark 12 is not detected, is estimated. In addition, a non-parametric regression model is used as a regression model for estimating the position measurement data of the non-sample shot area. This makes it possible to precisely obtain the high-order deformation components of the substrate 4 from the position measurement data (measurement value) of the sample shot area and the position measurement data (estimated value) of the non-sample shot area. Therefore, the precise position of each shot area of ​​the substrate 4, that is, the shot arrangement, can be obtained, and highly accurate alignment of each shot area of ​​the substrate 4 is possible.

[0025] In S305, the substrate 4 is exposed to light. Specifically, the substrate stage 6 is driven based on the precise position of each shot area of ​​the substrate 4 obtained by performing fine alignment, and the pattern of the original 2 is transferred onto each shot area of ​​the substrate 4 via the projection optical system 3.

[0026] In S306, the substrate 4 is unloaded from the exposure apparatus 1.

[0027] Here, a polynomial linear regression model, which is one of parametric regression models, has been conventionally known as a regression model used to precisely obtain the high-order deformation components of the substrate 4. Below, a third-order polynomial linear regression model (third-order polynomial regression model) will be described as a conventional technique.

[0028] When the deformation of the substrate 4 is represented by a third-order polynomial regression model, the positional shift (ShiftX, ShiftY) of each shot area is expressed by the following formula (1). Note that the positional shift of each shot area can also be considered as a correction value for correcting such positional shift.

[0029]

number

[0030] In formula (1), x and y indicate the position of the shot area of ​​the substrate 4. From the actual position measurement data of each shot area of ​​the substrate 4 (position measurement data in the sample shot area), k1 to k 20 Then, based on the equation (1) for which the coefficients have been determined, the positional deviation of each shot area is calculated.

[0031] As described above, in fine alignment, actual position measurement data of each shot area on the substrate 4 is acquired. For example, as shown in FIG. 4, the alignment optical system 7 detects alignment marks 12 assigned to some shot areas, so-called sample shot areas, among a plurality of shot areas on the substrate. In FIG. 4, 23 shot areas out of 96 shot areas on the substrate are set as sample shot areas. In order to correct high-order deformation components of the substrate 4, many shot areas need to be set as sample shot areas. However, since an increase in the number of sample shot areas is in a trade-off relationship with the measurement time (alignment time), the number of sample shot areas is actually determined taking into consideration the productivity of the device.

[0032] As described above, in the conventional technology, a polynomial linear regression model, which is a parametric regression model, is used to precisely determine the higher-order deformation components of the substrate 4. On the other hand, in the present embodiment, a non-parametric regression model is used instead of a parametric regression model to precisely determine the higher-order deformation components of the substrate 4.

[0033] Hereinafter, a comparison result between this embodiment (when a non-parametric regression model is used) and the conventional technology (when a parametric regression model is used) will be described. Here, in this embodiment, a Gaussian process regression model is used as the non-parametric regression model, and in the conventional technology, a quintic polynomial linear regression model (quintic polynomial regression model) is used as the parametric regression model. However, the non-parametric regression model is not limited to the Gaussian process regression model, and may be, for example, a kernel regression model, a spline regression model, a neighborhood regression model, or the like.

[0034] Fig. 5 is a diagram showing the regression error 3σ (overall error of the substrate) of each substrate when this embodiment is applied to a semiconductor exposure process, and the regression error 3σ of each substrate when the conventional technology is applied. Fig. 5 shows the regression error 3σ of each substrate in each of the X direction and the Y direction, and shows the comparison results when the number of sample shot areas for detecting alignment marks among a plurality of shot areas on a substrate is set to 30, 50, and 70.

[0035] Referring to FIG. 5, whether comparing the regression error 3σ for each substrate or the average value of the regression error 3σ for substrates in a lot, it can be seen that the present embodiment using a Gaussian process regression model produces better results than the conventional technology using a fifth-order polynomial regression model.

[0036] Fig. 6 is a diagram showing the average value of regression error 3σ for each of 250 substrates corresponding to the number (number) of sample shot areas when this embodiment and the conventional technology are applied to a semiconductor exposure process. Fig. 6 shows the average value of regression error 3σ for each of 250 substrates corresponding to the number of sample shot areas in each of the X direction and Y direction. In Fig. 6, the horizontal axis shows the number of sample shot areas, and the vertical axis shows the average value of regression error 3σ. Furthermore, the solid line shows this embodiment using a Gaussian process regression model, and the dotted line shows the conventional technology using a 5th order polynomial regression model.

[0037] 6, regardless of the number of sample shot areas, when comparing any value, it can be seen that the present embodiment using the Gaussian process regression model has obtained better results than the conventional technology using the quintic polynomial regression model. Also, as the number of sample shot areas increases, the average value of the regression error 3σ in this embodiment (Gaussian process regression model) becomes smaller, and the improvement effect is greater compared to the conventional technology (quintic polynomial regression model). Furthermore, when the number of sample shot areas is small, the conventional technology (quintic polynomial regression model) has a tendency for the average value of the regression error 3σ to drop significantly due to the occurrence of overlearning. On the other hand, in this embodiment (Gaussian process regression model), even if the number of sample shot areas is small, overlearning does not occur, and there is no tendency for the average value of the regression error 3σ to drop.

[0038] In this way, according to this embodiment, by using a non-parametric regression model, it is possible to estimate with high accuracy the positions of non-sample shot areas where alignment marks are not detected, and to determine the precise positions of each shot area on substrate 4, i.e., the shot arrangement.

[0039] In this embodiment, in the Gaussian process regression model used as the non-parametric regression model, it is necessary to determine the kernel function and hyperparameters used in the regression model. In this embodiment, the kernel function and hyperparameters in the Gaussian process regression model are obtained in advance using a grid search, but this is not limited to this. For example, the kernel function and hyperparameters in the Gaussian process regression model may be determined using machine learning, specifically, the Markov chain Monte Carlo method (MCMC method) or the gradient method.

[0040] Furthermore, in the Gaussian process regression model, in addition to the position of the non-sample shot area where the alignment mark is not detected, the standard deviation of the distribution (distribution of predicted values) can be obtained. Such standard deviation represents the uncertainty of the position of the non-sample shot area estimated using the Gaussian process regression model (error at each position on the substrate). Therefore, when the standard deviation of the distribution (predicted distribution) of the position of the non-sample shot area estimated using the Gaussian process regression model exceeds a threshold value (specific value), it is preferable to detect the alignment mark of the non-sample shot area and obtain actual position measurement data. This makes it possible to precisely obtain the high-order deformation component (shot arrangement) of the substrate 4 from the position measurement data (measurement value) in the sample shot area and the position measurement data (measurement value) in the non-sample shot area.

[0041] Furthermore, in the exposure apparatus 1, information on the positions of the non-sample shot areas estimated from a non-parametric regression model such as a Gaussian process regression model may be provided so that the user can visually confirm (understand). In this embodiment, in the control unit CN, a user interface that displays information on the positions of the non-sample shot areas is displayed (provided) on the display unit DP. The information on the positions of the non-sample shot areas includes, for example, information indicating the positions of the non-sample shot areas estimated using the Gaussian process regression model and information indicating the standard deviation of the distribution of the positions of the non-sample shot areas estimated using the Gaussian process regression model.

[0042] 7 and 8 are diagrams showing an example of a screen showing information on the positions of non-sample shot areas estimated from a regression model, displayed on the display unit DP as a user interface. In FIG. 7, the positions of the non-sample shot areas estimated using a Gaussian process regression model are displayed as an image together with the positions of the sample shot areas. In addition, in FIG. 7, the standard deviation of the distribution of the positions of the non-sample shot areas estimated using the Gaussian process regression model among the non-sample shot areas is displayed in a distinguishable manner, for example, by highlighting it with a color or the like. Meanwhile, in FIG. 8, the positions of the non-sample shot areas estimated using the Gaussian process regression model are displayed as a graph together with the positions of the sample shot areas. In addition, in FIG. 8, the average value and standard deviation of the distribution of the positions of the non-sample shot areas estimated using the Gaussian process regression model are also displayed.

[0043] 7 and 8 may be configured to be displayed not only by the control unit CN of the exposure apparatus 1, but also by an external computer (information processing device). The external computer is communicatively connected to the exposure apparatus 1 (control unit CN) and includes a processing unit, a display unit, a storage unit, and an input unit. The external computer displays (provides) the user interfaces shown in FIGS. 7 and 8 on the display unit according to a program stored in the storage unit or the like. The external computer acquires information related to position measurement data by the above-mentioned method, and estimates information related to the positions of non-sample shot regions using a Gaussian process regression model.

[0044] In this way, by displaying information on the positions of the non-sample shot areas estimated from a non-parametric regression model such as a Gaussian process regression model as an image or graph, the user can visually grasp the high-order deformation components (shot arrangement) of the substrate 4. Therefore, the user can easily determine changes in the number and arrangement of sample shot areas depending on the accuracy of the positions of the non-sample shot areas estimated from the non-parametric regression model.

[0045] The manufacturing method of the article in the embodiment of the present invention is suitable for manufacturing articles such as liquid crystal display elements, semiconductor elements, flat panel displays, and MEMS. The manufacturing method includes a step of exposing a substrate coated with a photosensitive agent using the above-mentioned exposure apparatus 1 or exposure method, and a step of developing the exposed photosensitive agent. In addition, an etching step, an ion implantation step, and the like are performed on the substrate using the developed pattern of the photosensitive agent as a mask, and a circuit pattern is formed on the substrate. These steps of exposure, development, etching, and the like are repeated to form a circuit pattern consisting of multiple layers on the substrate. In a post-process, dicing (processing) is performed on the substrate on which the circuit pattern is formed, and chip mounting, bonding, and inspection steps are performed. In addition, the manufacturing method may include other well-known steps (oxidation, film formation, deposition, doping, planarization, resist peeling, etc.). The manufacturing method of the article in the present embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article compared to the conventional method.

[0046] 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.

[0047] In this embodiment, an exposure apparatus has been described as an example of a lithography apparatus for forming a pattern on a substrate, but the present invention is not limited thereto. For example, the lithography apparatus includes an imprinting apparatus for forming a pattern on a substrate by molding an imprint material on the substrate with a mold, and a planarizing apparatus for planarizing a composition on the substrate using a mold having a flat surface. The lithography apparatus also includes a drawing apparatus for drawing a pattern on a substrate using a charged particle beam (such as an electron beam or an ion beam).

[0048] The disclosure of this specification includes the following method for determining an arrangement of a plurality of regions on a substrate, an exposure method, an exposure apparatus, a method for manufacturing an article, a program, and an information processing apparatus.

[0049] (Item 1) 1. A method for determining an alignment of a plurality of regions on a substrate, comprising the steps of: measuring a mark assigned to a sample area among a plurality of areas on the substrate to obtain position measurement data; estimating the positions of non-measurement regions of the plurality of regions excluding the sample region by using a regression model for estimating the arrangement from the position measurement data; having The method of claim 1, wherein the regression model is a non-parametric regression model.

[0050] (Item 2) 2. The method according to item 1, further comprising a step of determining the array from the position measurement data and the position of the non-measurement area estimated from the regression model.

[0051] (Item 3) 3. The method of claim 1 or 2, wherein the non-parametric regression model comprises a Gaussian process regression model.

[0052] (Item 4) 4. The method according to item 3, wherein the kernel function and hyperparameters in the Gaussian process regression model are determined by machine learning.

[0053] (Item 5) 5. The method according to claim 4, wherein the machine learning includes a Markov chain Monte Carlo method or a gradient method.

[0054] (Item 6) a step of acquiring position measurement data by measuring a mark assigned to the non-measurement area when a standard deviation of a distribution of positions of the non-measurement area estimated from the regression model exceeds a threshold value; determining the array from position measurement data of the sample area and position measurement data of the non-measurement area; 6. The method according to any one of items 2 to 5, further comprising:

[0055] (Item 7) An exposure method for exposing a substrate through a mask, comprising the steps of: A step of determining an arrangement of a plurality of regions on a substrate by using the method according to any one of items 1 to 6; transferring a pattern of the original onto each of the plurality of regions while positioning the substrate based on the arrangement obtained in the above step; An exposure method comprising the steps of:

[0056] (Item 8) An exposure apparatus that exposes a substrate through an original, comprising: A processing unit that determines an arrangement of a plurality of regions on a substrate; a stage that positions the substrate based on the arrangement determined by the processing unit; having The processing unit includes: measuring a mark assigned to a sample region among a plurality of regions on the substrate to obtain position measurement data; estimating positions of non-measurement regions of the plurality of regions excluding the sample region using a regression model for estimating the sequence from the position measurement data; 11. An exposure apparatus, wherein the regression model is a non-parametric regression model.

[0057] (Item 9) 9. The exposure apparatus according to item 8, wherein the processing unit provides a user interface that displays information regarding the position of the non-measurement region estimated from the regression model.

[0058] (Item 10) the non-parametric regression model comprises a Gaussian process regression model; The information includes information indicating a position of the non-measurement area and information indicating a standard deviation of a distribution of the positions of the non-measurement area estimated from the regression model. 10. The exposure apparatus according to item 9,

[0059] (Item 11) 11. The exposure apparatus according to item 10, wherein the processing unit displays, in the user interface, non-measurement regions in which the standard deviation exceeds a threshold value in an identifiable manner.

[0060] (Item 12) Exposing a substrate using the exposure method according to item 7; developing the exposed substrate; producing an article from the developed substrate; A method for producing an article, comprising:

[0061] (Item 13) A program for causing a computer to execute a method for determining an arrangement of a plurality of regions on a substrate, comprising: The computer includes: measuring a mark assigned to a sample area among a plurality of areas on the substrate to obtain position measurement data; estimating the positions of non-measurement regions of the plurality of regions excluding the sample region by using a regression model for estimating the arrangement from the position measurement data; Run the command, The program, wherein the regression model is a non-parametric regression model.

[0062] (Item 14) 7. An information processing device that executes the method according to any one of items 1 to 6.

[0063] (Item 15) An information processing device that provides a user interface, acquiring position measurement data obtained by measuring a mark assigned to a sample region among a plurality of regions on a substrate; estimating positions of non-measurement areas of the plurality of areas excluding the sample area using a regression model for estimating an arrangement of the plurality of areas from the position measurement data; providing a user interface for displaying information regarding the position of the non-measurement region estimated from the regression model; 13. The information processing device, wherein the regression model is a non-parametric regression model.

[0064] (Item 16) the non-parametric regression model comprises a Gaussian process regression model; The information includes information indicating a position of the non-measurement area and information indicating a standard deviation of a distribution of the positions of the non-measurement area estimated from the regression model. 16. The information processing device according to item 15,

[0065] (Item 17) Item 17. The information processing device according to item 16, characterized in that, in the user interface, of the non-measurement regions, non-measurement regions in which the standard deviation exceeds a threshold value are displayed in an identifiable manner.

[0066] The invention is not limited to the above-described embodiments, and various modifications and variations are possible without departing from the spirit and scope of the invention. Accordingly, the following claims are appended to apprise the public of the scope of the invention. [Explanation of symbols]

[0067] 1: Exposure device 2: Original 3: Projection optical system 4: Substrate 5: Substrate chuck 6: Substrate stage 7: Alignment optical system CN: Control unit SU: Memory unit DP: Display unit

Claims

1. A first acquisition step of acquiring position measurement data by measuring a mark assigned to a sample region among a plurality of regions on a substrate, An estimation step is performed to estimate the position of the non-measured region, excluding the sample region, from the multiple regions, using a regression model for estimating the arrangement of the multiple regions from the position measurement data acquired in the first acquisition step, It has, The information processing method is characterized in that the regression model is a nonparametric regression model.

2. The information processing method according to claim 1, further comprising a first calculation step of determining the arrangement from the position measurement data and the position of the non-measured region estimated using the regression model.

3. The information processing method according to claim 1, characterized in that the nonparametric regression model includes a Gaussian process regression model.

4. The information processing method according to claim 3, characterized in that the kernel function and hyperparameters in the Gaussian process regression model are determined by machine learning.

5. The information processing method according to claim 4, characterized in that the machine learning includes a Markov chain Monte Carlo method or a gradient method.

6. If the standard deviation of the distribution of the positions of the non-measured region estimated using the regression model in the estimation step exceeds a threshold, a second acquisition step is performed to measure the marks assigned to the non-measured region and acquire position measurement data, A second calculation step of determining the arrangement from the position measurement data of the sample region and the position measurement data of the non-measured region, The information processing method according to claim 2, further comprising the above.

7. An exposure method for exposing a substrate via a master plate, An information processing step of determining the arrangement of multiple regions on a substrate using the information processing method described in any one of claims 1 to 6, A transfer step in which the pattern of the original plate is transferred to each of the multiple regions while positioning the substrate based on the arrangement obtained in the information processing step, An exposure method characterized by having the following:

8. An exposure apparatus for exposing a substrate via a master plate, A processing unit that determines the arrangement of multiple regions on a substrate, A stage for positioning the substrate based on the arrangement determined by the processing unit, It has, The aforementioned processing unit, Position measurement data is obtained by measuring the marks assigned to the sample region among the multiple regions on the substrate. Using a regression model for estimating the sequence from the position measurement data, the position of the non-measured region excluding the sample region from the plurality of regions is estimated. The exposure apparatus is characterized in that the regression model is a nonparametric regression model.

9. The exposure apparatus according to claim 8, characterized in that the processing unit provides a user interface that displays information regarding the position of the non-measured region estimated using the regression model.

10. The aforementioned nonparametric regression model includes a Gaussian process regression model. The information includes information indicating the location of the non-measured region and information indicating the standard deviation of the distribution of the location of the non-measured region estimated using the regression model. The exposure apparatus according to feature 9.

11. The exposure apparatus according to claim 10, characterized in that the processing unit displays in the user interface in a manner that allows identification of non-measurement regions among the non-measurement regions in which the standard deviation exceeds a threshold.

12. An exposure step of exposing a substrate using the exposure method described in claim 7, A developing step for developing the exposed substrate, A process for manufacturing an article from the developed substrate, A method for manufacturing an article, characterized by having the following:

13. A computer, A first acquisition step involves measuring a mark assigned to a sample area among multiple areas on a substrate to obtain position measurement data, An estimation step is performed in which a regression model for estimating the arrangement of the multiple regions from the position measurement data acquired in the first acquisition step is used to estimate the position of the non-measured region excluding the sample region from the multiple regions. The program is characterized in that the regression model is a nonparametric regression model.

14. An information processing apparatus characterized by performing the information processing method described in any one of claims 1 to 6.

15. An information processing device that provides a user interface, Position measurement data is obtained by measuring the marks assigned to the sample area among multiple regions on the substrate. Using a regression model for estimating the arrangement of the multiple regions from the position measurement data, the position of the non-measured region excluding the sample region from the multiple regions is estimated. A user interface is provided that displays information regarding the location of the non-measured region estimated using the regression model. The information processing device is characterized in that the regression model is a nonparametric regression model.

16. The aforementioned nonparametric regression model includes a Gaussian process regression model. The information includes information indicating the location of the non-measured region and information indicating the standard deviation of the distribution of the location of the non-measured region estimated using the regression model. The information processing apparatus according to feature 15.

17. The information processing device according to claim 16, characterized in that the user interface displays, in a manner that allows identification of non-measurement regions among the non-measurement regions, in which the standard deviation exceeds a threshold.

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