Method of obtaining position of each of plurality of regions on substrate, information processing apparatus, exposure method, exposure apparatus, method of manufacturing article, determination method, and storage medium

Abstract

To provide a technique advantageous for obtaining respective positions of a plurality of regions on a substrate.SOLUTION: A method for determining a position of each of a plurality of regions on a substrate, the method comprising a first step of calculating an estimated position of each of the plurality of regions from position measurement data of a mark provided in a sample region of the plurality of regions using a plurality of calculation methods different from each other, a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with an actual position of each of the plurality of regions, and a third step of calculating, for each of the plurality of regions, and a third step of selecting a calculation method to be used for calculating the estimated position of the region from the plurality of calculation methods based on the comparison result acquired in the second step.SELECTED DRAWING: Figure 6

Description

[Technical Field]

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

[0002] The exposure equipment transfers 10 or more layers of patterns (circuit patterns) onto the substrate in layers, but if the overlay accuracy between each layer is poor, problems with the circuit characteristics may occur. In such cases, the chip will not meet the desired characteristics, resulting in a defective chip and reduced yield. Therefore, it is necessary to precisely align each of the multiple areas (shot 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 the position information of the alignment marks and the position information of the pattern on the original. Ideally, the most accurate alignment would be possible by detecting alignment marks in all regions on the substrate, but this is not realistic from the viewpoint of productivity. Therefore, global alignment methods are 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 region on a substrate can be expressed by a function model of the region's position coordinates, and the positions of alignment marks arranged in multiple sample regions on the substrate are measured. Next, parameters of the function model are estimated using regression analysis-like statistical calculation processing based on the assumed function model and the measurement results of the alignment mark positions. The parameters and function model are then used to calculate the position coordinates of each region in the stage coordinate system (the arrangement of regions on the substrate) to perform alignment. Global alignment methods generally use polynomial models with stage coordinates as variables, and primarily use scaling, rotation, and uniform offset, which are first-order polynomials of the stage coordinates (see Patent Document 2). A technology using a regression model that also considers higher-order components of the arrangement of regions 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] However, in the conventional technology, a single function model is applied to the entire substrate as a calculation method for calculating the position (coordinates) of each region on the substrate. Specifically, multiple calculation methods for calculating the position of each region on the substrate are prepared, and the one calculation method that is optimal after evaluation across the entire substrate is applied to the entire substrate. Therefore, the calculation method applied to the entire substrate may or may not be suitable depending on the region on the substrate, and is not necessarily optimal.

[0007] The present invention has been made in view of the above problems in the prior art, and has as its exemplary object to provide a technique that is advantageous for determining the respective positions of a plurality of regions on a substrate. [Means for solving the problem]

[0008] In order to achieve the above-mentioned object, one aspect of the present invention is a method for determining the position of each of a plurality of regions on a substrate, characterized in that it comprises: a first step of calculating an estimated position for each of the plurality of regions using each of a plurality of different calculation methods from position measurement data of a mark provided in a sample region of the plurality of regions; a second step of obtaining a comparison result for each of the plurality of calculation methods by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions; and a third step of selecting, for each of the plurality of regions, a calculation method to be used to calculate the estimated position of that region from the plurality of calculation methods based on the comparison result obtained in the second step.

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

[0010] According to the present invention, for example, it is possible to provide a technique that is advantageous for determining the respective positions of a plurality of regions on a substrate. [Brief explanation of the drawings]

[0011] [Figure 1] 1 is a schematic diagram showing the configuration of an exposure apparatus according to one aspect of the present invention. [Figure 2] FIG. 2 is a schematic diagram illustrating the configuration of an alignment optical system. [Figure 3] 10 is a flowchart for explaining an exposure process in the exposure apparatus. [Figure 4] 10 is a flowchart for explaining a method for determining the positions of each of a plurality of shot areas on a substrate. [Figure 5] FIG. 5 is a diagram showing an example of a comparison result acquired in S406 shown in FIG. [Figure 6] FIG. 5 is a diagram showing an example of a calculation method selected in S408 shown in FIG. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. Note that the following embodiments do not limit the invention according to the claims. Although multiple features are described in the embodiments, not all of these multiple features are necessarily essential to the invention, and multiple features may be combined arbitrarily. Furthermore, in the accompanying drawings, the same reference numerals are used to designate the same or similar components, and redundant explanations will be 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, and exposes a substrate 4 via an original 2 (reticle or mask). In this embodiment, the exposure apparatus 1 projects the pattern of the original 2 onto the substrate 4 via a projection optical system 3, and transfers the pattern of the original 2 onto the substrate 4.

[0014] 1, the exposure apparatus 1 has a projection optical system 3 that projects (reduces projection) a pattern of 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 supports the chuck 5 and positions the substrate 4 at a predetermined position, an alignment optical system 7 that measures the position of the alignment marks on the substrate, a control unit CN, and a memory unit DP.

[0015] The control unit CN is configured, for example, by a computer (information processing device) including a CPU, memory, etc., and comprehensively controls each unit of the exposure apparatus 1 in accordance with a program stored in the storage unit SU, etc., to operate the exposure apparatus 1. In addition to controlling the exposure process in which the substrate 4 is exposed via the original 2, the control unit CN also functions as a processing unit that performs processing to determine the positions of each of the multiple shot areas (multiple areas) on the substrate and the arrangement of the shot areas, i.e., the so-called shot arrangement.

[0016] The storage unit SU stores programs and various information (data) required to control each part of the exposure apparatus 1 and perform exposure processing to expose the substrate 4. The storage unit SU also stores programs and various information (data) required to determine the positions and shot arrangements of each of a plurality of shot areas on the substrate.

[0017] The display unit DP is a display device for displaying various types of information related to the exposure apparatus 1. The display unit DP includes, for example, a touch panel, and displays various user interfaces (screens) and accepts operations from the user. The display unit DP may be configured integrally with the exposure apparatus 1 (in a common housing), or may be configured separately from the exposure apparatus 1 (in a different housing).

[0018] FIG. 2 is a schematic diagram showing the configuration of the alignment optical system 7. The alignment optical system 7 functions as an acquisition unit that optically detects marks (alignment marks) provided in each shot area of ​​the substrate 4 and acquires 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. Light from the light source 8 is reflected by the beam splitter 9 and passes through the lens 10 to illuminate the alignment mark 11 or 12 formed on the substrate 4. The light diffracted by the alignment mark 11 or 12 passes through the lens 10, the beam splitter 9, and the lens 13 and is received by the sensor 14.

[0019] 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.

[0020] In S101, 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 supported by a substrate stage 6.

[0021] In S102, pre-alignment is performed. Specifically, alignment marks 11 for pre-alignment on the substrate are detected by the alignment optical system 7, and the position of the substrate 4 is roughly determined. At this time, detection of the alignment marks 11 is performed for multiple shot areas on the substrate 4, and the overall shift and first-order linear components (magnification and rotation) of the substrate 4 are determined.

[0022] In S103, fine alignment is performed. Specifically, based on the results of the pre-alignment, the substrate stage 6 is first driven to a position where the alignment marks 12 for fine alignment on the substrate can be detected by the alignment optical system 7. Then, the alignment marks 12 provided in each of the multiple shot areas on the substrate 4 are detected by the alignment optical system 7, and the overall shift and first-order linear components (magnification and rotation) of the substrate 4 are precisely determined. At this time, by measuring the positions of multiple shot areas, it is also possible to precisely determine higher-order deformation components of the substrate 4 (shot arrangement). This makes it possible to determine the precise position of each shot area on the substrate 4, i.e., the shot arrangement.

[0023] In S104, the substrate 4 is exposed. Specifically, each shot area on the substrate 4 is exposed while the substrate 4 is positioned via the substrate stage 6 based on the shot arrangement determined by fire alignment. As a result, the pattern of the original 2 is transferred onto each shot area on the substrate 4 via the projection optical system 3.

[0024] In S105, the substrate 4 is unloaded from the exposure apparatus 1.

[0025] In this embodiment, when distortion (for example, a high-order deformation component) occurs in the substrate 4, fine alignment (S103) has a function of correcting distortion of the substrate 4. In order to realize this correction function, in this embodiment, a fifth-order polynomial model is used as an example of a model (regression model) for estimating the positions (shot arrangement) of each of a plurality of shot areas on the substrate, but the present invention is not limited to this. For example, a model of any order may be used, or a model other than a polynomial (such as a trigonometric function model or a logarithmic model) may be used.

[0026] When the deformation of the substrate 4 is expressed by a fifth-order polynomial model, the position of each shot area, more specifically, the positional shift (ShiftX, ShiftY) of each shot area is expressed by the following equation: Note that the positional shift of each shot area is also a correction value (alignment correction value) for correcting such positional shift.

[0027]

number

[0028] In the formula, x and y indicate the position of the shot area on the substrate 4. From the actual position measurement data of each shot area on the substrate 4, k1 to k 42 Coefficients up to are determined. Then, the positional deviation of each shot area is calculated based on the equation for which the coefficients have been determined. The overall position of substrate 4 is corrected based on the positional deviation of each shot area calculated in this way.

[0029] To obtain the position measurement data, the alignment optical system 7 detects alignment marks 12 provided in, for example, some of the multiple shot areas on the substrate, so-called sample areas. The number of sample areas is approximately 4 to 50. By increasing the number of sample areas, higher-order deformation components of the substrate 4 can be corrected, enabling more accurate alignment.

[0030] Here, in the conventional technology, a single model is applied to the entire substrate 4 as a calculation method for calculating the position (estimated position) of each shot area on the substrate, but such a model is not necessarily optimal when considering each shot area.

[0031] Therefore, in this embodiment, a calculation method (a model as a calculation method) for calculating the estimated position of a shot area is optimized for each shot area on a substrate, and the calculation method used for calculating the estimated position of the shot area is made different for each shot area. In other words, for each of a plurality of shot areas on a substrate, a calculation method to be used for calculating the shot area is selected (determined) from a plurality of calculation methods.

[0032] 4, a method for determining the position of each of a plurality of shot areas on a substrate in this embodiment will be described, focusing on determining a calculation method for calculating an estimated position. In this embodiment, this method is executed by the control unit CN of the exposure apparatus 1, but it can also be executed by an information processing device that is an external device separate from the exposure apparatus 1.

[0033] In S402, position measurement data of the marks provided in each of the multiple shot areas on the substrate 4 is acquired. As described above, the position measurement data can be acquired by optically detecting the marks provided in each shot area of ​​the substrate 4 using the alignment optical system 7.

[0034] In S404 (first step), an estimated position of each of the multiple shot areas on the substrate is calculated using a calculation method for calculating (estimating) the estimated position of the shot area from the position measurement data acquired in S402. Specifically, position measurement data of the mark provided in the sample area is extracted from the position measurement data acquired in S402, and an estimated position of each of the multiple shot areas on the substrate is calculated from the position measurement data using each of multiple different calculation methods.

[0035] In this embodiment, a third-order polynomial model and a fifth-order polynomial model are used as multiple calculation methods, and the estimated position of each shot area on the substrate is calculated using each model. For example, by applying the position measurement data of the mark provided in the sample area acquired in S402 to each of the third-order polynomial model and the fifth-order polynomial model, the positional deviation of each shot area is obtained as the estimated position of each shot area on the substrate.

[0036] In S406 (second step), for each of the multiple calculation methods, the estimated position of each of the multiple shot areas calculated in S404 is compared with the actual position (the actual position of each of the multiple shot areas), and a comparison result is obtained. The comparison result may be, for example, the difference between the estimated position of each of the multiple shot areas and the actual position of each of the multiple shot areas. Since position measurement data of the marks provided in each of the multiple shot areas on the substrate is acquired in S402, the actual position of each of the multiple shot areas can be determined from this position measurement data. Another possible comparison result may be a correction result obtained by correcting the positional deviation of each of the multiple shot areas based on the estimated position of each of the multiple shot areas.

[0037] In this embodiment, for the third-order polynomial model, as shown in FIG. 5(a), correction results are obtained by correcting the positional deviation of each shot area based on the estimated position (alignment correction value) of each shot area calculated using the third-order polynomial model. Similarly, for the fifth-order polynomial model, as shown in FIG. 5(b), correction results are obtained by correcting the positional deviation of each shot area based on the estimated position (alignment correction value) of each shot area calculated using the fifth-order polynomial model. In FIGS. 5(a) and 5(b), the correction results are represented as correction residuals, which are the differences between the estimated positions of each shot area and the actual positions of each shot area, and are represented by the length and direction of the arrows in each shot area. Thus, in this embodiment, correction residuals, which are the correction results of each shot area, are obtained as comparison results for each of the third-order polynomial and fifth-order polynomial (two different calculation methods). Note that in S406, the difference between the correction residuals shown in FIG. 5(a) and FIG. 5(b) may further be calculated, as shown in FIG. 5(c). In addition, the correction residuals shown in Figures 5(a) and 5(b) and the difference shown in Figure 5(c) may be displayed on the display unit DP of the exposure apparatus 1 so that the user can visually recognize the differences in correction residuals (correction results) due to differences in calculation methods.

[0038] In S408 (third step), for each of the multiple shot areas on the substrate, a calculation method to be used to calculate the estimated position of the shot area is selected (determined) from the multiple calculation methods based on the comparison result acquired in S406. For example, for each shot area, a calculation method that results in a difference between the estimated position and the actual position of the shot area within an allowable range, preferably a calculation method that results in the smallest difference, is selected as the calculation method to be used to calculate the estimated position of the shot area.

[0039] In this embodiment, the correction residual shown in Fig. 5(a) and the correction residual shown in Fig. 5(b) are compared for each shot area, and the polynomial model corresponding to the smaller correction residual, i.e., the one with the shorter arrow, is selected. In this way, by selecting a third-order polynomial model or a fifth-order polynomial model as the calculation method for each shot area, as shown in Fig. 6, the third-order polynomial model is selected for shot area SRA, and the fifth-order polynomial model is selected for shot area SRB.

[0040] According to this embodiment, the optimal calculation method (or model) can be selected for each of the multiple shot areas on the substrate, and an estimated position close to the actual position of the shot area can be calculated, thereby improving alignment accuracy.

[0041] In this embodiment, the unit of area for selecting (determining) the calculation method to be used for calculating the estimated position of the shot area is the shot area, but this is not limited to this and can be applied to any area on the substrate. For example, the calculation method to be used for calculating the estimated position of the shot area may be selected for each mark area on the substrate where a mark (such as alignment mark 11 or 12) is provided. Also, the calculation method to be used for calculating the estimated position of the shot area may be selected for each specific area on the substrate. Here, the specific area on the substrate is an area with characteristics different from other areas, such as a peripheral area including the periphery of the substrate 4. Note that the same (common) calculation method may be selected for the specific area on the substrate, and calculation methods may be selected individually for the other areas.

[0042] Furthermore, the comparison result between the estimated position and the actual position of each shot area on the substrate may be the comparison result of one of the shift component, magnification component, and rotation component of the positional deviation, or may be the comparison result of a combination of the shift component, magnification component, and rotation component.

[0043] Furthermore, a weight corresponding to each of the multiple calculation methods may be assigned to the comparison result obtained by comparing the estimated position and actual position of each shot area on the substrate. By selecting the calculation method to be used for calculating the estimated position of each shot area based on the weighted comparison result obtained in this manner, it is possible to suppress variations in the calculation method selected due to slight differences in the calculation method. Furthermore, if a specific calculation method is effective, it is possible to preferentially select the specific calculation method by increasing the weight for the specific calculation method. For example, if a high-order calculation method has high reliability, it is possible to increase the weight for the high-order calculation method so that the high-order calculation method is selected more frequently. Furthermore, a threshold may be set for the comparison result obtained by comparing the estimated position and actual position of each shot area on the substrate, and the calculation method to be used for calculating the estimated position of each shot area may be selected by comparing the result with the threshold.

[0044] Furthermore, the multiple calculation methods may be calculation methods of different types, or may be calculation methods with different parameters of the same type. For example, if polynomials for estimating the positions of each shot area are considered as calculation methods, the multiple calculation methods include calculation methods with different types of polynomials or calculation methods with different parameters of the polynomials. When the hyperparameters are different, some coefficients of the polynomials may be removed or weights may be changed. Specifically, weights may be assigned to specific terms of the polynomials to make the parameters different, or when a model (regression model) is generated using machine learning or the like, the hyperparameters may be made different.

[0045] The method for manufacturing an article according to an embodiment of the present invention is suitable for manufacturing articles such as semiconductor devices, liquid crystal display devices, flat panel displays, and MEMS. This manufacturing method includes the steps of exposing a substrate coated with a photosensitive agent using the exposure apparatus 1 (exposure process) described above and developing the exposed photosensitive agent. The developed photosensitive agent pattern is then used as a mask to perform etching and ion implantation processes on the substrate, forming a circuit pattern on the substrate. These exposure, development, etching, and other processes are repeated to form a circuit pattern consisting of multiple layers on the substrate. In subsequent processes, the substrate on which the circuit pattern has been formed is diced (processed), followed by chip mounting, bonding, and inspection. This manufacturing method may also include other well-known processes (such as oxidation, film formation, vapor deposition, doping, planarization, and resist stripping). The method for manufacturing an article according to this embodiment is advantageous over conventional methods in at least one of the performance, quality, productivity, and production cost of the article.

[0046] The present invention can also be realized by supplying a program that realizes one or more functions of the above-described embodiments to a system or device via a network or a storage medium, and having one or more processors in the computer of the system or device read and execute the program. It can also be realized by a circuit (e.g., ASIC) that realizes one or more functions.

[0047] The disclosure of this specification includes the following methods, information processing apparatus, exposure method, exposure apparatus, article manufacturing method, determination method, and program for determining the positions of each of a plurality of regions on a substrate.

[0048] (Item 1) 1. A method for determining the location of each of a plurality of regions on a substrate, comprising: a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; 10. A method comprising:

[0049] (Item 2) 2. The method according to item 1, wherein the area includes a shot area on the substrate, a mark area on the substrate where a mark is provided, or a specific area on the substrate.

[0050] (Item 3) 3. The method according to item 1 or 2, wherein the comparison result includes a difference between the estimated position of each of the plurality of regions and the actual position of each of the plurality of regions.

[0051] (Item 4) 3. The method according to claim 1, wherein the comparison result includes one of a shift component, a magnification component, and a rotation component of a positional deviation between the estimated position of each of the plurality of regions and the actual position of each of the plurality of regions.

[0052] (Item 5) 3. The method according to claim 1, wherein the comparison result includes a combination of a shift component, a magnification component, and a rotation component of a positional deviation between the estimated position of each of the plurality of regions and the actual position of each of the plurality of regions.

[0053] (Item 6) Item 3. The method according to item 3, wherein in the third step, for each of the plurality of regions, a calculation method with the smallest difference is selected from the plurality of calculation methods as a calculation method to be used for calculating the estimated position of that region.

[0054] (Item 7) 7. The method according to any one of items 1 to 6, wherein in the third step, for each of the plurality of regions, a calculation method to be used for calculating the estimated position of the region is selected based on a weighted comparison result obtained by assigning a weight according to each of the plurality of calculation methods to the comparison result obtained in the second step.

[0055] (Item 8) 8. The method according to any one of items 1 to 7, wherein the plurality of calculation methods include calculation methods in which types of polynomials for estimating the positions of the plurality of regions are different from each other, or calculation methods in which parameters of polynomials for estimating the positions of the plurality of regions are different from each other.

[0056] (Item 9) 9. The method according to any one of items 1 to 8, wherein the second step includes determining an actual position of each of the plurality of regions from position measurement data of a mark provided in each of the plurality of regions.

[0057] (Item 10) 3. The method according to item 1 or 2, characterized in that in the second step, a correction result obtained by correcting the positional deviation of each of the plurality of regions based on the estimated positions calculated in the first step is obtained as the comparison result.

[0058] (Item 11) 11. The method according to item 10, wherein the correction result includes a correction residual which is a difference between an estimated position of each of the plurality of regions and an actual position of each of the plurality of regions.

[0059] (Item 12) An information processing device, a processing unit that performs processing to determine the positions of each of a plurality of regions on the substrate; The processing unit a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result of comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; An information processing device characterized by performing the above.

[0060] (Item 13) An exposure method for exposing a substrate, comprising: determining the position of each of a plurality of regions on the substrate; exposing each of the plurality of regions while positioning the substrate based on the positions determined in the step above; and The step of determining the position includes: a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result of comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; Including, An exposure method characterized by:

[0061] (Item 14) An exposure apparatus for exposing a substrate, an acquisition unit that acquires position measurement data of a mark provided in a sample region among a plurality of regions on a substrate; a processing unit that performs processing to determine the positions of the plurality of regions using the position measurement data acquired by the acquisition unit; and The processing unit a first step of calculating an estimated position for each of the plurality of regions from the position measurement data using a plurality of different calculation methods; a second step of acquiring a comparison result of comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; To do An exposure apparatus characterized by:

[0062] (Item 15) Exposing a substrate using the exposure method according to Item 13; developing the exposed substrate; manufacturing an article from the developed substrate; A method for manufacturing an article, comprising:

[0063] (Item 16) A method for determining a calculation method for calculating an estimated position of each of a plurality of regions on a substrate, the method comprising: a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result of comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; A method for determining whether a parameter is a parameter that is a function of a parameter.

[0064] (Item 17) An information processing device, a processing unit for performing processing to determine a calculation method for calculating an estimated position of each of a plurality of regions on a substrate; The processing unit a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result of comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; To do 1. An information processing device comprising:

[0065] (Item 18) A program for causing a computer to execute each step of the method according to any one of items 1 to 11.

[0066] (Item 19) Item 17. A program for causing a computer to execute each step of the determination method according to Item 16.

[0067] The invention is not limited to the above-described embodiments, and various changes and modifications can be made 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]

[0068] 1: Exposure device 2: Original 3: Projection optical system 4: Substrate 5: Chuck 6: Substrate stage 7: Alignment optical system CN: Control unit

Claims

1. 1. A method for determining the location of each of a plurality of regions on a substrate, comprising: a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; 10. A method comprising:

2. 2. The method according to claim 1, wherein the area includes a shot area on the substrate, a mark area on the substrate where a mark is provided, or a specific area on the substrate.

3. The method of claim 1 , wherein the comparison results include a difference between the estimated position of each of the plurality of regions and the actual position of each of the plurality of regions.

4. 2. The method of claim 1, wherein the comparison result includes one of a shift component, a magnification component, and a rotation component of a positional deviation between the estimated position of each of the plurality of regions and the actual position of each of the plurality of regions.

5. 2. The method of claim 1, wherein the comparison result includes a combination of a shift component, a magnification component, and a rotation component of a positional deviation between the estimated position of each of the plurality of regions and the actual position of each of the plurality of regions.

6. 4. The method according to claim 3, wherein in the third step, for each of the plurality of regions, a calculation method from among the plurality of calculation methods that results in the smallest difference is selected as the calculation method to be used to calculate the estimated position of that region.

7. 2. The method according to claim 1, wherein in the third step, for each of the plurality of regions, a calculation method to be used for calculating the estimated position of the region is selected based on a weighted comparison result obtained by assigning a weight corresponding to each of the plurality of calculation methods to the comparison result obtained in the second step.

8. 2. The method according to claim 1, wherein the plurality of calculation methods include calculation methods in which types of polynomials for estimating the positions of the plurality of regions are different from each other, or calculation methods in which parameters of polynomials for estimating the positions of the plurality of regions are different from each other.

9. 2. The method according to claim 1, wherein the second step includes determining an actual position of each of the plurality of regions from position measurement data of a mark provided in each of the plurality of regions.

10. 2. The method according to claim 1, wherein the second step acquires, as the comparison result, a correction result obtained by correcting the positional deviation of each of the plurality of regions based on the estimated positions calculated in the first step.

11. The method of claim 10 , wherein the correction results include correction residuals that are differences between the estimated positions of each of the plurality of regions and the actual positions of each of the plurality of regions.

12. An information processing device, a processing unit that performs processing to determine the positions of each of a plurality of regions on the substrate; The processing unit a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; To do 1. An information processing device comprising:

13. An exposure method for exposing a substrate, comprising: determining the position of each of a plurality of regions on the substrate; exposing each of the plurality of regions while positioning the substrate based on the positions determined in the step above; and The step of determining the position includes: a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; Including, An exposure method characterized by:

14. An exposure apparatus for exposing a substrate, an acquisition unit that acquires position measurement data of a mark provided in a sample region among a plurality of regions on a substrate; a processing unit that performs processing to determine the positions of the plurality of regions using the position measurement data acquired by the acquisition unit; and The processing unit a first step of calculating an estimated position for each of the plurality of regions from the position measurement data using a plurality of different calculation methods; a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; To do An exposure apparatus characterized by:

15. exposing a substrate using the exposure method according to claim 13; developing the exposed substrate; manufacturing an article from the developed substrate; A method for manufacturing an article, comprising:

16. A method for determining a calculation method for calculating an estimated position of each of a plurality of regions on a substrate, the method comprising: a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; A method for determining whether a parameter is a parameter that is a function of a parameter.

17. An information processing device, a processing unit for performing processing to determine a calculation method for calculating an estimated position of each of a plurality of regions on a substrate; The processing unit a first step of calculating an estimated position for each of the plurality of regions from position measurement data of a mark provided in a sample region among the plurality of regions using each of a plurality of calculation methods different from each other; a second step of acquiring a comparison result obtained by comparing the estimated position of each of the plurality of regions calculated in the first step with the actual position of each of the plurality of regions for each of the plurality of calculation methods; a third step of selecting, for each of the plurality of regions, a calculation method to be used for calculating an estimated position of the region from the plurality of calculation methods based on the comparison result obtained in the second step; To do 1. An information processing device comprising:

18. A program for causing a computer to execute each step of the method according to claim 1.

19. A program for causing a computer to execute each step of the determination method according to claim 16.

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