Exposure apparatus, exposure method, information processing apparatus, program, and method for manufacturing articles

Abstract

This invention provides a technology advantageous for accurately acquiring the shape of a planar mirror in an exposure apparatus having an interferometer system without redundant axes. [Solution] The exposure apparatus comprises a stage, a drive mechanism for driving the stage, a first interferometer having a first optical axis parallel to a first direction, a second interferometer having a second optical axis parallel to the first direction and spaced apart from the first optical axis, a plane mirror shared by the first and second interferometers, and a control unit. The control unit controls the drive mechanism based on the output of each interferometer so that the stage is positioned at a predetermined exposure position along a second direction perpendicular to the first direction, transferring the marks to each of the multiple shot regions of the substrate, and obtaining the shape of the plane mirror based on position error and rotation error data in the first direction for each of the multiple shot regions obtained based on the marks transferred to each of the multiple shot regions.

Description

[Technical Field]

[0001] The present invention relates to an exposure apparatus, an exposure method, an information processing apparatus, a program, and a method for manufacturing articles. [Background technology]

[0002] Exposure systems for manufacturing semiconductor devices may be equipped with plane mirrors and laser interferometers to drive the stage in the XY direction and for small rotations. Here, a plane mirror aligned with the X direction and a plane mirror aligned with the Y direction are fixed to the stage, and at least two laser interferometers may be positioned so that the measurement light is incident perpendicularly on the reflective surface of each plane mirror. Ideally, the reflective surfaces of these plane mirrors should be perfectly flat, but in reality, there is distortion (shape error) in their shape. Such shape errors can reduce the accuracy of the stage movement.

[0003] Therefore, the shape of the planar mirror is calculated in advance, and the movement characteristics of the stage are corrected based on the calculation results. This can achieve highly accurate movement characteristics. For example, in Patent Document 1, the shape of the planar mirror is calculated from the measured values ​​of the redundant axis by providing a redundant axis in the interferometer system. However, providing a redundant axis means providing an interferometer separate from the interferometer that controls the movement of the stage, which is disadvantageous in terms of cost.

[0004] When an interferometer does not have redundant axes, a common method is to calculate the shape of a planar mirror using a reference substrate with measurement marks and measuring instruments such as a camera mounted on the device. Patent Document 2 is one example of this. However, the technique of measuring marks on a reference substrate requires storage space for the reference substrate and is cumbersome to transport, which reduces the work efficiency when adjusting the exposure device.

[0005] One method for calculating the shape of a planar mirror that does not require a reference substrate is to expose a substrate with an exposure apparatus that constitutes the planar mirror and use the measurement results for that substrate. For example, in Patent Document 3, the substrate is placed on a stage, exposed, then retrieved, then placed on the stage in a position rotated 180° and exposed again, and the shape of the planar mirror is calculated from the measurement results of the overlap marks formed by the first and second exposures.

[0006] Furthermore, Patent Document 4 describes a technique for measuring superposition marks formed between shots that overlap each other. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Utility Model Publication No. 59-98446 [Patent Document 2] Japanese Patent Application Publication No. 9-79829 [Patent Document 3] Japanese Patent Application Publication No. 10-308434 [Patent Document 4] Japanese Patent Publication No. 2000-299278 [Overview of the project] [Problems that the invention aims to solve]

[0008] However, as described in Patent Document 3, the method of rotating the substrate by 180° and overlapping the marks is limited by its principle to calculating the shape of the planar mirror only if it has an even function, and therefore cannot obtain sufficient calculation accuracy.

[0009] The present invention provides an advantageous technique for accurately acquiring the shape of a planar mirror in an exposure apparatus having an interferometer system without redundant axes. [Means for solving the problem]

[0010] According to one aspect of the present invention, the present invention includes a stage, a drive mechanism for driving the stage in mutually orthogonal first and second directions in a plane, and rotation around an axis orthogonal to the plane, a first interferometer having a first optical axis parallel to the first direction for measuring the position of the stage in the first direction, a second interferometer having a second optical axis parallel to the first direction and spaced apart from the first optical axis for measuring the rotation of the stage, a common plane mirror provided on the stage for measurement by the first and second interferometers, and a mechanism for sequentially moving the stage to project and transfer a mark formed on a master plate onto a substrate held on the stage. An exposure apparatus is provided, comprising a projection system and a control unit that controls the drive mechanism so that the stage is positioned based on the outputs of the first interferometer and the second interferometer, wherein the control unit controls the drive mechanism based on the outputs of the first interferometer and the second interferometer so that the stage is positioned at a predetermined exposure position along the second direction, transfers the marks to each of a plurality of shot regions of the substrate, and obtains the shape of the plane mirror based on position error and rotation error data in the first direction for each of the plurality of shot regions obtained based on the marks transferred to each of the plurality of shot regions. [Effects of the Invention]

[0011] According to the present invention, an advantageous technique is provided for acquiring the shape of a planar mirror with high precision in an exposure apparatus having an interferometer system without redundant axes. [Brief explanation of the drawing]

[0012] [Figure 1A] A top view showing the stage and surrounding components of an exposure apparatus. [Figure 1B] A perspective view showing the schematic configuration of the exposure apparatus. [Figure 1C] A block diagram showing the functional configuration of the control unit of the exposure apparatus. [Figure 2] A diagram showing the arrangement of exposed shots on the substrate. [Figure 3] A diagram illustrating the process of forming overlapping marks. [Figure 4] A diagram illustrating the outline of linear interpolation for shape errors in a planar mirror. [Figure 5] A diagram illustrating specific numerical values ​​for the coefficient matrix. [Figure 6] A diagram showing the procedure for adjusting the exposure apparatus ST in the second embodiment. [Modes for carrying out the invention]

[0013] The embodiments will be described in detail below with reference to the attached drawings. Note that the following embodiments do not limit the invention as defined in the claims. While the embodiments describe multiple features, not all of these features are essential to the invention, and the features may be combined in any way. Furthermore, in the attached drawings, identical or similar configurations are given the same reference numerals, and redundant descriptions are omitted.

[0014] <First Embodiment> In the following explanation, directions are described according to the XYZ coordinate system. In the XYZ coordinate system, the XY plane is the horizontal plane, and the Z axis can be parallel to the vertical. Furthermore, in the following, directions parallel to the X, Y, and Z axes in the XYZ coordinate system are referred to as the X direction, Y direction, and Z direction, respectively. Furthermore, in the following explanation, the Y direction will be used as the first direction and the X direction as the second direction for illustrative purposes, but the first and second directions are interchangeable. In other words, the Y direction may be the second direction and the X direction may be the first direction.

[0015] A first embodiment of the present disclosure will be described. Figure 1A is a top view showing the stage 1 and its surroundings of an exposure apparatus ST. The exposure apparatus ST may be configured to position the stage 1 as a positioning target. A substrate 3 (wafer) may be placed on the stage 1. In Figure 1A, planar mirrors 2X and 2Y are fixed to the right side and rear side of the stage 1, respectively. The outer sides (surfaces) of the planar mirrors 2X and 2Y are reflective surfaces of laser light from a laser interferometer (hereinafter referred to as "interferometer") and may be mirror-finished. The reflective surfaces of the planar mirrors 2X and 2Y are processed to be straight in their respective longitudinal directions, but may include straightness errors as processing errors.

[0016] Interferometers 4Y1 (first interferometer) and 4Y2 (second interferometer) are positioned to the side of the plane mirror 2Y. Interferometer 4Y1 has an optical axis (first optical axis) parallel to the Y direction (first direction) and measures the position of stage 1 in the Y direction. Interferometer 4Y2 has an optical axis (second optical axis) parallel to the Y direction and spaced apart from the optical axis (first optical axis) of interferometer 4Y1 and measures the rotation of stage 1. The distance between the optical axes of interferometers 4Y1 and 4Y2 is set to s [mm]. Therefore, plane mirror 2Y is a common plane mirror provided on stage 1 for measurement by interferometers 4Y1 and 4Y2. Interferometer 4X (third interferometer) is positioned to the side of the plane mirror 2X. Laser light emitted from interferometer 4X is incident on the reflective surface of plane mirror 2X. Let point O be the intersection of the optical axis of interferometer 4Y1 and the optical axis of interferometer 4X, and define this as the origin in the XY plane.

[0017] Figure 1B is a perspective view showing the schematic configuration of the exposure apparatus ST. As shown in Figure 1B, the projection system 5 can expose the mark pattern formed on the master plate 6 (also called a mask or reticle) onto the substrate 3 via a projection lens positioned on the origin O. In this embodiment, the projection system 5 can project and transfer the marks formed on the master plate 6 onto the substrate 3 held on the stage 1 by sequentially moving the stage 1.

[0018] Stage 1 is driven by a drive mechanism DM, such as a linear motor. The drive mechanism DM drives Stage 1 in mutually orthogonal directions in the Y direction (first direction) and X direction (second direction) within a plane (XY plane), and in rotation around the Z axis which is orthogonal to the XY plane. The control unit 8, described later, controls the drive mechanism DM so that Stage 1 is positioned based on the outputs of interferometers 4Y1 and 4Y2.

[0019] Stage 1 can be controlled as follows: For the translation of Stage 1 in the Y direction (first direction), the position of Stage 1 in the X direction (second direction) is controlled so that the measured value of interferometer 4X remains constant, and the measured value of interferometer 4Y1 is controlled so that it becomes an appropriate value calculated from the moving target position. For the translation of Stage 1 in the X direction (second direction), the position of Stage 1 in the Y direction (first direction) is controlled so that the measured value of interferometer 4Y1 remains constant, and the measured value of interferometer 4X is controlled so that it becomes an appropriate value calculated from the moving target position. For the rotation control of Stage 1, the value obtained by dividing the difference between the measured values ​​of interferometer 4Y1 and interferometer 4Y2 by the distance s is controlled so that it becomes an appropriate value calculated from the target rotation amount. Here, the position control and rotation control in the first and second directions can be performed in parallel. At this time, the movement of Stage 1 in the X and Y directions includes errors due to the straightness errors of the plane mirrors 2X and 2Y mentioned above. Therefore, when moving in the X direction, positional and rotational errors in the Y direction occur as a result of the movement, and when moving in the Y direction, positional errors in the X direction may occur as a result of the movement.

[0020] The relative positions of interferometers 4Y1 and 4Y2 may be reversed, and the average value of the measured values ​​of interferometer 4Y1 and interferometer 4Y2 may be used as the reference value for the interferometer in the first direction drive described above. However, in this embodiment, the reference value for the interferometer in the Y direction (first direction) drive will be described as the measured value of interferometer 4Y1. Furthermore, interferometer 4X does not necessarily have to be an interferometer; it may be replaced with, for example, a linear encoder, as long as it has a mechanism that can reference the current position.

[0021] The measuring instrument 7 may be an off-axis scope equipped with the function of measuring the relative displacement between the outer mark and the inner mark as superimposed marks formed with respect to the shot area on the substrate 3. The measuring instrument 7 may be positioned on the extension of the optical axis of the interferometer 4Y1 and on the -Y side (lower side in Figure 1A) of the origin O.

[0022] The exposure apparatus ST includes a control unit 8. The control unit 8 may be composed of, for example, a PLD (Programmable Logic Device) such as an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), a general-purpose or dedicated computer with a program installed, or a combination of all or part of these. The control unit 8 may be an information processing device located inside the exposure apparatus ST, or an information processing device located outside the exposure apparatus ST. Figure 1C shows the functional configuration of the control unit 8. As shown in Figure 1C, the control unit 8 comprehensively controls operations related to driving the stage 1, calculations using measured values ​​from the interferometer, and operations related to exposure by the projection system 5.

[0023] The control unit 8 may include a calculation unit 8a and a correction processing unit 8b. The calculation unit 8a calculates the shape errors of the plane mirrors 2X and 2Y from the measurement results of the superposition marks by the measuring instrument 7. The correction processing unit 8b corrects the shape errors of the plane mirrors 2X and 2Y calculated by the calculation unit 8a by correcting the output values ​​of the interferometers 4X, 4Y1, and 4Y2, and performs a correction process to reflect this correction in the control of the stage 1.

[0024] The correction process for correcting the shape error of the planar mirror can be performed by the correction processing unit 8b as follows:

[0025] For the translation of Stage 1 in the Y direction (first direction), the position of Stage 1 in the X direction (second direction) is controlled so that the measurement value of interferometer 4X is equal to the shape error on the optical axis of interferometer 4X on the plane mirror 2X. For the translation of Stage 1 in the X direction (second direction), the position of Stage 1 in the Y direction (first direction) is controlled so that the measurement value of interferometer 4Y1 is equal to the shape error on the optical axis of interferometer 4Y1 on the plane mirror 2Y. For the rotation control of Stage 1, the amount of rotation of Stage 1 is controlled so that the value obtained by dividing the difference between the measurement values ​​of interferometer 4Y1 and interferometer 4Y2 by distance s is equal to the value obtained by dividing the difference in shape errors on the optical axes of interferometer 4Y1 and interferometer 4Y2 on the plane mirror 2Y by distance s.

[0026] Under the aforementioned position control, the control unit 8 sequentially repeats exposure onto the substrate 3 by the projection system 5 and movement of the stage 1, thereby forming the pattern of the master plate 6 in each of the multiple shot areas on the substrate 3, as shown in Figure 2.

[0027] At this time, for each shot area that is exposed, positional and rotational errors occur relative to its original position due to the movement error of Stage 1 described above. The shot layout for exposure on the substrate 3 consists of R rows and C columns, with M shots per array. Each shot area can be represented as S(i,j), where i and j are the X and Y coordinates of the center of the substrate 3 in the coordinate system within the apparatus when the shot area is exposed. For example, the shot area located at the center of the substrate 3 is S(0,0), and the spacing between multiple shot areas in the X and Y directions is p, respectively. X , p Y Let's assume that in that case, the shot area in the lower left of S(0,0) is S(p X , p Y ) can be expressed as follows. Note that in Figure 2, the increasing directions of i and j are left and up, respectively, because i and j are not coordinates within the substrate 3, but rather the coordinates of the center of the substrate 3 when the shot area is exposed.

[0028] The control unit 8 controls the drive mechanism DM based on the outputs of the interferometers so that the stage 1 is positioned at a predetermined exposure position along the X direction (second direction), and transfers marks to each shot area so that a partial area overlaps between adjacent shot areas. Then, the control unit 8 obtains data on the position error and rotation error in the Y direction (first direction) based on the data measuring the relative distance between two marks in the overlapping mark formed by the overlap of two marks (for example, the outer mark and the inner mark described later with reference to FIG. 3) within each shot area where the mark has been transferred. For forming the overlapping mark, for example, the method described in Japanese Patent Application Laid-Open No. 2000-299278 (Patent Document 4) can be adopted. Hereinafter, an example of the process of forming the overlapping mark will be described.

[0029] As shown in FIG. 3(a), in the shot area where the original pattern has been transferred, there are M X 1, M X 2, M Y 1, M Y 2 as outer marks and m X 1, m X 2, m Y 1, m Y 2 as inner marks. Also, the X-direction distance between M X 1, M X 2 and m X 1, m X 2 is d X , and the Y-direction distance between M Y 1, M​​​​​​​​​​​​​​​​​​​​​​X -p Y ) and Mm X 2(p X -p Y ) is formed. Similarly, by the arrangement in the Y direction, the superimposed marks Mm Y 1(p X -p Y ) and Mm Y 2(p X -p Y ) is formed.

[0031] These superimposed marks formed in each shot area on the substrate 3 are measured by moving the stage 1 so that the mark to be measured is within the measurable area of ​​the measuring instrument 7, and the relative displacement (relative distance) between the outer mark and the inner mark is measured using the measuring instrument 7.

[0032] Each shot region formed on the substrate 3 is calculated as a relative value to the average value of all shot regions with respect to positional and rotational errors. Specifically, the positional error of each shot region is calculated using the coordinates of the center of the substrate 3 as a variable, ε X (i,j) and ε Y Let (i,j) be defined as the rotation error ε. θ (i,j) is defined as follows. Furthermore, known techniques can be used to calculate the positional and rotational errors of each shot region from the measured values ​​of the superposition marks formed between the overlapping shot regions. For example, the methods described in Japanese Patent Publication No. 2000-299278 (Patent Document 4), Japanese Patent Publication No. 2005-064268, and Japanese Patent Publication No. 2009-259966 can be used.

[0033] Here, the position error ε X (i,j) is due to the shape error of the plane mirror 2X, but not to the shape error of the plane mirror 2Y. Therefore, the X coordinate of the shot region is not needed as a variable when calculating the shape error of the plane mirror 2X. Thus, the position error ε of each shot region X By calculating the average of (i,j) for each i, we can determine the position error ε with Y coordinate j as the variable. X Calculate (j).

[0034] If N(j) is the number of shots that satisfy the Y coordinate = j of the center of substrate 3 during exposure, then the position error ε X (j) can be calculated using equation (1). Note that here, the subscript i below the summation symbol Σ represents the possible X coordinates of Stage 1 during shot exposure, and does not mean consecutive integers.

number

[0035] Similarly, position error ε Y (i,j) and rotation error ε θ (i,j) is due to the shape error of the plane mirror 2Y, but not to the shape error of the plane mirror 2X. Therefore, the position error ε of each shot region. Y (i,j) and rotation error ε θ By calculating the average of (i,j) for each j, the position error ε Y (i) and rotation error ε θ (i) can be calculated as shown in equations (2) and (3), respectively.

number

number

[0036] The control unit 8 obtains the shape of the plane mirror 2Y based on the spacing between multiple shot regions in the X direction (second direction), and the distance between the optical axis of interferometer 4Y1 (first optical axis) and the optical axis of interferometer 4Y2 (second optical axis).

[0037] When the X-coordinate of the center of substrate 3 is i, we formulate a relationship when Y-shift and rotation errors occur in stage 1 due to shape errors in the planar mirror 2Y. The position of stage 1 in the Y direction is controlled based on the measurement value of interferometer 4Y1, and the small amount of rotation is controlled based on the difference in the measurement values ​​of interferometers 4Y1 and 4Y2. Therefore, the shape error b lies at the intersection of the reflective surface on planar mirror 2Y and the optical axis of interferometer 4Y1. YIf (i) is present, as shown in Figure 1(a), the exposure position of the shot will be shifted in the Y position relative to the substrate 3.

[0038] When the X coordinate of the center of substrate 3 is i, the position error ε of the shot region Y (i) can be expressed by equation (4). Note that the position error ε of the shot region Y (i) The fixed error included in ε Y0、 Irregular calculation error ζ Y (i)

number

[0039] Also, the rotation error ε of the shot region θ (i) can be expressed by the following equation. Note that the rotation error W of Stage 1 θ (i) Rotation error ε of the shot region θ (i) The fixed error included in ε θ0、 Irregular calculation error ζ θ (i)

number

[0040] Here, the rotation error W of Stage 1 θ (i) can be expressed by the following equation:

number

[0041] Therefore, equation (5) is, b Y (i) and b Y It can be expressed as equation (7) with (i+s) as the variable.

number

[0042] Here, we will explain by assigning specific numerical values ​​to the aforementioned symbols as follows.

[0043] Distance between the optical axes of interferometers 4Y1 and 4Y2: s[mm]=80, Spacing of measurement marks: p X [mm]=30, Shot layout: 37 shots in a 7x7 grid (R=7, C=7, M=37) Furthermore, the X-coordinate [mm] of the center of the shot area relative to the center of substrate 3 is 0, ±30, ±60, and ±90.

[0044] Equations (4) and (7) are combined and solved as a system of linear equations using matrices. The number of equations formulated is ε for the position error of the shot region for a shot region of 7 columns. Y (i) and rotation error ε θ (i) There are two of these, so the total is 14. On the other hand, the number of unknowns is the shape error b Y (i) 7 items, shape error b Y There are 7 (i+s) values, and the fixed error is ε Y0 and ε θ0 There are a total of 16, including the two mentioned above, which is more than the number of equations mentioned earlier, so the result is indeterminate.

[0045] Therefore, b Y For (i+s), we formulate an equation using an approximation by linear interpolation with the adjacent i values. Figure 4(a) shows a part of the planar mirror 2Y. For example, when the X coordinate of the center of the substrate 3 is i[mm]=-90, the position error ε Y (i) and rotation error ε θ (i) In the formula b Y (i) is b Y (-90) and b Y (i+s) is b Y (-10).

[0046] Here, b Y For (-10), the neighboring cells i are b. Y (-30) and b Y Linear interpolation is performed at (0). That is, as shown in Figure 4(b), b Y (-10) is b Y (-30) and b Y We formulate the equation assuming that it lies on the line segment connecting (0).

[0047] b Y (i + s) can be expressed as in Equation 7.1 using quot(s, p X ) and mod(s, p X ). However, quot(s, p X ) is the integer part of the quotient when s is divided by p X , and mod(s, p X ) is the remainder when s is divided by p X . [Number] ···(8)

[0048] Therefore, substituting numerical values gives Equation (9). [Number] ···(9)

[0049] Note that such linear interpolation is not necessary for b X when the stage 1 is on the +X side (i.e., in the region where i + s > (C - 1) * p Y / 2 = 90) during the exposure of the leftmost shot region in Figure 1A. This is because in that region, even if we try to perform linear interpolation using the two adjacent b Y (i), the two target b Y (i) do not exist. In this example, i + s[mm] = 110, 140, 170 correspond to i[mm] = 30, 60, 90. Also, of course, when mod(s, p X ) = 0, the aforementioned linear interpolation is not necessary.

[0050] In this way, by performing linear interpolation using the two adjacent i for b Y (i + s) in a predetermined region, the number of unknowns can be suppressed, and a solution that minimizes the sum of the squares of ζ Y (i) and ζ θ (i) can be obtained.

[0051] In this example, the number of unknowns is bY (i) 7 times, b Y There are three (i+s) values, and the fixed error is ε Y0 and ε θ0 This results in a total of 12 equations, which is fewer than the 14 equations that were initially formulated, thus avoiding an indeterminate equation.

[0052] By substituting equation (8) into equation (7), we obtain equation (10).

number

[0053] Furthermore, there is a shape error b in the Y direction at the reflection point on the planar mirror 2Y. Y (i) has degrees of freedom for the mean value of the possible i, so b Y The mean value of (i) is not uniquely determined. To avoid this uncertainty, b Y We add the constraint condition in equation (11) that the mean value of (i) is 0. Therefore, the system of equations includes an equation that is a constraint on the mean value of the shape of the plane mirror 2Y.

number

[0054] Summarizing the equations we have formulated so far, the position error ε in the shot region is given by the following case distinctions based on i. Y (i) and rotation error ε θ Equation (i) can be formulated. ·i<(C-1)*p X For / 2-s: ε Y Formula (i): Formula (4) ε θ Formula (i): Formula (10) In this example, i[mm]<10, i[mm]=-90, -60, -30, 0. ·i>(C-1)*p X For / 2-s: ε Y Formula (i): Formula (4) ε θ Formula (i): Formula (7) In this example, i[mm] > 10, i[mm] = 30, 60, 90.

[0055] Measured value ε Y (i), ε θ (i) A column vector consisting of a single zero is r, the coefficient matrix consisting of each coefficient is A, the column vector consisting of the unknowns to be solved is x, and the irregular calculation error is ζ Y (i), ζ θ (i) Let e ​​be a column vector consisting of (i) and one zero. Using these, the above equations can be expressed collectively as follows: where matrix E is the identity matrix, and matrix A1 is the spacing p of the measurement marks based on equations (10) and (7). X This matrix includes values ​​calculated from the interaxial distance s between interferometers 4Y1 and 4Y2. Note that column vectors r, x, and e are represented by vector symbols in the following formulas.

number

number

number

number

number

[0056] In this example, column vector r is 15 rows and 1 column, matrix A is 15 rows and 12 columns, column vector x is 12 rows and 1 column, and column vector e is 15 rows and 1 column. The specific numerical values ​​on the right-hand side of equations (13) to (16), calculated from the coordinates and dimensions, are shown in Figures 5(a), (b), (c), and (d), respectively.

[0057] Here, by transforming the normal equation (17) into equation (18), the length of the column vector e is minimized (i.e., the irregular calculation error ζ Y (i), ζ θ (i) The column vector x that minimizes the sum of squares can be calculated. Note that matrix A T The transpose of matrix A is matrix A -1 This represents the inverse matrix of matrix A.

number

number

[0058] In this way, the control unit 8 can calculate the shape error of the plane mirror 2Y by treating the multiple equations that have been formulated as a single system of equations and performing a unified calculation process using the least squares method.

[0059] Next, we will explain the procedure for calculating the shape error of a 2X planar mirror.

[0060] When the Y coordinate of the center of substrate 3 is j, a shape error b is present at the intersection of the reflective surface on the plane mirror 2X and the optical axis of the interferometer 4X. X If (j) is present, as shown in Figure 1A, the exposure position of the shot area will be shifted in the X position relative to the substrate 3. Here, the rotation error is constant with respect to the movement of stage 1 in the Y direction at the same X coordinate. Therefore, the shape error b X (j) does not require consideration of rotational error, as was considered when calculating the shape error of the planar mirror 2Y, and b X (j) = ε XThis can be calculated by using (j).

[0061] Using the calculation method described above, the calculation unit 8a calculates the shape errors of the planar mirrors 2X and 2Y all at once. The correction processing unit 8b then corrects the shape errors of the planar mirrors 2X and 2Y calculated by the calculation unit 8a and adjusts the output values ​​of the interferometers 4X, 4Y1, and 4Y2, for example, in order to reflect this in the positioning (position correction) of the stage 1 when it moves.

[0062] As described above, the control unit 8 controls the drive mechanism DM based on the output of each interferometer to transfer marks to each of the multiple shot regions of the substrate 3 so that the stage 1 is positioned at a predetermined exposure position along the X direction (second direction). Then, the control unit 8 obtains the shapes of the planar mirrors 2X and 2Y based on the position error and rotation error data in the Y direction (first direction) of each of the multiple shot regions obtained based on the marks transferred to each of the multiple shot regions.

[0063] In this embodiment described above, the control unit 8 obtains the shape of the plane mirror 2Y by solving a system of equations formulated by setting the known and unknown variables as follows, using the least squares method. Known numbers: • Positional error and rotational error in the Y direction (first direction) of the shot area. • Spacing between multiple shot areas in the X direction (second direction) • Distance between the optical axis (first optical axis) of interferometer 4Y1 and the optical axis (second optical axis) of interferometer 4Y2 Unknown: • Flat mirror 2Y shape

[0064] According to this embodiment, the shape error of the planar mirrors 2X and 2Y can be measured with high precision.

[0065] In summary, the control method for the exposure apparatus ST may include an exposure step, a measurement step, a first calculation step, a second calculation step, and a control step. The exposure step, measurement step, first calculation step, second calculation step, and control step may be controlled by the control unit 8. In the exposure step, the pattern of superimposed marks configured on the master plate 6 is exposed onto the substrate 3 via a projection lens.

[0066] The measurement process is performed with a substrate 3 having multiple shot regions arranged at equal pitches placed on the stage 1. In this state, the measurement process controls the drive mechanism DM based on the output of each interferometer so that the overlapping marks of each shot region fall within the measurable area of ​​the measuring instrument 7, while the relative displacement between the outer and inner marks of the multiple marks is measured by the measuring instrument 7. In the first calculation process, the position and rotation errors of each shot region may be calculated based on the measurement results of the relative displacement between the outer and inner marks of the multiple marks by the measuring instrument 7. In the second calculation process, the shape error of the plane mirror 2Y may be calculated based on the calculation results of the position and rotation errors of each shot region in the first calculation process and the distance s (inter-optical axis distance) between the optical axis centers of interferometer 4Y1 and interferometer 4Y2, and shape error data may be created. In the control process, the drive mechanism DM may be controlled so that the stage 1 is positioned based on the outputs of interferometer 4Y1 and interferometer 4Y2, and the shape error data of the plane mirror 2Y calculated in the calculation process.

[0067] <Second Embodiment> The following describes a second embodiment of this disclosure. Matters not mentioned in the second embodiment may be the same as those in the first embodiment. In the second embodiment, the first calculation step and the second calculation step described in the first embodiment are not separated, but both are performed in a single calculation.

[0068] The first calculation step, which calculates the positional error and rotational error of each shot region from the measured values ​​of the superposition marks formed between overlapping shot regions and the coordinates of the superposition marks within each shot region, will be described below. The following explanation will be given in comparison with the description of Embodiment 1 in Japanese Patent Application Publication No. 2000-299278 (Patent Document 4).

[0069] First, let's explain how to calculate the shape error of the 2Y plane mirror. In Patent Document 4, the shot number is represented by a single letter (i, j, k, etc.), but here it is represented by two letters (i, j) as the matrix number, and the i in Patent Document 4 and the i in this document are different variables.

[0070] We formulate a system of equations. Let m be a column vector composed of the measured values ​​XX1(i,j), XX2(i,j), XY1(i,j), XY2(i,j), YX1(i,j), YX2(i,j), YY1(i,j), YY2(i,j), and seven zeros. Let B be the coefficient matrix composed of coefficients that include values ​​calculated from the coordinates of the superposition marks within each shot region, and let q be the column vector composed of the unknowns to be solved. And let ε be the irregular calculation error. XX1 (i), ε XX2 (i), ε XY1 (i), ε XY2 (i), ε YX1 (i), ε YX2 (i), ε YY1 (i), ε YY2 (i) Let f be a column vector consisting of seven zeros. In a layout with R rows and C columns and M shots, the number of overlapping parts in the X direction (shown as Nx in Patent Document 4) is MR, and the number of overlapping parts in the Y direction (shown as Ny in Patent Document 4) is MC.

[0071] Using these, the equations described in Patent Document 4 can be expressed collectively as equations (19) to (32). However, matrix O is the zero matrix, matrix E is the identity matrix, matrix F is a matrix with all elements being 1, and matrices B1 to B8 are matrices containing numerical values ​​derived from the equations described in Patent Document 4.

[0072] Let the matrix be composed of these coefficients. The two subscripts to the right of the matrix letter indicate the number of rows and columns, respectively. Furthermore, column vectors m, q, and f are represented by vector symbols in the following formulas.

number

number

number

number

number

number

number

number

number

number

number

number

number

number

[0073] Here, by transforming equation (33), which is a normal equation, into equation (34), we can calculate the column vector q that minimizes the length of the column vector f, which is composed of irregular calculation errors.

number

number

[0074] Next, we will explain the procedure for obtaining the column vector r shown in equation (13) from the obtained column vector q. Column vector q includes the position error and rotation error in the X and Y directions of each shot region, and a constant error for each overlapping mark. From this, the column vector q' is obtained by removing the elements related to the position error in the X direction and the constant error for each overlapping mark.

number

[0075] This transformation can be expressed using an operation with the coefficient matrix D, as shown in equations (36) and (37). Note that a matrix with a subscript in the lower right corner indicates that the dimension is the same as that subscript, making it a square matrix.

number

number

[0076] Here, the column vector r shown in equation (13), which is calculated as an expression for the variable i, is obtained by multiplying the column vector q' by the coefficient matrix G, as shown in equation (38). The coefficient matrix G is composed of the coefficients derived from equations (1) to (3).

number

[0077] Substituting equation (36) into the column vector q' in equation (38) yields equation (39).

number

[0078] Next, substituting equation (34) into the column vector q in equation (39) yields equation (40).

number

[0079] Furthermore, substituting equation (40) into the column vector r in equation (18) yields equation (41).

number

[0080] In the second embodiment described above, the control unit 8 obtains the shape of the plane mirror 2Y by solving a system of equations formulated by setting the known and unknown variables as follows, using the least squares method. Known numbers: • Results of relative distance measurement, • Coordinates of the overlapping marks in each of the multiple shot areas, • Spacing between multiple shot areas in the X direction (second direction) • Distance between the optical axis (first optical axis) of interferometer 4Y1 and the optical axis (second optical axis) of interferometer 4Y2 Unknown: • Flat mirror 2Y shape

[0081] As described above, by not separating the first calculation step and the second calculation step described in the first embodiment, and performing both in a single calculation, the shape error of the planar mirror 2Y can be directly calculated from the measured values ​​of the overlap marks formed between the overlapping shot regions. In this embodiment, even without data on the position and rotation errors of each shot region, the shape error of the planar mirror 2Y can be calculated if there is data that can be used to calculate them.

[0082] The shape error of a 2X planar mirror can also be calculated using a similar approach.

[0083] <Third Embodiment> A third embodiment of this disclosure will be described below. Matters not referred to as the third embodiment may be based on the first and second embodiments. In the first and second embodiments, the positional and rotational errors of each shot region were calculated using overlapping marks formed between overlapping shot regions. In contrast, in the third embodiment, the positional and rotational errors of each shot region are calculated based on the measured values ​​of marks that are superimposed on the background pattern pre-formed on the substrate 3 before the start of the exposure process. Furthermore, the exposure process, measurement process, and first calculation process are characterized by the following procedures.

[0084] In the exposure process of the third embodiment, one of the outer or inner mark of the overlapping mark is formed as a background pattern on the substrate 3 before exposure begins using another exposure device. Then, using the exposure position, the shot area is exposed to the background pattern so that the other of the outer or inner mark overlaps. At this time, at least two overlapping marks are provided within each shot area so that the position and rotation errors of each shot area can be calculated in the subsequent measurement process. In order to accurately calculate the shot rotation error, the distance between multiple overlapping marks within the shot area should be as long as possible. In addition, in the measurement process of the third embodiment, the overlapping marks formed between the substrate and the background pattern are measured. In the first calculation process of the third embodiment, the position and rotation errors of each shot area are calculated from the measurement results of the overlapping marks measured in the measurement process.

[0085] One possible method for calculating the positional and rotational errors of each shot area is as follows:

[0086] In the shot region S(i,j), find the regression line of the Y measurement value with respect to the X coordinate of the mark, and its intercept is ε y (i,j), slope ε θX Let (i,j). Similarly, find the regression line for the X measurement value with respect to the Y coordinate of the mark, and its intercept is ε. X (i,j), slope ε θY Let (i,j). Then ε θX (i,j) and ε θY The mean of (i,j) is ε θ Let (i,j) be the coordinates.

[0087] Subsequently, the shape errors of the planar mirrors 2X and 2Y can be obtained by following the first and second embodiments.

[0088] Thus, in the second embodiment, the control unit 8 controls the drive mechanism DM based on the output of each interferometer, transferring the marks to multiple shot regions so that the marks overlap the background patterns pre-formed in the multiple shot regions. This is done while controlling the drive mechanism DM based on the output of each interferometer so that the stage 1 is positioned at a predetermined exposure position along the X direction (second direction). In this way, overlapping marks are formed. The control unit 8 then obtains data on positional error and rotational error in the Y direction (first direction) based on data measured for the relative distance between the background pattern and the marks in the overlapping marks.

[0089] <Fourth Embodiment> The fourth embodiment of this disclosure is described below. Matters not mentioned as the fourth embodiment may be described in the first to third embodiments. In the fourth embodiment, a reference substrate (hereinafter referred to as the "reference substrate") is fabricated using an exposure apparatus ST adjusted according to the procedure shown in the first to third embodiments, and the shape error of the planar mirror 2Y in the measurement area of ​​the measuring instrument 7 is calculated with an expanded calculation range.

[0090] The reference substrate here has multiple measurement alignment marks arranged with high positional accuracy.

[0091] In one example, a measuring instrument 7 is used as an off-axis scope to perform alignment with the substrate 3. During alignment, when the stage 1 moves so that the alignment marks of the object to be measured on the substrate 3 are within the field of view of the measuring instrument 7, positional errors of the stage 1 may occur due to shape errors of the planar mirrors 2X and 2Y, similar to the exposure process. Regarding the shape error of the planar mirror 2Y, the positional error of the stage 1 can be reduced by correcting the shape error of the planar mirror 2Y in advance using the procedure shown in the first to third embodiments. On the other hand, in the procedure shown in the first to third embodiments, there is a range of the planar mirror 2X in the movement area of ​​the stage 1 during alignment where the shape cannot be calculated. This is because the position of the exposure shot area (i.e., the position of the projection lens) and the measuring instrument 7 are separated in the Y direction.

[0092] Therefore, when performing measurements using the measuring instrument 7, it is effective to pre-calculate the shape error of the planar mirror 2X using the measurement results obtained by measuring the alignment marks on the reference substrate with the measuring instrument 7. As a method for measuring the alignment marks on the reference substrate with an off-axis scope and calculating the shape error of the planar mirror based on the measurement results and the coordinates of the alignment marks (hereinafter referred to as the "reference substrate measurement method"), for example, the method described in Japanese Patent Application Publication No. 9-79829 (Patent Document 2) can be adopted.

[0093] In the reference substrate measurement method, it is also possible to measure alignment marks on the reference substrate using a through-the-lens (hereinafter referred to as "TTL") measurement system via a projection lens, rather than using an off-axis scope. By doing so, the shape error of the plane mirror range used in exposure can be calculated instead of the first to third embodiments. Furthermore, the shape error data of the plane mirror calculated from the measurement results using the measuring instrument 7 and the shape error data of the plane mirror calculated from the TTL measurement results are combined. This makes it possible to create shape error data that can be used commonly in both alignment and exposure.

[0094] However, the reference substrate measurement method has the constraint that a reference substrate must be prepared in advance. Naturally, creating a reference substrate with an exposure device whose planar mirror shape error has not been adjusted means that the positional accuracy of the alignment marks on the reference substrate cannot be guaranteed, making it unsuitable for use. Therefore, it is necessary to expose and prepare the reference substrate in advance using another exposure device whose stage positional accuracy has been sufficiently adjusted, but this requires storage space and transportation effort, which reduces the work efficiency when adjusting the exposure device.

[0095] Therefore, by adjusting the apparatus using the procedure shown in Figure 6, it is possible to obtain shape error data that is effective for both alignment and exposure by creating a reference substrate on-site using the exposure apparatus, without having to store the reference substrate.

[0096] In other words, the control unit 8 corrects the measurement results from each interferometer based on the shape of the planar mirror 2Y, and transfers multiple measurement marks onto the reference substrate while controlling the drive mechanism DM based on the corrected measurement results. The control unit 8 obtains the shape of the planar mirror 2Y based on the measurement data of the positions of the multiple measurement marks transferred onto the reference substrate (for example, measurement data obtained by measuring with a measuring instrument built into the exposure apparatus or an external measuring instrument) and the coordinate data of the measurement marks.

[0097] <Fifth Embodiment> The fifth embodiment of this disclosure is described below. Matters not referred to as the fifth embodiment may be described in the first to fourth embodiments. In the fifth embodiment, at least one of the measurement step, the first calculation step, and the second calculation step is performed by an external device of the exposure apparatus ST. The step performed by the external device is controlled not by the control unit 8, but by a control unit in the external device.

[0098] The following describes the case where the measurement process is performed using an external measuring device. In this case, the exposed substrate 3 is transferred to the external measuring device, multiple overlapping marks are measured, and the measurement result data is output. The output measurement result data is used in the first calculation process, which is performed either inside or outside the exposure device ST.

[0099] The following describes the case where the first and second calculation steps are performed by an external information processing device such as a computer (an information processing device that generates control data for the exposure device). In this case, the external information processing device receives measurement data obtained in the measurement step by the exposure device ST or an external measuring device. In the first calculation step, the external information processing device calculates the position and rotation errors of each shot area based on the received measurement data and outputs the calculation result data. In the second calculation step, the external information processing device calculates the shape error of the plane mirror 2Y based on the calculation result data obtained in the first calculation step and the optical axis distance between interferometer 4Y1 and interferometer 4Y2, and creates shape error data. After that, the external information processing device transfers the created shape error data to the exposure device ST. The exposure device ST then performs the control step using the received shape error data.

[0100] <Embodiment of Article Manufacturing Method> The following describes a method for manufacturing articles using the above-described exposure apparatus. This method may include an exposure step of exposing a substrate using the exposure apparatus, a developing step of developing the substrate after the exposure step, and a step of obtaining an article from the substrate after the developing step. The substrate provided to the exposure apparatus is coated with a photosensitive material (photoresist). In the exposure step, the pattern of the master plate is transferred to the photosensitive material as a latent image pattern. In the developing step, this latent image pattern is converted into a physical device pattern. The step of obtaining an article from the substrate after the developing step may include, for example, a step of patterning the underlying layer using the device pattern. The step of obtaining an article from the substrate after the developing step may also include a step of dicing the substrate.

[0101] <Other Embodiments> The present invention can also be realized by supplying a program that implements one or more of the functions of the above-described embodiments to a system or device via a network or storage medium, and by a process in which one or more processors in the computer of that system or device read and execute the program. It can also be realized by a circuit (e.g., an ASIC) that implements one or more functions.

[0102] <Disclosure Items> The disclosures herein include at least the following technologies: (Item 1) The stage and, A drive mechanism for driving the stage in mutually orthogonal first and second directions within a plane, and in rotation around an axis perpendicular to the plane, A first interferometer having a first optical axis parallel to the first direction and for measuring the position of the stage in the first direction, A second interferometer for measuring the rotation of the stage, having a second optical axis parallel to the first direction and spaced apart from the first optical axis, A common planar mirror is provided on the stage for measurement by the first interferometer and the second interferometer, A projection system that projects and transfers a mark formed on a master plate onto a substrate held on the stage by sequentially moving the aforementioned stage, The system comprises a control unit that controls the drive mechanism so that the stage is positioned based on the outputs of the first interferometer and the second interferometer, The control unit, The drive mechanism is controlled based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, and the marks are transferred to each of the multiple shot regions of the substrate. Based on the positional error and rotational error data in the first direction for each of the plurality of shot regions obtained based on the marks transferred to each of the plurality of shot regions, the shape of the planar mirror is obtained. An exposure apparatus characterized by the following features. (Item 2) The control unit, The drive mechanism is controlled based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, and the marks are transferred to each of the plurality of shot regions such that a portion of each adjacent shot region overlaps with the others. Based on data obtained by measuring the relative distance between two marks in an overlapping mark formed by the overlapping of two marks within each shot area on which the marks are transferred, the positional error and rotational error data in the first direction are obtained. The exposure apparatus according to item 1, characterized by the features described above. (Item 3) The control unit, The drive mechanism is controlled based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, and the marks are transferred to the multiple shot regions so that the marks overlap with the background patterns pre-formed in the multiple shot regions, thereby forming superimposed marks. Based on the data obtained by measuring the relative distance between the background pattern and the mark in the superimposed mark, the data for the position error and rotation error in the first direction are obtained. The exposure apparatus according to item 1, characterized by the features described above. (Item 4) The control unit further obtains the shape of the planar mirror based on the spacing between the plurality of shot regions in the second direction and the distance between the first optical axis and the second optical axis. An exposure apparatus according to any one of items 1 to 3, characterized by the features described above. (Item 5) The exposure apparatus according to item 4, characterized in that the control unit obtains the shape of the plane mirror by solving a system of equations formulated using the least squares method, where the position error and rotation error of the shot area in the first direction, the spacing between the plurality of shot areas in the second direction, and the distance between the first optical axis and the second optical axis are known variables, and the shape of the plane mirror is an unknown variable. (Item 6) The exposure apparatus according to item 2 or 3, characterized in that the control unit obtains the shape of the plane mirror by solving a system of equations formulated using the least squares method, where the measurement result of the relative distance, the coordinates of the superposition marks in each of the plurality of shot regions, the spacing between the plurality of shot regions in the second direction, and the distance between the first optical axis and the second optical axis are known variables, and the shape of the plane mirror is an unknown variable. (Item 7) The exposure apparatus according to item 5 or 6, characterized in that the simultaneous equations include an equation that serves as a constraint on the average value of the shape of the plane mirror. (Item 8) The control unit, The measurement results from the first interferometer and the second interferometer are corrected based on the shape of the plane mirror, and while controlling the drive mechanism based on the corrected measurement results, multiple measurement marks are transferred onto the reference substrate. Based on the measurement data of the positions of the plurality of measurement marks transferred onto the reference substrate and the coordinate data of the plurality of measurement marks, the shape of the planar mirror is obtained. An exposure apparatus according to any one of items 1 to 7, characterized by the above. (Item 9) An exposure method for exposing a substrate using an exposure apparatus comprising: a stage; a drive mechanism for driving the stage in mutually orthogonal first and second directions in a plane and rotation around an axis orthogonal to the plane; a first interferometer having a first optical axis parallel to the first direction and for measuring the position of the stage in the first direction; a second interferometer having a second optical axis parallel to the first direction and spaced apart from the first optical axis and for measuring the rotation of the stage; a common plane mirror provided on the stage for measurement by the first and second interferometers; and a projection system for sequentially moving the stage to project and transfer a mark formed on a master plate onto a substrate held on the stage, wherein the exposure apparatus comprises: a stage; a drive mechanism for driving the stage in mutually orthogonal first and second directions in a plane and rotation around an axis orthogonal to the plane; a first interferometer for measuring the position of the stage in the first direction; a second interferometer having a second optical axis parallel to the first direction and spaced apart from the first optical axis and for measuring the rotation of the stage; A step of transferring the marks to each of a plurality of shot regions of the substrate while controlling the drive mechanism based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, A step of obtaining the shape of the planar mirror based on positional error and rotational error data in the first direction for each of the plurality of shot regions obtained based on the marks transferred to each of the plurality of shot regions, A step of controlling the exposure of the substrate while controlling the drive mechanism so that the stage is positioned based on the outputs of the first interferometer and the second interferometer and the shape of the planar mirror, An exposure method characterized by having the following: (Item 10) An information processing device that generates control data for an exposure apparatus, The exposure apparatus comprises a stage, a drive mechanism for driving the stage in mutually orthogonal first and second directions in a plane, and rotation around an axis orthogonal to the plane, a first interferometer having a first optical axis parallel to the first direction for measuring the position of the stage in the first direction, a second interferometer having a second optical axis parallel to the first direction and spaced apart from the first optical axis for measuring the rotation of the stage, a common plane mirror provided on the stage for measurement by the first and second interferometers, and a projection system for projecting and transferring marks formed on a master plate onto a substrate held on the stage by sequentially moving the stage. The aforementioned information processing device is A first calculation means that controls the drive mechanism based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, and calculates the positional error and rotational error of each of the multiple shot regions in the first direction based on the measurement results of the marks transferred to each of the multiple shot regions of the substrate, A second calculation means calculates the shape error of the planar mirror based on the calculation result obtained by the first calculation means and the distance between the optical axes of the first interferometer and the second interferometer, and creates shape error data as control data. An information processing device characterized by having the following features. (Item 11) A program characterized by causing a computer to function as the first calculation means and the second calculation means of the information processing device described in item 10. (Item 12) An exposure step in which the substrate is exposed by the exposure method described in item 9, A processing step to obtain an article by processing the substrate exposed in the exposure step, A method for manufacturing articles, characterized by including the following:

[0103] The invention is not limited to the embodiments described above, and various modifications and variations are possible without departing from the spirit and scope of the invention. Accordingly, claims are attached to disclose the scope of the invention. [Explanation of Symbols]

[0104] ST: Stage equipment, DM: Drive mechanism, 1: Stage, 2X, 2Y: Planar mirrors, 3: Substrate, 4X, 4Y1, 4Y2: Interferometer, 5: Projection system, 6: Master plate, 7: Measuring instrument, 8: Control unit

Claims

1. The stage and, A drive mechanism for driving the stage in mutually orthogonal first and second directions within a plane, and in rotation around an axis perpendicular to the plane, A first interferometer having a first optical axis parallel to the first direction, for measuring the position of the stage in the first direction, A second interferometer for measuring the rotation of the stage, having a second optical axis parallel to the first direction and spaced apart from the first optical axis, A common planar mirror is provided on the stage for measurement by the first interferometer and the second interferometer, A projection system that projects and transfers a mark formed on a master plate onto a substrate held on the stage by sequentially moving the aforementioned stage, The system comprises a control unit that controls the drive mechanism so that the stage is positioned based on the outputs of the first interferometer and the second interferometer, The control unit, The drive mechanism is controlled based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, and the marks are transferred to each of the multiple shot regions of the substrate. Based on the positional error and rotational error data in the first direction for each of the multiple shot regions obtained based on the marks transferred to each of the multiple shot regions, the shape of the planar mirror is obtained. An exposure apparatus characterized by the following features.

2. The control unit, The drive mechanism is controlled based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, and the marks are transferred to each of the plurality of shot regions such that a portion of each adjacent shot region overlaps with the others. Based on data obtained by measuring the relative distance between two marks in an overlapping mark formed by the overlapping of two marks within each shot area on which the marks are transferred, the positional error and rotational error data in the first direction are obtained. The exposure apparatus according to feature 1.

3. The control unit, The drive mechanism is controlled based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, and the marks are transferred to the multiple shot regions so that the marks overlap with the background patterns pre-formed in the multiple shot regions, thereby forming superimposed marks. Based on the data obtained by measuring the relative distance between the background pattern and the mark in the superimposed mark, the data for the position error and rotation error in the first direction are obtained. The exposure apparatus according to feature 1.

4. The control unit further obtains the shape of the planar mirror based on the spacing between the plurality of shot regions in the second direction and the distance between the first optical axis and the second optical axis. The exposure apparatus according to feature 1.

5. The exposure apparatus according to claim 4, characterized in that the control unit obtains the shape of the plane mirror by solving a system of equations formulated using the least squares method, where the position error and rotation error of the shot region in the first direction, the spacing between the plurality of shot regions in the second direction, and the distance between the first optical axis and the second optical axis are known variables, and the shape of the plane mirror is an unknown variable.

6. The exposure apparatus according to claim 2, characterized in that the control unit obtains the shape of the plane mirror by solving a system of equations formulated using the least squares method, where the measurement result of the relative distance, the coordinates of the superposition marks in each of the plurality of shot regions, the spacing between the plurality of shot regions in the second direction, and the distance between the first optical axis and the second optical axis are known variables, and the shape of the plane mirror is an unknown variable.

7. The exposure apparatus according to claim 5, characterized in that the simultaneous equations include an equation that serves as a constraint on the average value of the shape of the plane mirror.

8. The control unit, The measurement results from the first and second interferometers are corrected based on the shape of the plane mirror, and while controlling the drive mechanism based on the corrected measurement results, multiple measurement marks are transferred onto the reference substrate. Based on the measurement data of the positions of the plurality of measurement marks transferred onto the reference substrate and the coordinate data of the plurality of measurement marks, the shape of the planar mirror is obtained. The exposure apparatus according to any one of claims 1 to 7.

9. An exposure method for exposing a substrate using an exposure apparatus comprising: a stage; a drive mechanism for driving the stage in mutually orthogonal first and second directions in a plane and rotation around an axis orthogonal to the plane; a first interferometer having a first optical axis parallel to the first direction and for measuring the position of the stage in the first direction; a second interferometer having a second optical axis parallel to the first direction and spaced apart from the first optical axis and for measuring the rotation of the stage; a common plane mirror provided on the stage for measurement by the first and second interferometers; and a projection system for sequentially moving the stage to project and transfer a mark formed on a master plate onto a substrate held on the stage, wherein the exposure apparatus comprises: A step of transferring the marks to each of a plurality of shot regions of the substrate while controlling the drive mechanism based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction, A step of obtaining the shape of the planar mirror based on positional error and rotational error data in the first direction for each of the plurality of shot regions obtained based on the marks transferred to each of the plurality of shot regions, A step of controlling the exposure of the substrate while controlling the drive mechanism so that the stage is positioned based on the outputs of the first interferometer and the second interferometer and the shape of the planar mirror, An exposure method characterized by having the following:

10. An information processing device that generates control data for an exposure apparatus, The exposure apparatus comprises a stage; a drive mechanism for driving the stage in mutually orthogonal first and second directions in a plane, and rotation around an axis orthogonal to the plane; a first interferometer having a first optical axis parallel to the first direction for measuring the position of the stage in the first direction; a second interferometer having a second optical axis parallel to the first direction and spaced apart from the first optical axis for measuring the rotation of the stage; a common plane mirror provided on the stage for measurement by the first and second interferometers; and a projection system for sequentially moving the stage to project and transfer a mark formed on a master plate onto a substrate held on the stage. The aforementioned information processing device is A first calculation means calculates the positional error and rotational error in the first direction for each of the multiple shot regions of the substrate, based on the measurement results of the marks transferred to each of the multiple shot regions of the substrate, while controlling the drive mechanism based on the outputs of the first and second interferometers so that the stage is positioned at a predetermined exposure position along the second direction. A second calculation means calculates the shape error of the plane mirror based on the calculation result obtained by the first calculation means and the distance between the optical axes of the first interferometer and the second interferometer, and creates shape error data as control data. An information processing device characterized by having the following features.

11. A program characterized by causing a computer to function as the first calculation means and the second calculation means of the information processing device described in claim 10.

12. An exposure step of exposing a substrate by the exposure method described in claim 9, A processing step to obtain an article by processing the substrate exposed in the exposure step, A method for manufacturing articles, characterized by including the following:

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