Substrate for mask blanks and method for manufacturing the same

Abstract

SOLUTION: A substrate for mask blanks has flatness (TIR) of 100 nm or less at a calculation surface if the calculation surface is a map at a calculation height obtained by adding up heights from a reference plane of a height map of a first region surface and a reverse height map of a second region surface, the flatness obtained through setting a calculation region extending horizontally passing through central portions of first and second principal surfaces of 152 mm square, cutting out the first region surface, setting the reference plane being a vertical surface to a central axis of the calculation region and a rotational axis, rotating the substrate by 180 degrees, cutting out the second region surface, calculating a least square plane in each of the first and second region surfaces, converting the first and second region surfaces into height maps of the first and second region surfaces referencing each location on each least square plane, and symmetrically moving the height map of the second region surface to be the reverse height map.EFFECT: To provide a substrate for mask blanks capable of producing a mask for exposure in which, when the mask for exposure is held at an exposure device by absorption, a principal surface of the substrate is in a highly flat shape in exposure using the mask for exposure.SELECTED DRAWING: Figure 5

Description

Technical Field

[0001] The present invention relates to a substrate for a mask blank used in photolithography and a method for manufacturing the same, and more particularly to a substrate for a mask blank suitable for a mask blank used for manufacturing a transfer mask for photolithography in which EUV (Extreme Ultra Violet) light is used as exposure light, and a method for manufacturing the same.

Background Art

[0002] In recent years, with the increasing interest in AI and IoT, huge amounts of data need to be processed computationally, and accordingly, higher speed and lower power consumption of computational processing are required. To meet this demand, it is necessary to improve the performance of IC chips. Generally, miniaturization of electrical wiring is adopted as an effective means. For miniaturization of wiring, mainly, increasing the NA and shortening the wavelength of exposure light are adopted. In recent years, EUV (extreme ultraviolet) lithography (EUVL) using EUV light is being put into practical use.

[0003] In EUVL, an exposure mask is one of the important elements, and improving the flatness of a glass substrate for the original plate (mask blank) of the exposure mask is extremely important for realizing accurate exposure. As a general method for manufacturing a glass substrate, double-sided simultaneous polishing is the mainstream, but good flatness sufficient for use in EUVL cannot be obtained only by double-sided simultaneous polishing. To achieve high flatness, it is necessary to correct the flatness according to the surface shape by polishing one side at a time, and local processing techniques such as local etching and local processing are used. These are methods for making the entire substrate closer to flat by removing relatively convex regions.

[0004] Even if a glass substrate with high flatness on both sides can be obtained in this way, during exposure, the surface without the pattern of the exposure mask (the back surface) will be adsorbed and held on the mask stage of the exposure apparatus. Therefore, depending on the surface shape of the back surface, the surface shape of the patterned surface (the front surface) will be deformed, and as a result, the flatness of the patterned surface (the front surface) will change. For this reason, not only the flatness of each surface of the glass substrate of the exposure mask before adsorption during exposure, but also the flatness of the surface of the glass substrate of the exposure mask after adsorption during exposure is important.

[0005] Regarding the flatness in the state where the exposure mask is adsorbed and held on the mask stage of the exposure apparatus, for example, in International Publication No. 2016 / 098452 (Patent Document 1), in order to obtain high transfer accuracy when performing exposure transfer by chucking a reflective mask manufactured using a substrate that has been subjected to conventional double-sided polishing and local processing on both main surfaces to the exposure apparatus, if the shape of the front-side main surface of the substrate when electrostatically chucked is made close to a shape (virtual surface shape) that can be defined by a Zernike polynomial that can be corrected by the wavefront correction function of the exposure apparatus, even if the substrate has a thickness variation that affects the change in the shape of the front-side main surface, it can be made into a thickness variation that tends to be easily corrected by the wavefront correction function of the exposure apparatus, and it is described that a transfer mask having such a substrate can perform exposure transfer of a transfer pattern to a transfer object with high precision.

[0006] In addition, Japanese Patent Application Laid-Open No. 2003-050458 (Patent Document 2) indicates that when a mask substrate is chucked on a mask stage of an exposure apparatus, a deterioration in flatness after chucking becomes a major factor in reducing the product yield. As a method for improving this, for each of a plurality of mask substrates, a step of acquiring first information indicating the surface shape of the main surface and second information indicating the flatness of the main surface before and after chucking on the mask stage of the exposure apparatus, a step of creating a correspondence relationship between each mask substrate, the first information, and the second information, a step of selecting second information indicating a desired flatness from the created correspondence relationship, and preparing, separately from the plurality of mask substrates, a mask substrate having the same surface shape as the surface shape indicated by the first information corresponding to the selected second information, and a step of forming a desired pattern on the prepared mask substrate are described. It is described that by this method, a reduction in product yield due to deterioration in flatness can be suppressed.

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0008] The method described in International Publication No. 2016 / 098452 is composed of a process of calculating the composite plane of the front main surface and the back main surface during adsorption to the exposure apparatus, and a process of predicting the surface shape after optical correction from the shape fitted with the Zernike polynomial. However, in this method, the flatness within a circular region with a diameter of 104 mm is defined, which is narrower than the region (132 mm square) actually used for exposure and is insufficient. Also, generally, it is known that the flatness tends to deteriorate toward the outer periphery of the main surface. From this point, a high-quality glass substrate for a mask blank cannot be obtained by this method. Furthermore, the surface shape during exposure calculated in the process of calculating the composite plane is a simple sum of the front main surface and the back main surface, which is likely to deviate from the actual surface shape, and high prediction accuracy cannot be obtained in the process of predicting the surface shape after optical correction.

[0009] Also, in the method described in Japanese Patent Application Laid-Open No. 2003-050458, it is shown that a difference in flatness with direction appears depending on the chuck position of the substrate. However, at the current technical level required for EUVL, further advanced flatness control is necessary, and this flatness management is insufficient.

[0010] The present invention has been made in view of the above circumstances, and an object thereof is to provide a substrate for a mask blank that gives an exposure mask having a highly flat shape of the main surface of the substrate as a shape without optical correction when the exposure mask is held by adsorption to an exposure machine, particularly in exposure using an exposure mask, especially EUVL, and a method for manufacturing the same.

Means for Solving the Problems

[0011] As a result of intensive studies to solve the above problems, the present inventors set a predetermined calculation area for two main surfaces, i.e., a first main surface and a second main surface of a substrate for a mask blank, cut out a first area surface and a second area surface within the calculation area, calculated least-squares planes of the first area surface and the second area surface, and converted them into height maps of the first area surface and the second area surface from the respective least-squares planes. When a calculated height map obtained by adding the height of the height map of the first area surface and the height of the inverted height map obtained by symmetrically moving the height map of the second area surface at each position on a reference plane set based on the calculation area is defined as a calculated surface, it has been found that a substrate for a mask blank with a flatness (TIR) of the calculated surface of 100 nm or less provides an exposure mask having a highly flat main surface of the substrate when the exposure mask is held by adsorption to an exposure machine in exposure using an exposure mask, particularly in exposure by EUVL.

[0012] Further, the present inventors, in a manufacturing method including a local processing step and a finishing polishing step following the local processing step for such a substrate for a mask blank, apply a previously grasped change in the shape of the main surface to the shape of the main surface after the local processing step and before the finishing polishing step, predict the shape of the main surface after the finishing polishing step, and evaluate whether the predicted shape of the main surface satisfies a predetermined flatness, thereby finding that it is possible to manufacture reliably and with high productivity, and thus arriving at the present invention.

[0013] Therefore, the present invention provides the following substrate for a mask blank and a method for manufacturing a substrate for a mask blank. A substrate for a mask blank having two main surfaces, i.e., a first main surface and a second main surface that are 1.152 mm × 152 mm square and having a thickness of 6.35 mm, (1) The substrate is arranged with the first main surface and the second main surface along a substantially vertical direction, and a regular square prism-shaped calculation area is set that extends horizontally through four sides of a 138 mm × 138 mm square along the four sides of the first main surface and the second main surface at the central portions of the first main surface and the second main surface. (2) With the state of facing the first main surface, cut out the portion within the calculation region from the first main surface to obtain a first region surface. (3) Set a reference plane as a vertical plane passing through a reference point, which is an arbitrary point on the central axis of the regular square prism of the calculation region and perpendicular to the central axis. Set a rotation axis parallel to any one of the four sides of the regular square formed by the intersection of the regular square prism of the calculation region and the vertical plane passing through the reference point. From the state of facing the first main surface, rotate the substrate 180 degrees along the rotation axis to face the second main surface, and cut out the portion within the calculation region from the second main surface to obtain a second region surface. (4) Calculate the least-squares plane for each of the first region surface and the second region surface. (5) Convert the first region surface and the second region surface into a height map of the first region surface and a height map of the second region surface based on the positions on the least-squares planes of the first region surface and the second region surface respectively. (6) Symmetrically move the height map of the second region surface with respect to a vertical plane passing through the rotation axis and along the 90-degree direction of the rotation to obtain an inverted height map of the second region surface. (7) At each position (X coordinate, Y coordinate) on the reference plane, add the height of the height map of the first region surface and the height of the inverted height map of the second region surface to create a map of the calculated height (Z coordinate). When the map of the calculated height is used as the calculated surface, the flatness (TIR) of the calculated surface is 100 nm or less. and In (5) above, as the height map of the second region surface, a height map obtained by processing with a Gaussian filter (20 mm × 20 mm) is applied A substrate for a mask blank, characterized in that. 2 . A substrate for a mask blank having two main surfaces, a first main surface and a second main surface, which are 152 mm × 152 mm squares and have a thickness of 6.35 mm (1) The substrate is arranged with the first main surface and the second main surface along a substantially vertical direction, and a square calculation region of 138 mm × 138 mm extending horizontally through the four sides of the first main surface and the second main surface at the central portions of the first main surface and the second main surface is set (2) With the state of facing the first main surface, the portion within the calculation region is cut out from the first main surface to form a first region surface (3) A reference plane is set as a vertical plane passing through an arbitrary point on the central axis of the square prism of the calculation region and perpendicular to the central axis. A rotation axis parallel to any one of the four sides of the square formed by the intersection of the square prism of the calculation region and the vertical plane passing through the reference point is set. From the state of facing the first main surface, the substrate is rotated 180 degrees along the rotation axis, and in the state of facing the second main surface, the portion within the calculation region is cut out from the second main surface to form a second region surface (4) A least-squares plane is calculated for each of the first region surface and the second region surface (5) The first region surface and the second region surface are converted into a height map of the first region surface and a height map of the second region surface based on the positions on the least-squares planes of the first region surface and the second region surface respectively (6) The height map of the second region surface is symmetrically moved with reference to a vertical plane passing through the rotation axis and along the 90-degree direction of the rotation to form an inverted height map of the second region surface (7) At each position (X coordinate, Y coordinate) on the reference plane, the height of the height map of the first region surface and the height of the inverted height map of the second region surface are added together to create a map of the calculated height (Z coordinate). When the map of the calculated height is used as the calculated surface The flatness (TIR) of the calculated surface is 100 nm or less In (5) above, as the height map of the second region surface, a height map obtained by fitting up to the 15th term of Legendre polynomials is applied. mask Substrate for mask blanks. 3 . as described in 1 A method for manufacturing a substrate for mask blanks, including a local processing step for one or both of the first main surface and the second main surface, and a finishing polishing step following the local processing step, wherein the local processing step (A) a step of grasping the change in the shape of the surface before and after the finishing polishing step of the first main surface and the second main surface; (B) a step of locally processing one or both of the first main surface and the second main surface; (C) a step of measuring the shape of the first main surface and the shape of the second main surface after the step (B) as the shape of the surface before the finishing polishing step; (D) a step of predicting the shape of the first main surface and the second main surface after the finishing polishing step by applying the change in the shape of the surface grasped in the step (A) to the shape of the surface before the finishing polishing step obtained in the step (C); (E) a step of evaluating whether the shape of the first main surface and the second main surface predicted in the step (D) satisfies a predetermined flatness. A method for manufacturing a substrate for mask blanks, characterized by including the above steps. 4 . The shape of the first main surface and the second main surface satisfying the predetermined flatness in the step (E) is 3, characterized in that it is the shape of the first main surface and the second main surface of the substrate for a mask blank as described in 1 the manufacturing method according to. 5 . as described in 2 A method for manufacturing a substrate for mask blanks, including a local processing step for one or both of the first main surface and the second main surface, and a finishing polishing step following the local processing step, wherein the local processing step (A) a step of grasping the change in the shape of the surface before and after the finishing polishing step of the first main surface and the second main surface; (B) a step of locally processing one or both of the first main surface and the second main surface; (C)(B) Measuring the shapes of the first major surface and the second major surface after the process as the shapes of the surfaces before the finish polishing process; (D)(C) Applying the change in the shape of the surface grasped in the (A) process to the shape of the surface before the finish polishing process obtained in the (C) process to predict the shapes of the first major surface and the second major surface after the finish polishing process; (E) Evaluating whether the shapes of the first major surface and the second major surface predicted in the (D) process satisfy the predetermined flatness; A method for manufacturing a substrate for a mask blank, comprising the above steps. 6 . The shapes of the first major surface and the second major surface satisfying the predetermined flatness in the (E) process are 5, characterized in that it is the shape of the first main surface and the second main surface of the substrate for a mask blank as described in 2 The manufacturing method according to the above. 7 . In the (E) process, when the shapes of the first major surface and the second major surface predicted in the (D) process do not satisfy the shapes of the first major surface and the second major surface with the predetermined flatness, the (A) process to the (E) process are repeated, characterized by 3 or 5 The manufacturing method according to the above. [Advantages of the Invention]

[0014] The substrate for a mask blank of the present invention can provide an exposure mask having a highly flat shape for the major surface of the substrate when the exposure mask is held by adsorption to an exposure machine, particularly in exposure using an EUVL exposure mask. Further, according to the method for manufacturing a substrate for a mask blank of the present invention, by predicting the shape of the major surface after the finish polishing process and performing local processing, an exposure mask having a highly flat shape for the major surface of the substrate can be surely and efficiently manufactured when the exposure mask is held by adsorption to an exposure machine, particularly in exposure using an EUVL exposure mask. [Brief Description of the Drawings]

[0015]

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Embodiments for Carrying Out the Invention

[0016] Hereinafter, the present invention will be described in detail. The substrate for mask blanks of the present invention has two main surfaces, a first main surface and a second main surface, which are 152 mm × 152 mm square, and has a thickness of 6.35 mm. A substrate of this size is so-called 6025 substrate, which has two main surfaces, a first main surface and a second main surface, which are 6 inches × 6 inches square, and has a thickness of 0.25 inches.

[0017] The material of the substrate for mask blanks of the present invention can use the conventionally used materials and is not particularly limited. However, for the drawing of fine patterns, since it is exposed to high-energy exposure light, TiO2-doped quartz glass containing 3 to 10% by mass of TiO2, which has very high dimensional stability at high temperatures, is preferably used. As the raw substrate for the mask blanks, those synthesized, molded, and processed according to conventional methods can be used.

[0018] A high flatness is required for the substrate for mask blanks. This is because the higher the flatness, the easier it is to achieve the desired exposure. A substrate with a higher flatness can be said to be a suitable substrate for mask blanks for the drawing of fine patterns.

[0019] The substrate for mask blanks has a first main surface on which an exposure pattern (such as a wiring pattern) is formed when used as an exposure mask, and a second main surface on which no exposure pattern is formed. The second main surface is adsorbed and held by the exposure machine. Since the second main surface deforms along the adsorption surface, the shape of the first main surface used for exposure also deforms accordingly. At the previous required level, the deterioration of flatness due to the adsorption of the exposure machine was tolerated to a certain extent, and in many cases, there was no problem even if the flatness of the second main surface was about one digit larger than the flatness of the first main surface. Therefore, by double-sided polishing in which the flatness of one of the two main surfaces becomes large, the two main surfaces are polished, and the one with the larger flatness is set as the second main surface, which was the mainstream.

[0020] However, in recent years, in order to realize extremely fine patterns, the same degree of flatness is required for both sides of the two main surfaces. Therefore, a local processing technique that processes each surface of the two main surfaces separately has been proposed. Furthermore, even if both sides of the two main surfaces are highly flat, depending on the shape of the second main surface, it has been found that sufficient flatness cannot be obtained when the exposure mask is held by adsorption to the exposure machine. For state-of-the-art products for realizing extremely fine patterns, it is important to obtain high flatness when the exposure mask is held by adsorption to the exposure machine.

[0021] It is extremely important to evaluate the shape of the main surface when a mask blank is used as an exposure mask after passing through a mask blank substrate and the exposure mask is held by adsorption on an exposure machine. However, generally, it is difficult to directly measure this. Therefore, an attempt is made to estimate the shape of the main surface when the exposure mask is held by adsorption on the exposure machine, for example, approximately calculating it from the shape of the main surface measured by a general laser interferometer. However, conventionally, in the area required for exposure, the flatness when held by adsorption on the exposure machine could not be accurately grasped. Therefore, a mask blank substrate that provides sufficient flatness when the exposure mask is held by adsorption on the exposure machine has not been obtained.

[0022] The mask blank substrate of the present invention has a flatness (TIR) of 100 nm or less of the calculated surface obtained by overlapping the surface shapes of two main surfaces located inside a 138 mm × 138 mm square with the center of the substrate as a reference and within a regular square prism-shaped calculation region extending in the thickness direction of the substrate. Specifically, the mask blank substrate of the present invention (1) The substrate is arranged with the first main surface and the second main surface substantially along the vertical direction, and a regular square prism-shaped calculation region is set that extends horizontally through the four sides of a 138 mm × 138 mm square along the four sides of the first main surface and the second main surface at the central portions of the first main surface and the second main surface. (2) With the state of facing the first main surface, the portion within the calculation region is cut out from the first main surface to obtain a first region surface. (3) A reference point, which is an arbitrary point on the central axis of the regular square prism of the calculation region, is passed through, and a vertical plane orthogonal to the central axis is set as a reference plane. A rotation axis parallel to any one of the four sides of the regular square formed by the intersection of the regular square prism of the calculation region and the vertical plane is set. From the state of facing the first main surface, the substrate is rotated 180 degrees along the rotation axis, and in the state of facing the second main surface, the portion within the calculation region is cut out from the second main surface to obtain a second region surface. (4) The least-squares plane is calculated for each of the first region surface and the second region surface. (5) Convert the first region surface and the second region surface into a height map of the first region surface and a height map of the second region surface based on the respective positions on the least-squares plane of each of the first region surface and the second region surface. (6) Symmetrically move the height map of the second region surface along the vertical plane passing through the rotation axis in (3) and along the 90-degree direction of the rotation in (3) with respect to the vertical plane as the reference to obtain the inverted height map of the second region surface. (7) At each position (X coordinate, Y coordinate) on the reference plane, add the height of the height map of the first region surface and the height of the inverted height map of the second region surface to create a map of the calculated height (Z coordinate). When the map of the calculated height is used as the calculated surface, The flatness (TIR) of the calculated surface is 100 nm or less.

[0023] Regarding the above (1) to (7), it will be specifically described with reference to FIGS. 1 to 4 for explaining the aspect of the substrate for mask blanks of the present invention. First, in FIG. 1, (A) is a side view of a state in which the first main surface and the second main surface of the substrate for mask blanks are arranged along the vertical direction, and (B) is a front view of the first main surface located on the right side in (A). In (1), as shown in FIG. 1(A), the 152 mm × 152 mm square first main surface 1 and second main surface 2 of the substrate 500 are arranged along the substantially vertical direction, and a regular square prism-shaped calculation region C extending horizontally through the four sides of a 138 mm × 138 mm square along the four sides of the first main surface 1 and the second main surface 2 at the central portions of the first main surface 1 and the second main surface 2 is set.

[0024] Next, in (2), as shown in FIG. 1(B), with the state of facing the first main surface 1, the portion within the calculation region C is cut out from the first main surface 1 to obtain the first region surface 11. Here, for the sake of convenience, it is assumed that there is a convex portion 11a on the first main surface 1, and there is also a convex portion 21a on the second main surface 2 as shown in FIG. 2(B) described later.

[0025] Next, in (3), as shown in FIGS. 1(A) and (B), a reference plane S is set as a vertical plane passing through a reference point P, which is an arbitrary point on the central axis CA of the regular square prism of the calculation region C, and perpendicular to the central axis CA (here, the reference plane S is a plane extending in the depth direction of the drawing). A rotation axis RA is set parallel to any one of the four sides of the square, which is the intersection line between the regular square prism of the calculation region C and the vertical plane, passing through the reference point P. Then, from the state facing the first main surface 1, the substrate 500 is rotated 180 degrees along the rotation axis RA (centered on the rotation axis RA).

[0026] On the other hand, in FIG. 2, (A) is a side view of the substrate for mask blanks after 180-degree rotation, and (B) is a front view of the second main surface located on the right side in (A) after rotation. After the rotation of the substrate 500, as shown in FIG. 2(B), in the state facing the second main surface 2, a portion within the calculation region C is cut out from the second main surface 2 to form a second region surface 21.

[0027] Next, in (4), a least-squares plane is calculated for each of the first region surface 11 and the second region surface 21. In (5), the first region surface 11 and the second region surface 21 are converted into a height map 111 of the first region surface as shown in FIG. 3(A) and a height map 211 of the second region surface as shown in FIG. 3(B), with reference to the positions of the first region surface 11 and the second region surface 21 on their respective least-squares planes. In (6), the height map 211 of the second region surface is symmetrically moved with reference to a vertical plane V passing through the rotation axis RA in (3) and extending along the 90-degree direction of the rotation in (3) (here, the vertical plane V is a plane extending in the depth direction of the drawing) to obtain an inverted height map 211R of the second region surface as shown in FIG. 3(C). Note that since the inverted height map 211R of the second region surface shown in FIG. 3(C) is obtained by symmetrically moving the height map 211, 21aR in the inverted height map 211R is not inverted in the height direction and is a convex portion similar to 21a.

[0028] Next, in (7), the height map 111 of the first region surface shown in FIG. 3(A) and the inverted height map 211R of the second region surface shown in FIG. 3(C) are overlaid, and at each position (X coordinate, Y coordinate) on the reference plane S shown in FIG. 1(A), the height of the height map 111 of the first region surface and the height of the inverted height map 211R of the second region surface are added together to create a map of the calculated height (Z coordinate), and the obtained map of the calculated height is made into a calculated surface 3 as shown in FIG. 4. Then, the flatness of this calculated surface 3 is evaluated.

[0029] When the substrate for the exposure mask (substrate for mask blanks) is adsorbed and held by the exposure machine, the flatness of the main surface changes according to the surface shape of the adsorption surface. In the 6025 substrate, the inside of a 138 mm × 138 mm square along the four sides of the second main surface in the central part of the second main surface is the region that is actually adsorbed by the exposure machine among the second main surfaces, and in the calculation region in the shape of a regular square prism that extends horizontally through the four sides of a 138 mm × 138 mm square along the four sides of the first main surface and the second main surface in the central parts of the first main surface and the second main surface, by taking the sum of the shapes of the first main surface and the second main surface, that is, the sum of the first region surface and the second region surface on the first main surface and the second main surface in the non-adsorbed state, the shape of the first main surface in the state where the exposure mask is adsorbed and held by the exposure machine can be grasped with high accuracy.

[0030] For the measurement of the shape of the main surface of the substrate for a photomask blank, there are no particular restrictions, but for example, a laser interferometer can be used. The shape that can be measured with a laser interferometer is the raw data of the height map of the main surface of the substrate. In this case, the reference for the height is the stage on which the substrate is placed during measurement. In the present invention, for the height map of the main surface of this substrate, the least-squares plane of the main surface (the least-squares plane of the surface or height map) is calculated, and by correcting the height map based on the least-squares plane, the influence of the shape of the stage on which the substrate is placed is removed. Among the height maps corrected in this way, in the height map of the second region surface, the inverted height map of the second region surface obtained by symmetrically moving along the plane passing through the rotation axis in (3) and along the 90-degree direction of the rotation in (3) has the same positive and negative in the height direction, but both sides in the direction orthogonal to the rotation axis in (3) are inverted. Further, the flatness (TIR) is the difference between the highest value (highest height) and the lowest value (lowest height) within a predetermined region of the difference when calculating the least-squares plane of the target surface (such as the first region surface, the second region surface, the calculated surface, etc.) and calculating the difference between the least-squares plane and the target surface.

[0031] The flatness (TIR) of the calculated surface is 100 nm or less, preferably 50 nm or less, and more preferably 30 nm or less. When the flatness (TIR) of the calculated surface is 100 nm or less, in the exposure using the exposure mask obtained from the mask blank substrate via the mask blank, exposure with good transfer accuracy can be realized. On the other hand, when the flatness (TIR) of the calculated surface is greater than 100 nm, good exposure cannot be realized.

[0032] Also, when obtaining the calculated surface, by separating the wavelength components that contribute to the shape of the first main surface and the wavelength components that do not contribute to the shape of the first main surface among the shapes of the second main surface, the shape of the first main surface in the state where the exposure mask is adsorbed and held by the exposure machine can be grasped with higher accuracy.

[0033] Among the shapes of the second main surface, the shorter the wavelength component, the smaller the influence on the change in the shape of the first main surface. Therefore, for example, in the above-mentioned (5), as the height map of the second region surface, it is preferable to apply the height map obtained by processing with a Gaussian filter (20 mm × 20 mm). Specifically, it is preferable to apply the height map obtained by relaxing the wavelength component of preferably 20 mm or less, more preferably 15 mm or less, and still more preferably 10 mm or less with a Gaussian filter.

[0034] A Gaussian filter is a smoothing process that performs smoothing over the entire surface within a minute region of the surface. A Gaussian filter of X mm means focusing on X mm × X mm around a certain measurement point and using the Gaussian distribution function so that the weight becomes smaller as the distance increases. According to the following formula

Equation

[0035] Also, among the shapes of the second main surface, the shorter the wavelength component, the smaller the influence on the change in the shape of the first main surface. Therefore, for example, in the above-mentioned (5), as the height map of the second region surface, it is preferable to apply the height map obtained by fitting with terms up to the 15th order of the Legendre polynomial, more preferably up to the 21st order, and still more preferably up to the 36th order. The Legendre polynomial is a polynomial that can well fit the long-wavelength component that has a large influence on the change in the shape of the first main surface among the shapes of the second main surface of the substrate for mask blanks. By performing fitting with at least terms up to the 15th order, it is possible to grasp the shape of the first main surface in a state where the exposure mask is adsorbed and held by the exposure machine with sufficiently high accuracy.

[0036] On the other hand, when obtaining the calculated surface, by separating the directional component that contributes to the shape of the first main surface and the directional component that does not contribute to the shape of the first main surface from the shape of the second main surface, the shape of the first main surface in the state where the exposure mask is adsorbed and held by the exposure machine can be grasped with higher accuracy. Among the shapes of the second main surface, the component perpendicular to the major axis of the adsorption holding region by the exposure machine has less influence on the change in the shape of the first main surface. Therefore, for example, in (5) described above, it is preferable that the height map of the second region surface is a height map obtained by excluding the component perpendicular to the major axis of the adsorption holding region by the exposure machine from the height map of the second region surface.

[0037] Next, the manufacturing process of the substrate for mask blanks of the present invention will be described. The manufacturing method of the substrate for mask blanks of the present invention includes a local processing step for one or both of the first main surface and the second main surface of the substrate for mask blanks, and a finishing polishing step following the local processing step.

[0038] In the manufacture of the substrate for mask blanks, before the local processing step, it is cut out from a glass ingot into the shape of the substrate for mask blanks, and then the outer shape, end faces, and main surfaces are roughly polished. The polishing in each of these steps is often composed of several stages and is not particularly limited. For example, an aqueous solution of cerium oxide or silica nanoparticles with a size of 10 to 100 nm is used as the polishing agent.

[0039] Next, local processing for adjusting the shape of the main surface is performed. In the local processing step, a process of selectively removing relatively convex portions is performed on one or both of the first main surface and the second main surface of the substrate for mask blanks. In this step, the processing can be repeated until a predetermined shape is obtained. For local processing, methods such as Magneto Rheological Finishing (MRF) can be used. However, generally, the surface defect level obtained only by local processing may not be sufficient, especially for substrates for mask blanks for state-of-the-art products. Therefore, a finishing polishing step is performed following the local processing step.

[0040] The method for manufacturing a substrate for a mask blank of the present invention is such that the local processing step includes (A) a step of grasping changes in the surface shape before and after the finish polishing step of the first main surface and the second main surface; (B) a step of locally processing one or both of the first main surface and the second main surface; (C) a step of measuring the shape of the first main surface and the shape of the second main surface after the step (B) as the surface shape before the finish polishing step; (D) a step of predicting the shape of the first main surface and the second main surface after the finish polishing step by applying the change in the surface shape grasped in the step (A) to the surface shape before the finish polishing step obtained in the step (C); (E) a step of evaluating whether or not the shapes of the first main surface and the second main surface predicted in the step (D) satisfy a predetermined flatness. It is characterized by including these steps.

[0041] The shape of the surface obtained only by local processing is not flat and usually has a shape that cancels out the change in the surface shape in the subsequent finish polishing step (generally, a convex shape (a shape in which the central part of the main surface protrudes) or a concave shape (a shape in which the central part of the main surface is recessed), etc.). Even if the flatness (TIR) of the surface shape obtained only by local processing is evaluated, it only results in an evaluation that deviates from the evaluation result of the shape of the main surface of the finally obtained substrate for a mask blank. The change in the shape of the main surface that occurs in the finish polishing step performed under predetermined polishing conditions after the local processing step has reproducibility. By grasping the change in the shape of the main surface after finish polishing under predetermined polishing conditions and applying this to the shape of the main surface after local processing, the shape of the surface after the finish polishing step performed under predetermined polishing conditions can be predicted. Thus, before the finish polishing, at the local processing stage, the shape of the surface obtained after the finish polishing can be evaluated, and the quality of the shape of the main surface obtained by the finish polishing can be evaluated. Therefore, in the method for manufacturing a substrate for a mask blank of the present invention, it is preferable to manufacture the substrate for a mask blank by a local processing step including the above steps (A) to (E).

[0042] (A) In the process, the change in the shape of the surfaces of the first main surface and the second main surface after the finishing polishing process with respect to the surfaces after the local processing process is grasped. This change can be grasped, for example, by selecting another substrate for the mask blank having the same shape of the main surface from the substrate for the mask blank on which the local processing has been performed, and from the shape of the main surface obtained by performing a predetermined finishing polish on this another substrate for the mask blank. Also, the grasp of this change in shape can also be estimated by simulation. In this case, as another substrate for the mask blank, those having a middle concave shape whose main surface shape is the target shape in the local processing process, those having a flatness (TIR) of less than 300 nm on the main surface, etc. are suitable. Note that the (A) process may be after the (B) process or after the (C) process.

[0043] (B) In the process, one or both of the first main surface and the second main surface are locally processed. The local processing sets the predetermined processing conditions in the local processing so that the first main surface and the second main surface have a predetermined shape, considering the shapes of the first main surface and the second main surface before and after the local processing and the change in the shape of the surface after the finishing polishing process. Specifically, for example, when the second main surface is convex, in order for the first main surface to be flat when the exposure mask is adsorbed and held by the exposure machine, the first main surface is preferably concave. When the second main surface is concave, in order for the first main surface to be flat when the exposure mask is adsorbed and held by the exposure machine, the first main surface is preferably convex. On the other hand, when the shape changes to convex due to the finishing polish, considering this change, the first main surface preferably has a shape that cancels out this change (for example, a low convex shape or a concave shape). When the shape changes to concave due to the finishing polish, considering this change, the first main surface preferably has a shape that cancels out this change (for example, a shallow concave shape or a convex shape).

[0044] (C) In the process, after the (B) process, that is, after the local processing is actually performed, the shapes of the first main surface and the second main surface are measured as the shapes of the surfaces before the finish polishing process. Although there are no particular restrictions on this measurement, for example, a laser interferometer can be used. Also, before the local processing, the shapes of the first main surface and the second main surface are appropriately measured. Again, there are no particular restrictions on this measurement, and for example, a laser interferometer can be used.

[0045] (D) In the (D) process, with respect to the shapes of the main surfaces obtained in the (C) process, the changes in the shapes of the main surfaces grasped in the (A) process are applied to predict the shapes of the first main surface and the second main surface after the finish polishing process. However, the changes in the shapes of the main surfaces grasped in the (A) process are selected according to the shapes of the main surfaces after the local processing obtained in the (C) process. Here, for example, when the shapes of the first main surface and the second main surface after the local processing process are S11a and S11b respectively, and the shape changes of the first main surface and the second main surface when a predetermined finish polishing is performed are measured and are SΔa and SΔb respectively, the following formulas (a) and (b) S11a + SΔa = S12a (a) S11b + SΔb = S12b (b) can be used to predict the shape (S12a) of the first main surface and the shape (S12b) of the second main surface after the finish polishing process.

[0046] (E) In the (E) process, it is evaluated whether the shapes of the first main surface and the second main surface predicted in the (D) process satisfy the predetermined flatness. As this evaluation method, a method composed of the measurement of the shape of the main surface and its numerical analysis can be used.

[0047] Specifically, for example, the shapes of the first main surface and the second main surface that satisfy the predetermined flatness in the (E) process are (1) Place the substrate with its first major surface and second major surface arranged along the substantially vertical direction, and set a calculation region in the shape of a regular square prism that extends horizontally through the four sides of a 138 mm × 138 mm square along the four sides of the first major surface and the second major surface at the central portions of the first major surface and the second major surface. (2) With the substrate facing the first major surface, cut out the portion within the calculation region from the first major surface to obtain a first region surface. (3) Set a reference plane as a vertical plane passing through an arbitrary point on the central axis of the regular square prism of the calculation region and perpendicular to the central axis. Set a rotation axis parallel to any one of the four sides of the regular square formed by the intersection of the regular square prism of the calculation region and the vertical plane and passing through the reference point. Starting from the state where the substrate is facing the first major surface, rotate the substrate 180 degrees along the rotation axis so that it faces the second major surface, and cut out the portion within the calculation region from the second major surface to obtain a second region surface. (4) Calculate the least-squares plane for each of the first region surface and the second region surface. (5) Convert the first region surface and the second region surface into a height map of the first region surface and a height map of the second region surface based on the positions of each on the least-squares plane of each of the first region surface and the second region surface. (6) Symmetrically move the height map of the second region surface with respect to a vertical plane passing through the rotation axis in (3) and along the 90-degree direction of the rotation in (3) to obtain an inverted height map of the second region surface. (7) At each position (X coordinate, Y coordinate) on the reference plane, add the height of the height map of the first region surface and the height of the inverted height map of the second region surface to create a map of the calculated height (Z coordinate). When the map of the calculated height is used as the calculated surface, It can be evaluated as a shape with a flatness (TIR) of the calculated surface of 100 nm or less. In this way, the flatness of the exposure mask during exposure using the exposure mask obtained from the mask blank substrate through the mask blank can be predicted with extremely high accuracy at the stage of the mask blank substrate, and the flatness of the exposure mask during exposure using the exposure mask can also be predicted.

[0048] In this case, from the shapes (S12a) of the aforementioned first main surface and the shape (S12b) of the second main surface, in the above (5), the following formula (c) S12a + S12b = S13 (c) As shown in, the calculated surface (S13) can be obtained by integrating the shape of the first main surface and the shape of the second main surface. Then, from the flatness (TIR) of the obtained calculated surface, the flatness (TIR) of the substrate for mask blanks finally obtained after finish polishing can be predicted.

[0049] In the step (E), when the shapes of the first main surface and the second main surface predicted in the step (D) are the shapes of the first main surface and the second main surface that satisfy a predetermined flatness, the process can proceed to the finish polishing step. On the other hand, in the step (E), when the shapes of the first main surface and the second main surface predicted in the step (D) are not the shapes of the first main surface and the second main surface that satisfy a predetermined flatness, the steps from (A) to (E) can be repeated.

[0050] The shapes of the first main surface and the second main surface of the substrate for mask blanks finally obtained after finish polishing can also be appropriately measured. There are no particular restrictions on this measurement either. For example, a laser interferometer can be used. Furthermore, from the results, the flatness (TIR) of the substrate for mask blanks finally obtained after finish polishing can also be evaluated.

[0051] The surface of the substrate for mask blanks after local processing is often not sufficient in terms of defects and roughness in the surface state. In order to improve them, finish polishing is carried out after local processing. Finish polishing can be carried out, for example, by double-sided simultaneous polishing using a soft polishing cloth and a polishing slurry composed of fine colloidal silica. Regarding the polishing conditions for finish polishing, they can be appropriately selected according to conventional methods and are not particularly limited. For example, a Swedish type soft polishing pad and an aqueous solution of colloidal silica abrasive grains with an average particle size of 10 to 100 nm can be used.

Example

[0052] Hereinafter, the present invention will be specifically described with reference to examples, but the present invention is not limited to the following examples.

[0053] [Examples 1 to 3] Ten glass substrates (with a size of 152 mm × 152 mm square and a thickness of 6.35 mm for the first main surface and the second main surface) formed of SiO2 and TiO2 (TiO2 concentration of about 7% by mass) were prepared. The end faces (four faces other than the main surfaces) of the glass substrates were chamfered and ground, and then rough polishing and fine polishing were performed using a polishing liquid containing cerium oxide abrasive grains. Thereafter, in Example 1, ten glass substrates (substrates 1-1 to 1-10), in Example 2, ten glass substrates (substrates 2-1 to 2-10), and in Example 3, ten glass substrates (substrates 3-1 to 3-10) were set on the carrier of a double-sided polishing apparatus applying a Swedish type soft polisher, and the first main surface and the second main surface were ultra-precision polished using a polishing liquid of colloidal silica abrasive grains.

[0054] After ultra-precision polishing, it was washed with a cleaning liquid containing KOH to remove silica nanoparticles, and after drying, the shapes of the first main surface and the second main surface were measured with a surface shape measuring device (UltraFlat, manufactured by Tropel). Thereafter, based on the shape of the obtained main surface, the processing conditions for the next local processing were determined.

[0055] Next, based on the determined processing conditions, both surfaces of the glass substrate were locally processed using a local processing apparatus. As the local processing apparatus, the one described in Japanese Patent Application Laid-Open No. 2010-194705 (Patent Document 3) was used. The local processing using this apparatus involves polishing the entire surface of the substrate while controlling the moving speed of a fine polishing tool. By moving the polishing tool slowly at relatively convex portions and quickly at relatively concave portions, the target shape can be obtained. For the processing tool of the local processing apparatus, a wool felt buff was used, and for the polishing slurry, a mixture of silica nanoparticles (AJ-3540, manufactured by Nissan Chemical Industries, Ltd.) and a small amount of defoaming agent (Shin-Etsu Silicone KS-537, manufactured by Shin-Etsu Chemical Co., Ltd.) was used. After local processing, the glass substrate was washed with a cleaning liquid containing KOH to remove the silica nanoparticles, and after drying, the shapes of the first major surface and the second major surface were measured using a surface shape measuring apparatus (UltraFlat, manufactured by Tropel).

[0056] Here, in order to grasp the change in the shape of the major surface after finish polishing with respect to the surface after local processing, another glass substrate was used to perform local processing in the same manner, and further, finish polishing similar to the finish polishing described later was performed to evaluate the change in the shape of the major surface after finish polishing with respect to the surface after local processing. Next, for the glass substrate, the change in the shape of the major surface that was grasped was applied to the shape of the major surface of the glass substrate after local processing to predict the shape of the surface after finish polishing. In this example, after predicting the shape of the surface after finish polishing with respect to the surface after the first local processing, the second local processing was performed on all 10 glass substrates, and for the surface after the second local processing as well, the shape of the surface after the finish polishing process was predicted.

[0057] Next, regarding the shape of the surface after actual local polishing and the predicted shape of the surface after finish polishing, the flatness (TIR) of the major surface of the glass substrate was evaluated by the following method. That is, (1) Place the substrate with its first major surface and second major surface arranged along the substantially vertical direction, and set a square calculation region in the central portions of the first major surface and the second major surface, which extends horizontally through the four sides of a 138 mm × 138 mm square along the four sides of the first major surface and the second major surface. (2) With the substrate facing the first major surface, cut out the portion within the calculation region from the first major surface to obtain a first region surface. (3) Set a reference plane as a vertical plane passing through an arbitrary point on the central axis of the square prism of the calculation region and perpendicular to the central axis. Set a rotation axis parallel to any one of the four sides of the square formed by the intersection of the square prism of the calculation region and the vertical plane and passing through the reference point. Rotate the substrate 180 degrees along the rotation axis from the state facing the first major surface to the state facing the second major surface, and cut out the portion within the calculation region from the second major surface to obtain a second region surface. (4) Calculate the least-squares plane for each of the first region surface and the second region surface. (5) Convert the first region surface and the second region surface into a height map of the first region surface and a height map of the second region surface based on the respective positions on the least-squares planes of the first region surface and the second region surface. (6) Symmetrically move the height map of the second region surface with respect to a vertical plane passing through the rotation axis in (3) and along the 90-degree direction of the rotation in (3) to obtain an inverted height map of the second region surface. (7) At each position (X coordinate, Y coordinate) on the reference plane, add the height of the height map of the first region surface and the height of the inverted height map of the second region surface to create a map of the calculated height (Z coordinate). When the map of the calculated height is taken as the calculated surface, the flatness (TIR) of the calculated surface is obtained. In Example 1, the surface obtained by cutting out the surface of the second region is directly used as the second region surface. In Example 2, in (5), as the height map of the second region surface, a height map obtained by processing with a Gaussian filter (20 mm × 20 mm) is applied. In Example 3, in (5), as the height map of the second region surface, a height map obtained by fitting with terms up to the 15th order of the Legendre polynomial is applied. The results are shown in Table 1.

[0058] Also, for the substrate 1-1, the shapes of the first major surface and the second major surface after the second local processing (the shape after local processing), and the shapes of the major surfaces predicted by applying the grasped changes in the shapes of the major surfaces are shown in FIG. 5. In this case, since the shape of the first major surface after the finish polishing process is convex, for the substrate 1-1, it is preferable to perform local processing so that the shape of the first major surface becomes concave after local processing, and for the substrate 1-1, local processing was performed in this manner.

[0059] In the measurement of the shape of the major surface of the glass substrate, the shapes of both the first major surface and the second major surface are measured from the outside of the glass substrate with the measuring instrument facing the first major surface and the second major surface directly.

[0060]

Table 1

[0061] As a result, in all of the glass substrates, since the flatness (TIR) of the predicted shape of the major surface after finish polishing with respect to the surface after the second local processing was 100 nm or less, finish polishing was performed.

[0062] The finish polishing was performed in two steps. First, to remove the scratches generated by the local processing, 10 glass substrates were set on the carrier of a double-sided polishing apparatus applying a Swedish type soft polishing pad, and the first major surface and the second major surface were ultra-precision polished using a polishing liquid with colloidal silica abrasive grains. After the ultra-precision polishing, they were washed with a cleaning liquid containing KOH to remove the silica nanoparticles. Next, 10 glass substrates were set on the carrier of a double-sided polishing apparatus applying a Swedish type soft polishing pad, and the first major surface and the second major surface were finally polished under conditions different from those of the ultra-precision polishing using a polishing liquid with colloidal silica abrasive grains. The glass substrates after the final polishing were washed with a cleaning liquid containing KOH to remove the silica nanoparticles, and after drying, the shapes of the first major surface and the second major surface were measured with a surface shape measuring apparatus (UltraFlat, manufactured by Tropel).

[0063] Next, regarding the shape of the surface after finish polishing, the shape of the main surface of the glass substrate was evaluated as flatness (TIR) in the same manner as the method for evaluating the flatness (TIR). The results are shown in Table 2. Also, for substrate 1-1, the shapes of the first main surface and the second main surface after finish polishing (shape after finishing) are shown in Fig. 5.

[0064]

Table 2

[0065] From the above results, there is no significant difference between the flatness (TIR) of the shapes of the first main surface and the second main surface after the finish polishing process predicted by applying the grasped changes in the shape of the main surface, and the flatness (TIR) of the actual shapes of the first main surface and the second main surface after finish polishing. It can be seen that the predicted flatness (TIR) after local processing can be applied to the determination of the acceptability of the shape of the main surface after local processing. Also, since the flatness (TIR) of the substrates for photomask blanks obtained in this example is around 50 nm after finish polishing, they can be suitably used as substrates for photomask blanks that provide an exposure mask in which the main surface of the substrate has a highly flat shape when adsorbed and held by an exposure machine, particularly in exposure using an EUVL exposure mask.

Explanation of Signs

[0066] 1 First main surface 11 First region surface 11a Convex portion 111 Height map of the first region surface 2 Second main surface 21 Second region surface 21a, 21aR Convex portions 211 Height map of the second region surface 211R Inverted height map of the second region surface 3 Calculated surface 500 Substrate C Calculated region CA Central axis P Reference point RA Rotation axis S Reference plane V vertical plane

Claims

1. A substrate for a mask blank having two main surfaces, a first main surface and a second main surface, which are 152 mm × 152 mm square, and having a thickness of 6.35 mm, (1) The substrate is arranged with the first main surface and the second main surface substantially along the vertical direction, and a calculation region in the shape of a regular square prism extending horizontally through the four sides of a 138 mm × 138 mm square along the four sides of the first main surface and the second main surface at the central portions of the first main surface and the second main surface is set, (2) With the state of facing the first main surface, the portion within the calculation region is cut out from the first main surface to form a first region surface, (3) A reference plane is set as a vertical plane passing through an arbitrary point on the central axis of the regular square prism of the calculation region and perpendicular to the central axis. A rotation axis parallel to any one of the four sides of the regular square formed by the intersection of the regular square prism of the calculation region and the vertical plane passing through the reference point is set. From the state of facing the first main surface, the substrate is rotated 180 degrees along the rotation axis. In the state of facing the second main surface, the portion within the calculation region is cut out from the second main surface to form a second region surface, (4) A least-squares plane is calculated for each of the first region surface and the second region surface, (5) The first region surface and the second region surface are converted into a height map of the first region surface and a height map of the second region surface based on the positions of each of the first region surface and the second region surface on their respective least-squares planes, (6) The height map of the second region surface is symmetrically moved with respect to a vertical plane passing through the rotation axis and along the 90-degree direction of the rotation to form an inverted height map of the second region surface, (7) At each position (X coordinate, Y coordinate) on the reference plane, the height of the height map of the first region surface and the height of the inverted height map of the second region surface are added together to create a map of the calculated height (Z coordinate). When the map of the calculated height is used as the calculated surface, the flatness (TIR) of the calculated surface is 100 nm or less, In (5) above, a height map obtained by processing with a Gaussian filter (20 mm × 20 mm) is applied as the height map of the second region surface, which is a characteristic of the substrate for a mask blank.

2. A substrate for a mask blank having two main surfaces, a first main surface and a second main surface, which are square with sides of 152 mm × 152 mm and have a thickness of 6.35 mm, (1) The substrate is arranged with the first main surface and the second main surface substantially along the vertical direction, and a calculation region in the shape of a regular square prism extending horizontally through the four sides of a 138 mm × 138 mm square along the four sides of the first main surface and the second main surface at the central portions of the first main surface and the second main surface is set. (2) With the state of facing the first main surface, the portion within the calculation region is cut out from the first main surface to form a first region surface. (3) A reference plane is set as a vertical plane passing through an arbitrary point on the central axis of the regular square prism of the calculation region and perpendicular to the central axis. A rotation axis parallel to any one of the four sides of the regular square formed by the intersection of the regular square prism of the calculation region and the vertical plane passing through the reference point is set. From the state of facing the first main surface, the substrate is rotated 180 degrees along the rotation axis, and with the state of facing the second main surface, the portion within the calculation region is cut out from the second main surface to form a second region surface. (4) A least-squares plane is calculated for each of the first region surface and the second region surface. (5) The first region surface and the second region surface are converted into a height map of the first region surface and a height map of the second region surface based on the respective positions on the least-squares planes of the first region surface and the second region surface. (6) The height map of the second region surface is symmetrically moved with reference to a vertical plane passing through the rotation axis and along the 90-degree direction of the rotation to form an inverted height map of the second region surface. (7) At each position (X coordinate, Y coordinate) on the reference plane, a map of the calculated height (Z coordinate) is created by adding the height of the height map of the first region surface and the height of the inverted height map of the second region surface, and when the map of the calculated height is used as the calculated surface, The flatness (TIR) of the calculated surface is 100 nm or less, In the above (5), as the height map of the second region surface, a height map obtained by fitting with terms up to the 15th order of Legendre polynomials is applied, and a substrate for a mask blank is characterized in that.

3. A method for manufacturing a substrate for a mask blank according to claim 1, including a local processing step for one or both of the first main surface and the second main surface, and a finishing polishing step following the local processing step, The local processing step is (A) a step of grasping the change in the shape of the surface before and after the finishing polishing step of the first main surface and the second main surface; (B) a step of locally processing one or both of the first main surface and the second main surface; (C) a step of measuring the shape of the first main surface and the shape of the second main surface after the step (B) as the shape of the surface before the finishing polishing step; (D) a step of applying the change in the shape of the surface grasped in the step (A) to the shape of the surface before the finishing polishing step obtained in the step (C) to predict the shape of the first main surface and the second main surface after the finishing polishing step; (E) a step of evaluating whether the shapes of the first main surface and the second main surface predicted in the step (D) satisfy the shape of the first main surface and the second main surface that satisfy a predetermined flatness and a method for manufacturing a substrate for a mask blank, characterized in that it includes.

4. The shape of the first main surface and the second main surface that satisfy the predetermined flatness in the step (E) is the shape of the first main surface and the second main surface of the substrate for a mask blank according to claim 1, and the manufacturing method according to claim 3 is characterized in that.

5. A method for manufacturing a substrate for a mask blank according to claim 2, including a local processing step for one or both of the first main surface and the second main surface, and a finishing polishing step following the local processing step, The local processing step is Step of grasping the change in the shape of the surface before and after the finish polishing process of the first main surface and the second main surface, Step of locally processing one or both of the first main surface and the second main surface, Step of measuring the shape of the first main surface and the shape of the second main surface after the step (B) as the shape of the surface before the finish polishing process, Step of applying the change in the shape of the surface grasped in the step (A) to the shape of the surface before the finish polishing process obtained in the step (C) to predict the shape of the first main surface and the second main surface after the finish polishing process, Step of evaluating whether the shape of the first main surface and the second main surface predicted in the step (D) satisfies the predetermined flatness of the shape of the first main surface and the second main surface, A method for manufacturing a substrate for a mask blank, comprising the above steps.

6. The shape of the first main surface and the second main surface satisfying the predetermined flatness in the step (E) is the shape of the first main surface and the second main surface of the substrate for a mask blank according to claim 2. The manufacturing method according to claim 5, characterized in that.

7. In the step (E), when the shape of the first main surface and the second main surface predicted in the step (D) does not satisfy the shape of the first main surface and the second main surface satisfying the predetermined flatness, the steps (A) to (E) are repeated. The manufacturing method according to claim 3 or 5, characterized in that.

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