Substrate for mask blanks and method for manufacturing the same

Abstract

SOLUTION: To provide a mask blank substrate which has two main surfaces of first and second main surfaces of 152 mm×152 mm square, and a thickness of 6.35 mm, and in which when a range of 132 mm×132 mm square centering on an intersection point of diagonal lines is a calculation region in each of the first and second main surfaces, a flatness on the basis of a least squares plane of a substrate surface in the calculation region on the substrate surface in at least one of the calculation regions of the first and second main surfaces is 100 nm or less, and a difference (PV) between a maximum value and a minimum value of a height of a calculation surface on the basis of the least squares plane, represented by a difference between a shape of the substrate surface before smoothing process by Gaussian filter (10 mm×10 mm) and a shape after the smoothing process is 20 nm or less.EFFECT: A mask blank substrate can provide an exposure mask in which a main surface of a substrate has a highly flat shape when the wave front of the exposure mask is corrected by an exposure device in exposure using the exposure mask, especially in exposure by EUVL.SELECTED DRAWING: None

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 extreme ultraviolet (EUV) light is used as exposure light, and a method for manufacturing the same.

Background Art

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

[0003] In EUVL, the exposure mask is one of the important elements, and improving the flatness of the 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 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 for this purpose, local processing techniques such as local etching and local processing are used. These are methods of making the entire substrate closer to flat by removing relatively convex regions.

[0004] Even if a highly flat glass substrate can be obtained in this way, since there are limitations to the high flatness technology, generally, this is solved by the wavefront correction function of the exposure apparatus. By optically correcting the surface shape of the exposure mask with the wavefront correction function, an optically highly flat exposure mask can be used even when the local processing technology is insufficient.

[0005] Regarding the flatness considering the wavefront correction function of the exposure apparatus, for example, in International Publication No. 2016 / 098452 (Patent Document 1), in order to obtain high transfer accuracy when a reflective mask manufactured using a substrate that has been subjected to conventional double-sided polishing and local processing on both the front and back main surfaces is chucked in an exposure apparatus and exposure transfer is performed, the shape of the front main surface of the substrate when electrostatically chucked should be approximated 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 main surface, it can be a thickness variation that tends to be easily corrected by the wavefront correction function of the exposure apparatus. It is described that a transfer mask having such a substrate can expose and transfer a transfer pattern to a transfer object with high accuracy.

[0006] Japanese Patent Application Laid-Open No. 2016-134509 (Patent Document 2) describes processing marks resulting from the processing pitch generated when using a local processing tool. The processing marks resulting from local processing generated on the chamfered surface at the end of the substrate have an adverse effect on flatness measurement, reducing measurement reproducibility. By performing polishing on the chamfered surface and removing the undulation component at the end face, it is described that the measurement reproducibility of flatness can be improved.

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 wavefront correction function corrects by approximating the three-dimensional shape of the exposure mask with a polynomial. However, relatively gentle surface shape components (long-wavelength components) can be described by low-order and simple polynomials, while high-order and complex polynomials are required to describe steep surface shape components (short-wavelength components). Therefore, the effect of correcting the long-wavelength components becomes relatively high, and even with the same flatness, the wavefront shape of the surface differs between a substrate mainly composed of long-wavelength components and a substrate mainly composed of short-wavelength components in terms of the effect of the wavefront correction function, resulting in a difference in optical flatness. For EUVL wiring miniaturization, a more highly flat exposure mask is required. Along with this trend, further improvement in the capabilities of the wavefront correction function can be fully expected. However, it is considered that it will become even more difficult to correct components with even shorter wavelengths by the wavefront correction function in the future. On the other hand, considering that the further improvement in flatness by the glass substrate processing technology is reaching its limit, reducing short-wavelength components that cannot be corrected by the wavefront correction function is important.

[0009] The method described in International Publication No. 2016 / 098452 (Patent Document 1) is composed of a process of calculating the synthetic 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 × 132 mm square) actually used for exposure and is insufficient. Also, the wavefront correction function considered here is only for long-wavelength components up to the 6th term of the Zernike polynomial, and does not consider components with shorter wavelengths.

[0010] Japanese Patent Application Laid-Open No. 2016-134509 (Patent Document 2) has a description regarding the waviness component derived from local processing, but it is about the chamfered surface not used for exposure. Also, it only has a description regarding the waviness within a very small region, and the method described in Japanese Patent Application Laid-Open No. 2016-134509 (Patent Document 2) does not consider the waviness component across the entire main surface.

[0011] The present invention has been made in view of the above circumstances, and in exposure using an exposure mask, particularly in exposure by EUVL, it is an object of the present invention to provide a substrate for a mask blank that gives an exposure mask having optically high flatness by the wavefront correction function of an exposure apparatus, and a method for manufacturing the same.

Means for Solving the Problems

[0012] As a result of intensive studies to solve the above problems, the present inventors have found that when a predetermined calculation region is set with respect to the main surface of the substrate for a mask blank, the flatness of the calculation region on the main surface of the calculation region is 100 nm or less, and also, the difference between the maximum value and the minimum value of the height of the calculated surface represented by the difference between the shapes before and after the smoothing process by a Gaussian filter (10 mm × 10 mm) is 20 nm or less. It has been found that a substrate for a mask blank can provide an exposure mask having high flatness by the wavefront correction function in an exposure apparatus in which a steep surface shape component (short wavelength component) of the main surface is reduced.

[0013] Further, the present inventors have manufactured such a substrate for a mask blank by a method including a local processing step and a finishing polishing step following the local processing step. In the local processing step, with respect to the shape of the main surface after the local processing step and before the finishing polishing step, the change in the shape of the main surface after the finishing polishing step of the main surface grasped in advance is applied to predict the shape of the main surface after the finishing polishing step, and it is evaluated whether the predicted shape of the main surface has a predetermined flatness. Furthermore, in the finishing polishing step, by performing polishing that reduces the short wavelength component, it has been found that a substrate for a mask blank that gives an exposure mask having high flatness by the wavefront correction function in an exposure apparatus can be manufactured reliably and with high productivity, and thus the present invention has been completed.

[0014] 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, a first main surface and a second main surface, which are 1.152 mm × 152 mm squares and have a thickness of 6.35 mm, When a range of 132 mm × 132 mm square centered on the intersection of the diagonals is defined as a calculation region on each of the first major surface and the second major surface, on the substrate surface of the calculation region of at least one of the first major surface and the second major surface, the flatness based on the least-squares plane of the substrate surface of the calculation region is 100 nm or less, and Target the area of 10 mm × 10 mm around the measurement point the difference between the height maximum value and the height minimum value (PV) of the calculated surface, which is represented by the difference between the shape of the substrate surface before the smoothing process using a Gaussian filter (10 mm × 10 mm) and the shape after the smoothing process, based on the least-squares plane, is 20 nm or less , in at least one arbitrary range of 6 mm × 6 mm square set within the calculation area of at least one of the first main surface and the second main surface (1) Measure the surface shape with a finer precision than a 10-μm pitch within the range of 6 mm × 6 mm square to create a height map (2) Create an x partial derivative map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the x direction (3) Create a y partial derivative map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the y direction (4) Create a total differential map from the x partial derivative map and the y partial derivative map (5) Calculate the difference (PVXY) between the maximum value and the minimum value of the total differential map when the PVXY is 0.1 nm / μm or less at any position within the calculation area is satisfied. A substrate for a mask blank, characterized in that. 2. In any range of 1 mm × 1 mm square within the calculation region of at least one of the first major surface and the second major surface, the difference between the height maximum value and the height minimum value (LS) based on the least-squares plane is 15 nm or less anywhere within the calculation region. The substrate for a mask blank according to 1, characterized in that. 3. The Gaussian filter (10 mm × 10 mm) is a filter that calculates a rate based on the following formula so that the weight decreases as it gets farther away in the area of 10 mm × 10 mm around the measurement point using a Gaussian distribution function f(x,y)=1 / (2πσ 2 )exp(-(x 2 +y 2 ) / (2σ 2 )) The substrate for a mask blank according to 1 or 2, characterized in that it is a filter for calculating a rate 4. The one described in 1 A method for manufacturing a substrate for a mask blank, comprising: a local processing step for at least one of the first major surface and the second major surface, and a finishing polishing step following the local processing step. The local processing step includes: (A) a step of grasping the change in the shape of the surface before and after the finish polishing step of the main surface; (B) a step of locally processing the main surface; (C) a step of measuring the shape of the main surface after the step (B) as the shape of the surface before the finish polishing step; (D) a step of predicting the shape of the main surface after the finish 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 finish polishing step obtained in the step (C); (E) a step of evaluating whether the shape of the main surface predicted in the step (D) has a predetermined flatness; and the finish polishing step includes: (F) a polishing step of reducing the short-wavelength component of the main surface and A method for manufacturing a substrate for a mask blank, characterized in that. 5. The manufacturing method according to 4, characterized in that the polishing for reducing the short-wavelength component of the main surface in the step (F) is polishing using a hard polishing cloth. 6. The shape having the predetermined flatness in the step (E) is: when a range of 132 mm × 132 mm square centered on the intersection of the diagonals of the main surface is set as the calculation area, a shape in which the flatness based on the least-squares plane of the substrate surface in the calculation area of at least one of the first main surface and the second main surface is 100 nm or less on the substrate surface in the calculation area. The manufacturing method according to 4 or 5, characterized in that. 7. The shape having the predetermined flatness in the step (E) is: when a range of 132 mm × 132 mm square centered on the intersection of the diagonals of the main surface is set as the calculation area, On the substrate surface of at least one of the calculation regions of the first main surface and the second main surface, the shape of the substrate surface before the smoothing process by the Gaussian filter (10 mm × 10 mm) and the shape after the smoothing process are represented by the difference between them. The difference (PV) between the maximum value and the minimum value of the height with respect to the least-squares plane of the calculated surface is 20 nm or less. The manufacturing method according to 6, characterized in that it is as described above. 8. The shape having the predetermined flatness in the step (E) is In an arbitrary range of 1 mm × 1 mm square within at least one of the calculation regions of the first main surface and the second main surface, the difference (LS) between the maximum value and the minimum value of the height with respect to the least-squares plane is 15 nm or less in any part of the calculation region. The manufacturing method according to 7, characterized in that it is as described above. 9. The shape having the predetermined flatness in the step (E) is In an arbitrary range of at least one 6 mm × 6 mm square set within at least one of the calculation regions of the first main surface and the second main surface, (1) Measure the surface shape with a finer accuracy than a 10 μm pitch within the range of 6 mm × 6 mm square to create a height map. (2) Create an x partial derivative map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the x direction. (3) Create a y partial derivative map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the y direction. (4) Create a total derivative map from the x partial derivative map and the y partial derivative map. (5) Calculate the difference (PVXY) between the maximum value and the minimum value of the total derivative map. When The manufacturing method according to 7, characterized in that the PVXY is 0.1 nm / μm or less in any part of the calculation region. 10. In the step (E), when the shape of the main surface predicted in the step (D) does not have the predetermined flatness, the local processing step is performed again. The manufacturing method according to 4 or 5, characterized in that it is as described above.

Advantages of the Invention

[0015] The substrate for a mask blank of the present invention can provide an exposure mask in which the main surface of the substrate has a highly flat shape when the exposure mask is wavefront-corrected by an exposure apparatus in exposure using an exposure mask, particularly in exposure by EUVL. Further, according to the method for manufacturing the substrate for a mask blank of the present invention, such a substrate for a mask blank can be manufactured reliably and with high productivity.

Embodiments for Carrying Out the Invention

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

[0017] The material of the substrate for a mask blank of the present invention may be a conventionally used material and is not particularly limited. However, for drawing a fine pattern, 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 material substrate for the substrate for a mask blank, those synthesized, molded, and processed according to a conventional method can be used.

[0018] Substrates for mask blanks are required to have high flatness. This is because the higher the flatness, the easier it is to achieve the desired exposure, and a substrate with higher flatness can be said to be a substrate for mask blanks suitable for drawing fine patterns. 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, and the second main surface is adsorbed and held by the exposure machine. Among these, in the most advanced applications, reflective masks are the mainstream, so the flatness of the first main surface is required to be at an extremely high level. Therefore, in order to improve the flatness of the first main surface, various planarization techniques by local processing technology are also being studied.

[0019] On the other hand, as a function of the exposure machine side, there is a wavefront correction function. This is a function that optically corrects the surface shape even for a substrate with low flatness. According to this, it is expected that even a substrate with low flatness can obtain the same exposure result as a substrate with high flatness. However, using the wavefront correction function does not mean that all shapes can be corrected. Generally, correction of a gentle wavefront shape is possible, but correction of a steep wavefront shape is difficult. Thus, even for mask blank substrates with the same flatness, there is a difference in exposure performance depending on the ratio of the local gentle wavefront shape and the steep shape.

[0020] In the substrate for mask blanks of the present invention, when a range of 132 mm × 132 mm square centered on the intersection of the diagonals is defined as the calculation region on each of the first main surface and the second main surface, it is preferable that the flatness is 100 nm or less on the substrate surface of at least one of the calculation regions of the first main surface and the second main surface. The calculation region is set such that each of the four sides of the main surface of the substrate for mask blanks and each of the four sides of the calculation region are parallel.

[0021] The measurement of the shape of the main surface of the substrate for mask blanks is not particularly limited. For example, a laser interferometer can be used. The shape that can be measured by the 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 can be removed. Further, flatness is the difference between the highest value (highest height) and the lowest value (lowest height) within the target surface when the difference between the least-squares plane of the target surface and the target surface is calculated with the least-squares plane of the target surface as the reference. In the present invention, the target surface is the surface of the calculation region, and with the least-squares plane of the surface of the calculation region as the reference, the difference between the least-squares plane of the surface of the calculation region and the surface of the calculation region is calculated, and the difference between the highest value (highest height) and the lowest value (lowest height) within the surface of the calculation region of the difference is defined as flatness.

[0022] The flatness of the calculation region is preferably 100 nm or less, more preferably 80 nm or less, and still more preferably 70 nm or less. If the flatness is 100 nm or less, in the exposure using the exposure mask obtained from the substrate for mask blanks via the mask blank, exposure with good transfer accuracy can be realized. On the other hand, if the flatness is greater than 100 nm, there is a possibility that good exposure cannot be realized.

[0023] Also, by separating the wavelength components that can be corrected by the wavefront correction function of the exposure machine (the influence of the wavefront shape is mitigated by the wavefront correction function) and the wavelength components that are difficult to correct (the influence of the wavefront shape is not substantially mitigated by the wavefront correction function) in the shape of the main surface, the shape of the main surface in the state where the exposure mask is corrected by the exposure machine can be grasped with higher accuracy. Here, the wavelength components that can be corrected are components corresponding to a relatively gentle wavefront shape (long wavelength components), and the wavelength components that are difficult to correct are components corresponding to a relatively steep wavefront shape (short wavelength components).

[0024] When calculating the range of 132 mm × 132 mm square with the intersection of the diagonals as the center on each of the first main surface and the second main surface of the substrate for a mask blank of the present invention, when the smoothing process is performed on the substrate surface of at least one of the calculated areas of the first main surface and the second main surface, the difference between the highest value and the lowest value of the height of the short-wavelength component is reflected. It is preferable that the difference (PV) between the highest value and the lowest value of the height of the calculated surface represented by the difference between the shape of the substrate surface before the smoothing process and the shape after the smoothing process is 20 nm or less. This height standard can be the least-squares plane of the main surface (i.e., the main surface before the smoothing process) of the calculated area.

[0025] This smoothing process is a process of converting a surface with a wavefront shape into a smoother surface by mathematical processing. For the smoothing process, a Gaussian filter used in image processing or the like can be used. Specifically, smoothing by a Gaussian filter (10 mm × 10 mm) is preferable. A Gaussian filter is a smoothing process that performs smoothing within a minute area of the surface over the entire surface. Specifically, an X mm Gaussian filter focuses on an area of X mm × X mm around a certain measurement point, and using the Gaussian distribution function, the weight becomes smaller as the distance increases, according to the following formula f(x,y)=1 / (2πσ 2 )exp(-(x 2 +y 2 ) / (2σ 2 )) is a filter for calculating the rate. By using a Gaussian filter, particularly a 10 mm × 10 mm Gaussian filter, in the surface shape of the exposure mask, the surface after the smoothing process can be estimated as a surface reflecting the wavelength components (long-wavelength components) that can be corrected by the wavefront correction function of the exposure machine, and this can be used as the height map of the long-wavelength components. On the other hand, the calculated surface represented by the difference between the shape of the substrate surface before the smoothing process and the shape after the smoothing process is a surface reflecting the wavelength components (short-wavelength components) that are difficult to correct by the wavefront correction function of the exposure machine in the surface shape of the exposure mask.

[0026] The difference (PV) between the maximum value and the minimum value of the surface height is preferably 20 nm or less, more preferably 18 nm or less, still more preferably 15 nm or less, and even more preferably 10 nm or less. If the PV is 20 nm or less, in the exposure using the exposure mask obtained from the mask blank substrate via the mask blank, an exposure with good transfer accuracy can be realized. On the other hand, if the PV is greater than 20 nm, there is a possibility that good exposure cannot be realized.

[0027] Further, in the mask blank substrate of the present invention, in any range of 1 mm × 1 mm square in at least one of the calculation regions on the first main surface and the second main surface, the difference (LS: Local Slope) between the maximum value and the minimum value of the height is preferably 15 nm or less (the maximum LS is 15 nm or less) anywhere in the calculation region (regardless of where the 1 mm × 1 mm square range is set within the calculation region). This height standard can be the least squares plane of the main surface of the calculation region (that is, the main surface before the smoothing process). LS is the flatness of a minute region and indicates the maximum value of the local slope in the surface shape. A large LS means the presence of an extreme short wavelength component, and since the extreme short wavelength component cannot be corrected by the wavefront correction function, sufficient exposure characteristics may not be obtained when the LS is large. Further, the LS is preferably 12 nm or less (the maximum LS is 12 nm or less), and more preferably 10 nm or less (the maximum LS is 10 nm or less). If the LS is 15 nm or less, in the exposure using the exposure mask obtained from the mask blank substrate via the mask blank, an exposure with better transfer accuracy can be realized.

[0028] In addition, for the substrate for a mask blank of the present invention, when measuring the surface shape with higher accuracy than a 10-μm pitch in at least one arbitrary range of 6 mm × 6 mm squares set in the calculation region on at least one of the first main surface and the second main surface, the difference (PVXY) between the maximum value and the minimum value of the total differential map obtained by totally differentiating the height map of the surface shape in that region is preferably 0.1 nm / μm or less. Specifically, in at least one arbitrary range of 6 mm × 6 mm squares set in the calculation region on at least one of the first main surface and the second main surface, (1) Measure the surface shape with a finer pitch than 10 μm within a range of 6 mm × 6 mm squares to create a height map, (2) Create an x partial differential map obtained by partially differentiating the height map within a range of 6 mm × 6 mm in the x direction, (3) Create a y partial differential map obtained by partially differentiating the height map within a range of 6 mm × 6 mm in the y direction, (4) Create a total differential map from the x partial differential map and the y partial differential map, (5) Calculate the difference (PVXY) between the maximum value and the minimum value of the total differential map when it is preferable that PVXY is 0.1 nm / μm or less.

[0029] PVXY is the slope of a minute region on the order of several μm and indicates the intensity of the local slope in the surface shape. A large PVXY means the presence of an extremely short wavelength component, and since the extremely short wavelength component cannot be corrected by the wavefront correction function, if PVXY is large, sufficient exposure characteristics may not be obtained. PVXY is preferably further 0.085 nm / μm or less, and more preferably 0.07 nm / μm or less. If PVXY is 0.1 nm / μm or less, in exposure using an exposure mask obtained from a mask blank substrate via a mask blank, exposure with better transfer accuracy can be realized. Also, it is preferable that the range of the central 6 mm × 6 mm square in the calculation region is within the above range, and further, in any part of the calculation region (regardless of where an arbitrary range of 6 mm × 6 mm square is set within the calculation region), it is more preferable that it is within the above range (the maximum PVXY is within the above range).

[0030] The above total differential map can be created, for example, as follows. First, a height map in the range of 6 mm × 6 mm within the calculation region is measured with an accuracy finer than a 10 μm pitch. For the measurement, for example, a 3D optical surface profiler (Nexview, manufactured by Zygo Corporation) can be used. Next, an x-direction partial differential map of the created height map in the range of 6 mm × 6 mm is created. This x-direction partial differential map, when the height at the coordinate for which the x partial differential is to be calculated is Z(x,y), the surrounding heights are Z1 to Z8, and the adjacent coordinate interval is P, is given by the following formula ∂Z(x,y) / ∂x=(2×Z5 - 2×Z4 + Z3 + Z8 - Z1 - Z6) / P is calculated. Also, the Y partial differential map, when the height at the coordinate for which the y partial differential is to be calculated is Z(x,y), the surrounding heights are Z1 to Z8, and the adjacent coordinate interval is P, is given by the following formula ∂Z(x,y) / ∂y=(2×Z7 - 2×Z2 + Z8 + Z6 - Z1 - Z3) / P is calculated. And the total differential map is given by the following formula ∂ 2 Z(x,y) / ∂x∂y=((∂Z(x,y) / ∂x) 2+(∂Z(x,y) / ∂y) 2 ) 0.5 can be obtained by

[0031] In this way, the precise surface shape within a minute region of 6 mm × 6 mm can be measured, and by further taking the total differential of this, information regarding short-wavelength components with a fine pitch of several μm on the surface can be extracted. When machining marks due to local processing occur, PVXY is a high value exceeding 0.1 nm / μm. However, for example, by finish polishing with a hard abrasive cloth as described later, the short-wavelength components with a pitch of several μm can be attenuated, and PVXY can be reduced to 0.1 nm / μm or less.

[0032] Next, a method for manufacturing a substrate for mask blanks of the present invention will be described. The method for manufacturing a substrate for mask blanks of the present invention includes a local processing step for at least one of the first main surface and the second main surface of the substrate for mask blanks, and a finish polishing step following the local processing step.

[0033] In the manufacture of a substrate for mask blanks, before the local processing step, a raw material substrate for the mask blank is prepared from a glass ingot. The raw material substrate for the mask blank can usually be prepared by first cutting out a predetermined shape from the glass ingot for external shape processing, and then polishing the main surface and the end surface. The polishing can be carried out in several stages such as rough polishing, precision polishing, and ultra-precision polishing. This polishing can be carried out using an abrasive cloth and an abrasive. The abrasive is not particularly limited, and for example, an aqueous dispersion of cerium oxide with an average primary particle diameter of 10 to 100 nm, an aqueous dispersion of silica nanoparticles with an average primary particle diameter of 10 to 100 nm (colloidal silica aqueous dispersion), etc. can be used.

[0034] The shape of the surface obtained only by local processing is not flat and usually has a shape (generally, a convex shape (a shape with the central part of the main surface protruding) or a concave shape (a shape with the central part of the main surface recessed)) that cancels out the change in the shape of the surface in the subsequent finish polishing. Even if the flatness of the surface obtained only by local processing is evaluated, it will only result in an evaluation that deviates from the evaluation result of the shape of the main surface of the finally obtained substrate for mask blanks. After local processing, the change in the shape of the main surface that occurs during finish polishing performed under predetermined polishing conditions 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 to predict the shape of the surface after finish polishing performed under predetermined polishing conditions, it is possible to evaluate the shape of the surface obtained after finish polishing and evaluate the quality of the shape of the main surface obtained by finish polishing at the stage of local processing before finish polishing. Note that the local processing step can be repeated until a predetermined shape is obtained.

[0035] In the production of the substrate for mask blanks of the present invention, the local processing step includes (A) a step of grasping the change in the shape of the surface before and after the finish polishing step of the main surface; (B) a step of locally processing the main surface; (C) a step of measuring the shape of the main surface after the step (B) as the shape of the surface before the finish 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 finish polishing step obtained in the step (C) to predict the shape of the main surface after the finish polishing step; and (E) a step of evaluating whether or not the shape of the main surface predicted in the step (D) has a predetermined flatness. It is preferably included.

[0036] In step (A), the change in the shape of the main surface before and after the finish polishing process (the change in the shape of the surface after the finish polishing process with respect to the surface after the local processing process) is grasped. This change can be grasped, for example, by selecting another substrate for a mask blank having a similar shape of the main surface from the substrate for a mask blank on which local processing has been performed, and from the shape of the main surface obtained by performing predetermined finish polishing on this other substrate for a mask blank. Further, the grasping of this change in shape can also be carried out by simulation. In this case, as the other substrate for a mask blank, those having a middle concave shape in which the shape of the main surface is the target shape in the local processing step are preferable, and those having a flatness of the main surface of less than 300 nm are also preferable. Note that step (A) may be after step (B) or after step (C).

[0037] In step (B), local processing of the main surface is performed. The local processing sets predetermined processing conditions in the local processing so that the main surface has a predetermined shape in consideration of the shape of the main surface before and after the local processing and the change in the shape of the surface after the finish polishing process. Specifically, for example, when the shape changes to convex by finish polishing, considering this change, the 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 by finish polishing, considering this change, the main surface preferably has a shape that cancels out this change (for example, a shallow concave shape or a convex shape). Before the local processing, if necessary, the shape of the main surface is appropriately measured. There are no particular restrictions on this measurement, but for example, a laser interferometer can be used.

[0038] In local processing, a process is performed to selectively remove relatively convex portions from the main surface of the substrate for mask blanks. The local processing can be carried out by polishing using a polishing cloth and an abrasive. The abrasive is not particularly limited, and for example, an aqueous dispersion of cerium oxide with an average primary particle size of 10 to 100 nm, an aqueous dispersion of silica nanoparticles with an average primary particle size of 10 to 100 nm (colloidal silica aqueous dispersion), etc. can be used. Also, for local polishing, methods such as Magneto Rheological Finishing (MRF) can be applied.

[0039] In step (C), after step (B), that is, the shape of the main surface after actual local processing is measured as the shape of the surface before the finishing polishing step. For this measurement, although not particularly limited, for example, a laser interferometer can be used.

[0040] In step (D), based on the shape of the main surface obtained in step (C), the change in the shape of the main surface grasped in step (A) is applied to predict the shape of the main surface after the finishing polishing step. The change in the shape of the main surface grasped in step (A) is selected according to the shape of the main surface after local processing obtained in step (C). Here, for example, when the shape of the main surface after the local processing step of the main surface is S1 and the change in the shape of the main surface when a predetermined finishing polishing is performed is ΔS, the following formula S1 + ΔS = S2 is used to predict the shape of the main surface (S2) after the finishing polishing step.

[0041] In step (E), it is evaluated whether the shape of the main surface predicted in step (D) has a predetermined flatness. As this evaluation method, a method of measuring the shape of the main surface and evaluating a predetermined value calculated from the measured shape or a predetermined value obtained by mathematically processing the measured shape can be used.

[0042] (E) As the shape having flatness in the process, for example, when a range of 132 mm × 132 mm square centered at the intersection of the diagonals of the main surface is set as the calculation area, on the substrate surface of the calculation area of at least one of the first main surface and the second main surface, the flatness based on the least-squares plane of the substrate surface of the calculation area is 100 nm or less, preferably 80 nm or less, more preferably 70 nm or less, and a shape can be applied.

[0043] Also, as the shape having flatness in the (E) process, when a range of 132 mm × 132 mm square centered at the intersection of the diagonals of the main surface is set as the calculation area, on the substrate surface of the calculation area of at least one of the first main surface and the second main surface, the difference between the maximum value and the minimum value of the height of the short-wavelength component, specifically, when a smoothing process is performed on the substrate surface of the calculation area, the difference between the shape of the substrate surface before the smoothing process and the shape after the smoothing process, the difference (PV) between the maximum value and the minimum value of the height of the calculated surface is 20 nm or less, preferably 18 nm or less, more preferably 15 nm or less, still more preferably 10 nm or less, and a shape can also be applied. This height standard can be the least-squares plane of the main surface of the calculation area (that is, the main surface before the smoothing process). The smoothing process is as described above, and a Gaussian filter, particularly, a smoothing process by a Gaussian filter (10 mm × 10 mm) is preferable.

[0044] Also, as the shape having flatness in the (E) process, in any range of 1 mm × 1 mm square within the calculation area of at least one of the first main surface and the second main surface, the difference (LS) between the maximum value and the minimum value of the height based on the least-squares plane is, in any position within the calculation area (regardless of where the arbitrary range of 1 mm × 1 mm square is set within the calculation area), 15 nm or less (the maximum LS is 15 nm or less), preferably 12 nm or less (the maximum LS is 12 nm or less), more preferably 10 nm or less (the maximum LS is 10 nm or less), and a shape can also be applied. This height standard can be the least-squares plane of the main surface of the calculation area (that is, the main surface before the smoothing process).

[0045] Also, as a shape having flatness in the (E) step, in any range of at least one 6 mm × 6 mm square set within the calculation region of at least one of the first main surface and the second main surface, when the surface shape is measured with higher accuracy than a 10-μm pitch, the difference (PVXY) between the maximum value and the minimum value of the total differential map obtained by totally differentiating the height map of the surface shape in that region is 0.1 nm / μm or less, preferably 0.085 nm / μm or less, more preferably 0.07 nm / μm or less. A shape that satisfies these conditions can also be applied. PVXY can be obtained by the aforementioned (1) to (5). Also, it is preferable that the range of the 6 mm × 6 mm square at the center of the calculation region is within the above range. Furthermore, it is more preferable that in any part of the calculation region (regardless of where the arbitrary range of 6 mm × 6 mm square is set within the calculation region), it is within the above range (the maximum PVXY is within the above range).

[0046] In the (E) step, when the shape of the main surface predicted in the (D) step is a shape having a predetermined flatness, the finishing polishing step can be carried out. On the other hand, in the (E) step, when the shape of the main surface predicted in the (D) step is not a shape having a predetermined flatness, the local processing step, specifically, the local processing step including steps (A) to (E) can be carried out again, and the local processing step, specifically, the local processing step including steps (A) to (E) can be repeated until the shape of the main surface predicted in the (D) step becomes a shape having a predetermined flatness.

[0047] The defect level of the surface obtained only by local processing may not be sufficient, especially for substrates for mask blanks for state-of-the-art products. In the manufacture of substrates for mask blanks, generally, a finishing polishing step is carried out following the local processing step. In the method for manufacturing a substrate for a mask blank of the present invention, a finishing polishing step following the local processing step is also carried out. This finishing polishing step (F) A polishing step for reducing the short-wavelength component of the main surface is preferably included.

[0048] In the (F) process, the sharp surface shape components (short wavelength components) in the surface shape generated in the local processing steps up to the (E) process are reduced (the amplitude of the wavefront is attenuated). Generally, in the polishing before the local processing steps, a method of polishing the entire surface of the substrate simultaneously is adopted, and the surface shape cannot be finely adjusted. In the local processing steps, by integrating the processing of minute regions, the surface shape can be finely adjusted over the entire substrate. However, since this process is a continuation of local processing, short wavelength components derived from the processing pitch may be generated. Therefore, even if the flatness becomes sufficient by local processing, in many cases, the short wavelength components increase after local processing.

[0049] The polishing for reducing the short wavelength components in the (F) process is preferably polishing using a hard polishing cloth. In the case of a soft polishing cloth, the polishing cloth is likely to deform along the fine irregularities on the substrate surface, and an equal load is applied to the concave and convex portions. Therefore, there is no difference in the polishing removal amount, and as a result, the convex portions remain. On the other hand, in the case of a hard polishing cloth, the polishing cloth is less likely to deform along the fine irregularities on the substrate surface, and the load on the convex portions increases. Therefore, it is considered that the removal amount of the convex portions increases and as a result, the convex portions decrease. Thus, a hard polishing cloth is effective for polishing to reduce short wavelength components.

[0050] As the hard abrasive cloth, it is preferable to use a two-layer structure of a NAP layer and a base layer (for example, a hard abrasive cloth of the suede type). As the material of the NAP layer, a material containing an ester-based, ether-based, or polycarbonate-based urethane resin is preferable. The average surface opening diameter of the NAP layer is preferably 10 μm or more, preferably 50 μm or less, and more preferably 30 μm or less. Also, the thickness of the NAP layer is preferably 400 μm or more, more preferably 450 μm or more, still more preferably 500 μm or more, and preferably 650 μm or less. On the other hand, the base layer is a part that does not directly contact the substrate, and the base layer preferably has a high hardness such that short-wavelength components derived from the surface plate are less likely to be transferred to the surface to be polished. The material of the base layer is not particularly limited, and examples thereof include PET (polyethylene terephthalate). In the case of a PET base layer, those with a base layer thickness of 0.1 to 0.2 mm are preferably used from the viewpoints of stretchability and heat dissipation. The hardness of the abrasive cloth is preferably 40 or more, more preferably 50 or more, and still more preferably 60 or more in terms of Shore A hardness. Note that the abrasive cloth can be appropriately selected by converting it to different rubber hardness indicators such as Shore E and Asker C.

[0051] Also, the polishing in the (F) step can be carried out by causing the abrasive cloth to carry a polishing slurry (colloidal silica aqueous dispersion) mainly composed of colloidal silica having an average primary particle diameter of 10 to 100 nm. As the polishing method, batch-type double-sided polishing is common, but single-wafer polishing or single-sided polishing may also be used. The (F) step can be carried out with a polishing pressure of 50 to 200 gf / cm 2 (4.9 to 19.6 kPa), but this can be appropriately set depending on the polishing method and processing conditions and is not particularly limited.

[0052] Also, the finish polishing step may further include, after carrying out the polishing using the hard abrasive cloth in the (F) step, (G) a polishing step using a soft abrasive cloth being included.

[0053] (F) In the process, it is preferable to use a hard polishing cloth to reduce the short-wavelength components on the substrate surface. However, when using a hard polishing cloth, it may be difficult to achieve the quality levels required for state-of-the-art products in terms of defects and surface roughness. Therefore, if necessary, as step (G), it is preferable to improve the surface quality by polishing using a soft polishing cloth.

[0054] (G) In the polishing in step (G), for example, it can be carried out by double-sided simultaneous polishing using a relatively soft polishing cloth and a polishing slurry (colloidal silica aqueous dispersion) composed of fine colloidal silica. The polishing in step (G) can use, for example, a soft polishing cloth with a Shore A hardness of less than 40 (e.g., a Swedish-type soft polishing cloth) and an aqueous dispersion of colloidal silica with an average primary particle diameter of 10 to 100 nm. Note that the hardness can be appropriately converted to different rubber hardness indicators such as Shore E and Asker C to select the polishing cloth. The polishing conditions can be appropriately selected according to conventional methods and are not particularly limited.

[0055] The shape of the main surface of the substrate for mask blanks finally obtained after the finishing polishing process can also be appropriately measured, and this measurement is not particularly limited either. For example, a laser interferometer can be used. Furthermore, from the results, the flatness of the substrate for mask blanks finally obtained after finishing polishing can also be evaluated.

[0056] According to the method for manufacturing a substrate for mask blanks of the present invention, the flatness of the exposure mask after wavefront correction using the exposure mask obtained from the substrate for mask blanks via the mask blank, in other words, the flatness of the exposure mask during exposure using the exposure mask, can be predicted with extremely high accuracy at the stage of the substrate for mask blanks. In this case, the shape (S2) of the main surface after the finishing polishing process predicted in step (D) can be made the shape of the substrate for mask blanks finally obtained after finishing polishing. Furthermore, the mask blank of the present invention substrateAccording to the manufacturing method, based on this prediction, a substrate for mask blanks with good flatness can be manufactured.

Example

[0057] Hereinafter, the present invention will be specifically described with reference to examples, but the present invention is not limited to the following examples.

[0058] [Examples 1 and 2] Nine glass substrates (size of the first main surface and the second main surface: 152 mm × 152 mm square, thickness 6.35 mm) formed of SiO2 and TiO2 (TiO2 concentration: 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 further, rough polishing treatment and precision polishing were performed with a polishing liquid containing cerium oxide abrasive grains. Then, in Example 1, five glass substrates (substrates 1-1 to 1-5), and in Example 2, four glass substrates (substrates 2-1 to 2-4) were set on the carrier of a double-sided polishing apparatus to which a Swedish type soft polishing cloth was applied, and the first main surface and the second main surface were ultra-precision polished using a polishing liquid containing colloidal silica abrasive grains. After ultra-precision polishing, the substrates were 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 apparatus (UltraFlat, manufactured by Tropel).

[0059] Next, a local processing step was performed. First, based on the shape of the obtained main surface, the processing conditions for local processing were determined, and based on the determined processing conditions, the first main surface and the second main surface of the glass substrate were locally processed with a local processing apparatus ((B) step). As the local processing apparatus, the local processing apparatus described in Japanese Patent Application Laid-Open No. 2010-194705 (Patent Document 3) was used. The local processing using this apparatus polishes the entire surface of the substrate while controlling the moving speed of a fine polishing tool, moving the polishing tool slowly at a relatively convex portion and moving the polishing tool quickly at a relatively concave portion, thereby obtaining a target shape. As the processing tool of the local processing apparatus, a wool felt buff was used, and as the polishing slurry, silica nanoparticles (AJ-3540, manufactured by Nissan Chemical Industries, Ltd.) mixed with a small amount of defoaming agent (Shin-Etsu Silicone KS-537, manufactured by Shin-Etsu Chemical Co., Ltd.) was used. The glass substrate after local processing was washed with a cleaning liquid containing KOH to remove the silica nanoparticles, and after drying, the shapes of the first main surface and the second main surface were measured with a surface shape measuring apparatus (UltraFlat, manufactured by Tropel) ((C) step).

[0060] Here, in order to grasp the change in the shape of the main surface after finish polishing with respect to the surface after local processing, another glass substrate was used to perform the same local processing up to the same point, and further, finish polishing similar to the finish polishing described later was performed ((A) step). Then, for nine glass substrates (substrates 1-1 to 2-4) after local processing, the change in the shape of the main surface that was grasped was applied to the shape of the main surface of the glass substrate after local processing to predict the shape of the surface after finish polishing ((D) step). The shape of the surface of the glass substrate after local processing and the predicted shape of the surface after finish polishing were evaluated as the flatness based on the least-squares plane of the substrate surface in the calculation region, which is a range of 132 mm × 132 mm square centered on the intersection of the diagonals of the main surface of the glass substrate ((E) step). As a result of predicting the shape of the surface after finish polishing, in the first local processing step, in any case, the predicted flatness of the surface after finish polishing exceeded 100 nm, so it was evaluated that the shape did not have a predetermined flatness, and as the second local processing step, steps (B), (C), (A), (D), and (E) were performed again.

[0061] In the first local processing step, the shapes of the first major surface and the second major surface after the predicted finish polishing step are both convex shapes, and it is preferable that the shape of the major surface after local processing is a concave shape. Therefore, in Example 1 (substrates 1-1 to 1-5), in step (B) of the second local processing step, only the first major surface was locally processed so that the shape of the major surface after local processing would be a concave shape. On the other hand, in Example 2 (substrates 2-1 to 2-4), both surfaces were locally processed so that both the first major surface and the second major surface would be concave shapes. Table 1 shows the predicted surface shapes of each glass substrate after finish polishing in terms of flatness.

[0062]

Table 1

[0063] As a result, for all of the glass substrates, since the flatness of the shape of the major surface after predicted finish polishing for the surface after the second local processing was 100 nm or less, it was evaluated as having a shape with a predetermined flatness, and a finish polishing step was performed on the glass substrates after the second local processing step.

[0064] In order to reduce the short-wavelength component of the major surface of the glass substrate, the glass substrate was set on a carrier of a polishing apparatus to which a two-layered structure suede-type hard polishing cloth formed with an ester-based urethane resin for the NAP layer and PET for the base layer was applied, polished using a colloidal silica polishing liquid, and after polishing, washed with a cleaning liquid containing KOH to remove the colloidal silica. After drying, the shape of the major surface was measured with a surface shape measuring device (UltraFlat, manufactured by Tropel). The shape of the surface after finish polishing was evaluated as the flatness based on the least-squares plane of the calculated area of the surface after finish polishing in a calculated area that is a range of 132 mm × 132 mm square centered on the intersection of the diagonals of the major surface of the glass substrate.

[0065] In Example 1 (substrates 1-1 to 1-5), in addition to the flatness of the first main surface, the shape of the substrate surface before the smoothing process by the Gaussian filter (10 mm × 10 mm) in the calculation region of the first main surface, and the difference from the shape after the smoothing process, the difference (PV) between the maximum and minimum values of the height with respect to the least-squares plane of the calculation region of the surface after finish polishing, and the difference (LS) between the maximum and minimum values of the height with respect to the least-squares plane of the calculation region of the surface after finish polishing in an arbitrary range of a 1 mm × 1 mm square within the calculation region of the first main surface were evaluated, and the maximum value of LS was obtained. Also, in the range of the central 6 mm × 6 mm square within the calculation region of the first main surface, (1) The surface shape was measured with a finer accuracy than a 10-μm pitch within the range of a 6 mm × 6 mm square to create a height map, (2) An x partial derivative map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the x direction was created, (3) A y partial derivative map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the y direction was created, (4) A total derivative map was created from the x partial derivative map and the y partial derivative map, (5) The difference (PVXY) between the maximum and minimum values of the total derivative map was calculated and PVXY was evaluated, and the maximum value of PVXY was obtained. For the measurement of this surface shape, a 3D optical surface profiler (Nexview, manufactured by Zygo Corporation) was used. The results are shown in Table 2.

[0066] [Table 2]

[0067] In Example 2 (substrates 2-1 to 2-4), in addition to the flatness of the first main surface and the second main surface, the PV of the first main surface and the second main surface, and the LS of the first main surface and the second main surface were evaluated, and the maximum value of LS was obtained. The results are shown in Table 3.

[0068] [Table 3]

[0069] [Comparative Example 1] Five glass substrates (size of the first main surface and the second main surface: 152 mm × 152 mm square, thickness 6.35 mm) formed of SiO2 and TiO2 (TiO2 concentration: about 7% by mass) were prepared. In the same manner as in Example 1, rough polishing treatment and precision polishing were performed. Then, the five glass substrates (substrates C1-1 to C1-5) were ultra-precision polished in the same manner as in Example 1. After ultra-precision polishing, the substrates were washed with a cleaning solution 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).

[0070] Next, the local processing step was carried out in the same manner as in Example 1. As a result of performing step (E) to predict the shape of the surface after finish polishing, in the first local processing step, in all cases, the predicted flatness of the surface after finish polishing exceeded 100 nm, so it was evaluated that the shape did not have a predetermined flatness. As the second local processing step, steps (B), (C), (A), (D), and (E) were carried out again.

[0071] Since the shapes of the first main surface and the second main surface after the finish polishing step predicted in the first local processing step were both convex shapes, and it is preferable that the shape of the main surface after local processing is a concave shape, in step (B) of the second local processing step, only the first main surface was locally processed so that the shape of the main surface after local processing would be a concave shape. The predicted flatness of the surface after finish polishing of each glass substrate is shown in Table 4 as the flatness.

[0072] [Table 4]

[0073] As a result, for all of the glass substrates, since the flatness of the shape of the main surface after finish polishing predicted for the surface after the second local processing was 100 nm or less, it was evaluated as having a predetermined flatness, and a finish polishing step was carried out on the glass substrates after the second local processing step.

[0074] The glass substrate was set on the carrier of a polishing apparatus to which a Swedish type soft polishing cloth was applied, polished using a colloidal silica polishing liquid, and after polishing, washed with a cleaning liquid containing KOH to remove the colloidal silica. After drying, in the same manner as in Example 1, the flatness, PV, and LS of the first main surface were evaluated, and the maximum value of LS was determined. Also, in the same manner as in Example 1, PVXY of the first main surface was evaluated, and the maximum value of PVXY was determined. The results are shown in Table 5.

[0075]

Table 5

[0076] From the above results, it can be seen that by the manufacturing method of the present invention, a substrate for a mask blank having a flatness of 100 nm or less and a PV of 20 nm or less after finish polishing, and further a substrate for a mask blank having a maximum value of LS of 15 nm or less and a maximum value of PVXY of 0.1 nm / μm or less can be manufactured. Such a substrate for a mask blank is a substrate for a mask blank in which the short wavelength component of the main surface is reduced, and by using an exposure mask using such a substrate for a mask blank, high-quality exposure can be realized as an exposure mask for state-of-the-art products.

Claims

1. A substrate for a mask blank having two main surfaces, a first main surface and a second main surface, in the shape of a 152 mm × 152 mm square, and having a thickness of 6.35 mm, In each of the first main surface and the second main surface, when a range of 132 mm × 132 mm square centered on the intersection of the diagonals is defined as a calculation area, On the substrate surface of at least one of the calculation areas of the first main surface and the second main surface, the flatness with respect to the least squares plane of the substrate surface of the calculation area is 100 nm or less, and the difference between the shape of the substrate surface before the smoothing process by a Gaussian filter (10 mm × 10 mm) targeting a 10 mm × 10 mm area around the measurement point and the shape after the smoothing process, represented by the calculated surface with respect to the least squares plane, has a difference (PV) in height between the maximum value and the minimum value of 20 nm or less. In at least one arbitrarily defined range of 6 mm × 6 mm square set within at least one of the calculation areas of the first main surface and the second main surface, (1) Measure the surface shape with a finer accuracy than a 10 µm pitch within the range of 6 mm × 6 mm square to create a height map, (2) Create an x partial differential map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the x direction, (3) Create a y partial differential map obtained by partially differentiating the height map within the range of 6 mm × 6 mm in the y direction, (4) Create a total differential map from the x partial differential map and the y partial differential map, (5) Calculate the difference (PVXY) between the maximum value and the minimum value of the total differential map, when the PVXY is 0.1 nm / µm or less anywhere within the calculation area. A substrate for a mask blank, characterized by the above.

2. In any 1 mm × 1 mm square range within the calculation region on at least one of the first main surface and the second main surface, the difference (LS) between the maximum value and the minimum value of the height with respect to the least-squares plane is 15 nm or less anywhere within the calculation region. The substrate for a mask blank according to claim 1, characterized in that.

3. The Gaussian filter (10 mm × 10 mm) uses a Gaussian distribution function so that the weight becomes smaller as it gets farther in the region of 10 mm × 10 mm around the measurement point, in the following formula f(x, y) = 1 / (2πσ2) exp(−(x2 + y2) / (2σ2)) Based on this, it is a filter that calculates a rate. The substrate for a mask blank according to claim 1 or 2, characterized in that.

4. A method for manufacturing the substrate for a mask blank according to claim 1, comprising A local processing step for at least one 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 main surface, (B) A step of locally processing the main surface, (C) A step of measuring the shape of the 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 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 main surface predicted in the step (D) has a predetermined flatness including, The finishing polishing step is (F) A polishing step of reducing the short-wavelength component of the main surface including A method for manufacturing a substrate for a mask blank, characterized in that.

5. The manufacturing method according to claim 4, characterized in that the polishing for reducing the short-wavelength component of the main surface in the (F) step is polishing using a hard polishing cloth.

6. The shape having the predetermined flatness in the (E) step is when a range of 132 mm × 132 mm square centered on the intersection of the diagonals of the main surface is set as the calculation region, a shape in which the flatness based on the least-squares plane of the substrate surface in the calculation region of at least one of the first main surface and the second main surface is 100 nm or less. The manufacturing method according to claim 4 or 5, characterized in that it is as described above.

7. The shape having the predetermined flatness in the (E) step is when a range of 132 mm × 132 mm square centered on the intersection of the diagonals of the main surface is set as the calculation region, a shape in which the difference (PV) between the highest value and the lowest value of the height based on the least-squares plane of the calculated surface, which is represented by the difference between the shape of the substrate surface before the smoothing process by the Gaussian filter (10 mm × 10 mm) and the shape after the smoothing process, on the substrate surface in the calculation region of at least one of the first main surface and the second main surface is 20 nm or less. The manufacturing method according to claim 6, characterized in that it is as described above.

8. The shape having the predetermined flatness in the (E) step is in an arbitrary range of 1 mm × 1 mm square within the calculation region of at least one of the first main surface and the second main surface, the difference (LS) between the highest value and the lowest value of the height based on the least-squares plane is 15 nm or less in any part within the calculation region. The manufacturing method according to claim 7, characterized in that it is as described above.

9. The shape having the predetermined flatness in the (E) step is in an arbitrary range of at least one 6 mm × 6 mm square set within the calculation region of at least one of the first main surface and the second main surface, (1) Measure the surface shape within the range of a 6 mm × 6 mm angle with a precision finer than a 10-μm pitch to create a height map, (2) Create an x partial derivative map obtained by partially differentiating the height map within the range of the 6 mm × 6 mm in the x direction, (3) Create a y partial derivative map obtained by partially differentiating the height map within the range of the 6 mm × 6 mm in the y direction, (4) Create a total derivative map from the x partial derivative map and the y partial derivative map, (5) Calculate the difference (PVXY) between the maximum value and the minimum value of the total derivative map When, The PVXY is a shape that is 0.1 nm / μm or less at any position within the calculation region The manufacturing method according to claim 7, characterized in that it is so.

10. In the step (E), when the shape of the main surface predicted in the step (D) is not a shape having the predetermined flatness, the local processing step is performed again. The manufacturing method according to claim 4 or 5, characterized in that it is so.

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