Glass substrate and mask blank for EUV lithography

Abstract

Provided is a glass substrate that reduces errors in the correction of thermal deformation.　This glass substrate has a rectangular main surface (MS1). When the main surface is divided into nine equal parts in a direction perpendicular to a first side (S1) and divided into nine equal parts in a direction perpendicular to a second side (S2), thereby dividing the main surface into a group of 81 rectangular regions (A11-A99), the rectangular regions, in the group of 81 rectangular regions, the centers of which are located on a diagonal line of the main surface passing through a first vertex (P1) that is an intersection point of the first side and the second side, satisfy expression (1A), where TZ11、TZ22、TZ33、TZ44、TZ55、TZ66、TZ77、TZ88、and TZ99 are zero crossover temperatures in ˚C, at which the thermal expansion coefficient of the glass substrate becomes 0 ppb / K, starting from the closest to the first vertex. (1A): (TZ11+TZ99)-(TZ22+TZ88)＜0.00

Description

Glass substrates and mask blanks for EUV lithography

[0001] This invention relates to glass substrates. Furthermore, this invention also relates to mask blanks for EUV (Extreme Ultra Violet) lithography.

[0002] In recent years, EUV lithography, which uses EUV light with a central wavelength of around 13.5 nm as a light source, has been investigated for further miniaturization of semiconductor devices. Due to the characteristics of EUV light, EUV lithography employs a reflective optical system and a reflective mask. The reflective mask used in EUV lithography has a mask pattern formed on a glass substrate, with regions that reflect EUV light and regions where EUV light reflection is suppressed. This mask pattern is transferred onto a wafer as a resist pattern through an exposure apparatus, and subsequent processing is carried out.

[0003] Reflective masks used in EUV lithography are obtained by processing a reflective mask blank, which is the original plate. Glass substrates with a low coefficient of thermal expansion are often used as the substrate for the reflective mask blank. For example, in Patent Document 1, SiO ２ -TiO ２ It has been disclosed that a reflective mask blank was obtained using a glass substrate.

[0004] International Publication No. 2019 / 225736

[0005] In EUV lithography, corrections were sometimes made to account for the deformation of the mask blank due to the heat generated during EUV exposure (thermal deformation) in order to form the desired resist pattern. The present inventors investigated obtaining a mask blank using a glass substrate as described in Patent Document 1 and performing the above correction, and found that errors sometimes occurred after the correction. With the recent demand for miniaturization of patterns, it has been required to reduce the above-mentioned errors after correction.

[0006] The present invention has been made in view of the above problems, and an object thereof is to provide a glass substrate with a small error when correcting thermal deformation. Another object of the present invention is to provide a mask blank for EUV lithography.

[0007] As a result of intensive studies on the above problems, the present inventors have found that by adjusting the distribution of the zero crossover temperature at which the coefficient of thermal expansion becomes 0 ppb / K, the error when correcting thermal deformation is reduced, leading to the completion of the present invention.

[0008] That is, the inventors have found that the above problems can be solved by the following configuration. [1] A glass substrate having a rectangular main surface, wherein the main surface is divided into nine equal parts in a direction perpendicular to a first side, which is one side of the main surface, and the main surface is divided into nine equal parts in a direction perpendicular to a second side, which is a side adjacent to the first side, so that the main surface is partitioned into a rectangular region group composed of 81 rectangular regions. Among the rectangular region group, the zero crossover temperature at which the coefficient of thermal expansion of the glass substrate in the rectangular region whose center is located on the diagonal of the main surface passing through a first vertex, which is the intersection of the first side and the second side, becomes 0 ppb / K is, in units of °C, in order from the side closer to the first vertex, T Ｚ１１ , T Ｚ２２ , T Ｚ３３ , T Ｚ４４ , T Ｚ５５ , T Ｚ６６ , T Ｚ７７ , T Ｚ８８ , and, T Ｚ９９ . When it is set as, a glass substrate that satisfies the following formula (1A). (1A) (T Ｚ１１ + T Ｚ９９ ) - (T Ｚ２２ + T Ｚ８８ ) < 0.00 [2] The glass substrate according to [1], which satisfies the following formula (2A). (2A) (T Ｚ２２ + T Ｚ８８ ) - (T Ｚ３３ + T Ｚ７７ ) > -1.00 [3] The glass substrate according to [1] or [2], which satisfies the following formula (3A). (3A) (T Ｚ２２ + T Ｚ８８ ) - (T Ｚ４４ + T Ｚ６６) > 0.00 [4] A glass substrate described in any one of [1] to [3] that satisfies the following formula (4A). (4A) (T Ｚ２２ +T Ｚ８８ ) - 2 × T Ｚ５５ >0.00 [5] A glass substrate according to any one of [1] to [4] that satisfies the following formulas (2A), (5A), and (6A). (2A) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ３３ +T Ｚ７７ )>-1.00 (5A) (T Ｚ３３ +T Ｚ７７ )-(T Ｚ４４ +T Ｚ６６ )>0.00 (6A) (T Ｚ４４ +T Ｚ６６ ) - 2 × T Ｚ５５ >0.00 [6] A glass substrate according to any one of [1] to [5], wherein the distribution of the zero crossover temperature in the above rectangular region is point-symmetric with respect to the intersection of the diagonals of the main surface. [7] Among the group of above rectangular regions, the zero crossover temperature in the rectangular region whose center is located on the diagonal of the main surface passing through the fourth vertex, which is the intersection of the fourth side opposite the second side and the first side, is determined in order from the one closest to the fourth vertex, T Ｚ１９ , T Ｚ２８ , T Ｚ３７ , T Ｚ４６ , T Ｚ５５ , T Ｚ６４ , T Ｚ７３ , T Ｚ８２ , and, T Ｚ９１ In this case, a glass substrate described in any one of [1] to [6] that satisfies the following requirements 1, 2, 3, and 4. Requirement 1: The above zero crossover temperature T Ｚ１１ , T Ｚ１９ , T Ｚ９１ , and, T Ｚ９９ The maximum temperature difference within the range is 2.00°C or less. Requirement 2: The above zero crossover temperature T Ｚ２２ , T Ｚ２８ , T Ｚ８２ , and, T Ｚ８８ The maximum temperature difference within the range is 2.00°C or less. Requirement 3: The above zero crossover temperature TＺ３３ , T Ｚ３７ , T Ｚ７３ , and, T Ｚ７７ The maximum temperature difference within the range is 2.00°C or less. Requirement 4: The above zero crossover temperature T Ｚ４４ , T Ｚ４６ , T Ｚ６４ , and, T Ｚ６６ The maximum temperature difference within is 2.00°C or less. [8] Among the group of rectangular regions, the zero crossover temperature in the rectangular region whose center is located on the diagonal of the main plane passing through the fourth vertex, which is the intersection point of the fourth side opposite the second side and the first side, is given in units of °C, in order from the one closest to the fourth vertex, T Ｚ１９ , T Ｚ２８ , T Ｚ３７ , T Ｚ４６ , T Ｚ５５ , T Ｚ６４ , T Ｚ７３ , T Ｚ８２ , and, T Ｚ９１ In this case, a glass substrate described in any one of [1] to [7] that satisfies the following formula (1B). (1B) (T Ｚ１９ +T Ｚ９１ )-(T Ｚ２８ +T Ｚ８２ ) < 0.00 [9] A glass substrate according to any one of [1] to [8], wherein the maximum temperature difference of the zero crossover temperature in each of the rectangular regions of the group of rectangular regions is 1.00°C or more.

[10] A glass substrate according to any one of [1] to [9], wherein the average value of the zero crossover temperature in each of the rectangular regions of the group of rectangular regions is 20.00°C or more.

[11] A mask blank for EUV lithography having a glass substrate according to any one of [1] to

[10] .

[0009] According to the present invention, it is possible to provide a glass substrate that reduces errors when correcting for thermal deformation. Furthermore, according to the present invention, it is also possible to provide a mask blank for EUV lithography.

[0010] This is a perspective view of the glass substrate of the present invention. Figure 1 is a top view of the glass substrate as seen from the direction normal to the first main surface. The substrate is rotated while SiO ２ -TiO ２It is a cross-sectional view showing the positional relationship when depositing glass microparticles. It is a perspective view showing an example of a multiple-tube burner. It is a top view when viewed from the flame radiation axis side of the multiple-tube burner used when obtaining the glass substrate of the example.

[0011] Hereinafter, the present invention will be described in detail. The description of the constituent elements described below may be made based on typical embodiments of the present invention, but the present invention is not limited to such embodiments.

[0012] <Glass substrate> [Formula regarding zero-crossing temperature] The glass substrate of the present invention is a glass substrate having a rectangular main surface. A perspective view of the glass substrate of the present invention is shown in FIG. 1. The glass substrate 10 shown in FIG. 1 has opposing first main surface MS1 and second main surface MS2. The first main surface MS1 has a first side S1 and a second side S2 which is a side adjacent to the first side S1. The first main surface MS1 and the second main surface MS2 are each rectangular. Further, the material constituting the glass substrate 10 shown in FIG. 1 is silicon dioxide (SiO ２ ) and titanium dioxide (TiO ２ ) containing SiO ２ - TiO <了 ２ - based glass.

[0013] The glass substrate of the present invention satisfies the following formula (1A). (1A) (T Ｚ１１ + T Ｚ９９ ) - (T Ｚ２２ + T [[ID=了4]] Ｚ８８ ) < 0.00 In the above formula (1A), the units of the above T Ｚ８８ [[ID=了7]]、the above T Ｚ２２ 、the above T Ｚ８８ 、and the above T Ｚ９９ are each °C. In the above formula (1A), the unit of the value on the right side is °C. Hereinafter, the above T Ｚ１１ 、the above T Ｚ２２ 、the above T Ｚ８８ 、and the above T Ｚ９９ [ will be described.

[0014] First, divide the rectangular main surface (the first main surface MS1) of the glass substrate (glass substrate 10) of the present invention into nine equal parts in a direction perpendicular to the first side (the first side S1) which is one side of the rectangle, and divide the rectangular main surface into nine equal parts in a direction perpendicular to the second side (the second side S2) which is the side adjacent to the first side, thereby dividing the main surface into a group of rectangular regions composed of 81 rectangular regions. Among the group of rectangular regions, the zero crossover temperature at which the thermal expansion coefficient of the glass substrate in the rectangular region whose center is located on the diagonal line of the main surface passing through the first vertex which is the intersection of the first side and the second side becomes 0 ppb / K, in units of °C, in order from the side closer to the first vertex, T Ｚ１１ , T Ｚ２２ , T Ｚ３３ , T Ｚ４４ , T Ｚ５５ , T Ｚ６６ , T Ｚ７７ , T Ｚ８８ , and, T Ｚ９９ be set as. First, the above-mentioned rectangular regions and the group of rectangular regions composed of rectangular regions will be described while referring to the drawings. The zero crossover temperature will be described in the following section.

[0015] Figure 2 is a top view of the glass substrate 10 shown in Figure 1, viewed from the direction normal to the first main surface MS1. In Figure 2, the first main surface MS1 is rectangular, with the side on the upper side of the paper being the first side S1 and the side on the left side of the paper being the second side S2. In the first main surface MS1 shown in Figure 2, the intersection of the first side S1 and the second side S2 is defined as the first vertex P1, and the intersection of the third side S3, which is opposite to the first side S1, and the second side S2 is defined as the second vertex P2. Also in the first main surface MS1 shown in Figure 2, the intersection of the third side S3 and the fourth side S4, which is opposite to the second side S2, is defined as the third vertex P3, and the intersection of the first side S1 and the fourth side S4 is defined as the fourth vertex P4. Specifically, of the four vertices of the first principal plane MS1 shown in Figure 2, the intersection of the first edge S1 and the second edge S2 is designated as the first vertex P1, and the vertices moving counterclockwise from the first vertex P1 are designated as the second vertex P2, the third vertex P3, and the fourth vertex P4. Here, the first edge S1 is divided into nine equal parts from the first vertex P1 toward the fourth vertex P4, and eight dashed lines are drawn perpendicular to the first edge S1. Furthermore, the second edge S2 is divided into nine equal parts from the first vertex P1 toward the second vertex P2, and eight dashed lines are drawn perpendicular to the second edge S2. As a result, the first principal plane MS1 is divided into 81 rectangular regions demarcated by the dashed lines. The 81 rectangular regions are, in order of proximity to the first edge S1, rectangular region A １１ , rectangular area A １２ , rectangular area A １３ , ..., and rectangular area A １９ Let's assume that the second closest rectangular region from the first side S1 is the rectangular region A, in order of proximity to the second side S2. ２１ , rectangular area A ２２ , rectangular area A ２３ , ..., and rectangular region A ２９ Let's define it as follows: The rectangular region that is the nth closest to the first side S1 and the mth closest to the second side S2 is defined as rectangular region A. ｎｍ Therefore, among the above group of rectangular regions, the rectangular region whose center lies on the diagonal of the first principal surface MS1 passing through the intersection of the first side S1 and the second side S2 (first vertex P1) is rectangular region A. １１ , rectangular area A ２２ , rectangular area A ３３ , rectangular area A ４４ , rectangular area A５５ , rectangular area A ６６ , rectangular area A ７７ , rectangular area A ８８ , and rectangular area A ９９ That is the case.

[0016] Next, in each of the above rectangular regions, the zero crossover temperature at which the thermal expansion coefficient of the glass substrate becomes 0 ppb / K (hereinafter referred to as "T") is determined. ＺＣ It is also called ". ) measures SiO ２ -TiO ２ In glass systems, TiO ２ It is known that the thermal expansion coefficient of glass changes depending on the content of SiO. Specifically, ２ -TiO ２ TiO ２ As the content of increases, the coefficient of thermal expansion decreases, and TiO ２ It is known that when the content exceeds a certain amount, it exhibits a negative coefficient of thermal expansion. Therefore, a predetermined amount of TiO ２ SiO containing ２ -TiO ２ The glass system has a thermal expansion coefficient of 0 ppb / K. ＺＣ It has. In this specification, unless otherwise specified, the coefficient of thermal expansion refers to the linear thermal expansion coefficient at 22°C. Hereinafter, the T of the glass substrate of the present invention ＺＣ The measurement method for SiO will be explained below. ２ -TiO ２ T of a glass substrate made of a system material ＺＣ The measurement method will be explained below, but the same method can also be used for other glass substrates. ＺＣ It can measure [something].

[0017] First, in each rectangular region, TiO was analyzed using X-ray fluorescence analysis. ２ The content of TiO will be measured. The measuring device used will be a Rigaku Primus 400 X-ray fluorescence analyzer, with an X-ray irradiation spot diameter of φ10 mm. ２ When quantifying the content of TiO, the calibration curve method is used. Specifically, TiO ２ SiO2 with known concentration ２ -TiO ２Using glass, the fluorescence X-ray intensity of Ti and TiO ２ Create a calibration curve for the concentration of TiO ２ Quantify the content of [the substance].

[0018] Next, the obtained TiO ２ The thermal expansion coefficient in each rectangular region is calculated from the content of TiO. ２ This is done using a conversion formula that expresses the relationship between the content and the coefficient of thermal expansion. The above conversion formula is TiO ２ The SiO content is known. ２ -TiO ２ The thermal expansion coefficient of the glass system was measured, and TiO ２ The relationship between the content and the coefficient of thermal expansion is plotted, and the equation of the approximation curve of the above plot is obtained.

[0019] Furthermore, a sample of a predetermined size (e.g., 100 mm in length and 35 mm in width) is cut from the center of the glass substrate that has been analyzed by the above-mentioned X-ray fluorescence analysis method, and the temperature dependence of the thermal expansion coefficient is measured. For the measurement of the temperature dependence of the thermal expansion coefficient, a laser heterodyne interferometer is used to perform precise measurements in the range of 0 to 50°C. The rate of temperature change is set to 1°C / min or less. When the temperature dependence of the thermal expansion coefficient is measured, a nearly linear relationship is usually obtained within the above measurement range. From the temperature dependence of the thermal expansion coefficient, the rate of change of the thermal expansion coefficient with respect to temperature (unit: ppb / K) is calculated. ２ This yields the slope when temperature is plotted on the horizontal axis and the coefficient of thermal expansion on the vertical axis.

[0020] From the rate of change of the thermal expansion coefficient with respect to temperature obtained by the above procedure, and the thermal expansion coefficient in each of the above rectangular regions, the temperature at which the thermal expansion coefficient becomes 0 ppb / K can be calculated. Specifically, first, we assume that the temperature dependence of the thermal expansion coefficient is represented by a straight line. That is, when temperature is taken on the x-axis and the thermal expansion coefficient on the y-axis, we assume that the temperature dependence of the thermal expansion coefficient is represented by the straight line equation y = ax + b. In the above straight line equation, the rate of change of the thermal expansion coefficient is the slope (a) of the line. Also, since the above straight line equation passes through the points of the thermal expansion coefficient (value at 22°C) in each of the above rectangular regions, the intercept (b) can also be obtained from the measured value. Thus, from the above straight line equation, the temperature (value of x) T at which the thermal expansion coefficient becomes 0 ppb / K (y = 0) can be calculated. ＺＣ This is required.

[0021] Following the above procedure, T in each of the above rectangular regions ＺＣ This is what is required. In other words, by following the procedure described above, T in each rectangular region (rectangular region Amn) of the group of rectangular regions in Figure 2 is obtained. ＺＣ This is required. For example, rectangular region A in Figure 2. １１ , rectangular area A ２２ , rectangular area A ３３ , rectangular area A ４４ , rectangular area A ５５ , rectangular area A ６６ , rectangular area A ７７ , rectangular area A ８８ , and rectangular area A ９９ T in each of ＺＣ T Ｚ１１ , T Ｚ２２ , T Ｚ３３ , T Ｚ４４ , T Ｚ５５ , T Ｚ６６ , T Ｚ７７ , T Ｚ８８ , and, T Ｚ９９ This is required.

[0022] In the glass substrate of the present invention, the T in each of the above rectangular regions is determined. ＺＣ The above equation (1A) is satisfied. If equation (1A) is satisfied, the rectangular region near the edge (rectangular region A) １１ and rectangular area A ９９ ) T ＺＣHowever, the second closest rectangular region to the edge (rectangular region A) ２２ and rectangular area A ８８ ) T ＺＣ It can be said that it tends to be lower than that. When heating, T ＺＣ A lower value of tends to result in a larger coefficient of thermal expansion, and thus a larger amount of deformation during heating. However, our inventors' research has shown that making the amount of deformation during heating larger in the rectangular region near the edges reduces the error when correcting for thermal deformation. Hereafter, this reduction in error when correcting for thermal deformation will also be referred to simply as "smaller error during correction."

[0023] Furthermore, in the glass substrate of the present invention, it is also preferable that the following formula (2A) is satisfied, in that the error during correction is reduced. (2A) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ３３ +T Ｚ７７ )>-1.00 T in equation (2A) Ｚ２２ , T Ｚ８８ , T Ｚ３３ and T Ｚ７７ This can be determined using the method described above.

[0024] Furthermore, in the glass substrate of the present invention, it is also preferable that the following formula (3A) is satisfied, in that the error during correction is further reduced. (3A) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ４４ +T Ｚ６６ ) > 0.00 T in equation (3A) Ｚ２２ , T Ｚ８８ , T Ｚ４４ and T Ｚ６６ This can be determined using the method described above.

[0025] Furthermore, in the glass substrate of the present invention, it is also preferable that the following formula (4A) is satisfied, in that the error during correction is reduced. (4A) (T Ｚ２２ +T Ｚ８８ ) - 2 × T Ｚ５５ >0.00 T in formula (4A) Ｚ２２ , T Ｚ８８ and T Ｚ５５ This can be determined using the method described above.

[0026] In the glass substrate of the present invention, it is also preferable that the above formulas (2A), (3A), and (4A) are satisfied, as this reduces the error during correction.

[0027] In the glass substrate of the present invention, it is also preferable that the following formula (1A-1) is satisfied. (1A-1) (T Ｚ１１ +T Ｚ９９ )-(T Ｚ２２ +T Ｚ８８ ) < -0.50

[0028] In the glass substrate of the present invention, it is also preferable that the following formula (1A-2) is satisfied. (1A-2) (T Ｚ１１ +T Ｚ９９ )-(T Ｚ２２ +T Ｚ８８ ) < -1.00

[0029] In the glass substrate of the present invention, it is also preferable that the following formula (2A-1) is satisfied, in that the error during correction is further reduced. (2A-1) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ３３ +T Ｚ７７ ) > 0.00

[0030] In the glass substrate of the present invention, it is also preferable that the following formula (2A-2) is satisfied, in that the error during correction is further reduced. (2A-2) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ３３ +T Ｚ７７ ) > 0.30

[0031] In the glass substrate of the present invention, it is also preferable that the following formula (3A-1) is satisfied, in that the error during correction is further reduced. (3A-1) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ４４ +T Ｚ６６ ) > 1.00

[0032] In the glass substrate of the present invention, it is also preferable that the following formula (3A-2) is satisfied, in that the error during correction is further reduced. (3A-2) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ４４ +T Ｚ６６ ) > 2.00

[0033] In the glass substrate of the present invention, it is also preferable that the following formula (4A-1) is satisfied, in that the error during correction is further reduced. (4A-1) (T Ｚ２２ +T Ｚ８８ ) - 2 × T Ｚ５５ >2.00

[0034] In the glass substrate of the present invention, it is also preferable that the following formula (4A-2) is satisfied, in that the error during correction is further reduced. (4A-2) (T Ｚ２２ +T Ｚ８８ ) - 2 × T Ｚ５５ >4.00

[0035] Furthermore, in the glass substrate of the present invention, it is also preferable that one or more of the above formulas (2A), (2A-1), and (2A-2), one or more of the above formulas (3A), (3A-1), and (3A-2), and one or more of the above formulas (4A), (4A-1), and (4A-2) be satisfied, in that the error during correction is further reduced.

[0036] In the glass substrate of the present invention, it is also preferable that the following formula (1A-3) is satisfied. (1A-3) (T Ｚ１１ +T Ｚ９９ )-(T Ｚ２２ +T Ｚ８８ ) > -6.00

[0037] In the glass substrate of the present invention, it is also preferable that the following formula (1A-4) is satisfied. (1A-4) (T Ｚ１１ +T Ｚ９９ )-(T Ｚ２２ +T Ｚ８８ ) > -4.00

[0038] In the glass substrate of the present invention, it is also preferable that the following formula (2A-3) is satisfied. (2A-3) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ３３ +T Ｚ７７ ) < 4.00

[0039] In the glass substrate of the present invention, it is also preferable that the following formula (2A-4) is satisfied. (2A-4) (T Ｚ２２ +T Ｚ８８)-(T Ｚ３３ +T Ｚ７７ ) < 2.00

[0040] In the glass substrate of the present invention, it is also preferable that the following formula (3A-3) is satisfied. (3A-3) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ４４ +T Ｚ６６ ) < 7.00

[0041] In the glass substrate of the present invention, it is also preferable that the following formula (3A-4) is satisfied. (3A-4) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ４４ +T Ｚ６６ ) < 5.00

[0042] In the glass substrate of the present invention, it is also preferable that the following formula (4A-3) is satisfied. (4A-3) (T Ｚ２２ +T Ｚ８８ ) - 2 × T Ｚ５５ <12.00

[0043] In the glass substrate of the present invention, it is also preferable that the following formula (4A-4) is satisfied. (4A-4) (T Ｚ２２ +T Ｚ８８ ) - 2 × T Ｚ５５ <10.00

[0044] In the glass substrate of the present invention, it is also preferable that the following formula (5A) is satisfied, in that the error during correction is further reduced. (5A) (T Ｚ３３ +T Ｚ７７ )-(T Ｚ４４ +T Ｚ６６ ) > 0.00 T in equation (5A) Ｚ３３ , T Ｚ７７ , T Ｚ４４ and T Ｚ６６ This can be determined using the method described above.

[0045] In the glass substrate of the present invention, it is also preferable that the following formula (6A) is satisfied, in that the error during correction is reduced. (6A) (T Ｚ３３ +T Ｚ７７ ) - 2 × T Ｚ５５ >0.00 T in formula (6A) Ｚ３３ , T Ｚ７７ and TＺ５５ This can be determined using the method described above.

[0046] Furthermore, in the glass substrate of the present invention, it is also preferable that the above formulas (2A), (5A), and (6A) are satisfied, in that the error during correction is reduced.

[0047] In the glass substrate of the present invention, it is also preferable that the following formula (5A-1) is satisfied, in that the error during correction is further reduced. (5A-1) (T Ｚ３３ +T Ｚ７７ )-(T Ｚ４４ +T Ｚ６６ ) > 1.00

[0048] In the glass substrate of the present invention, it is also preferable that the following formula (5A-2) is satisfied, in that the error during correction is further reduced. (5A-2) (T Ｚ３３ +T Ｚ７７ )-(T Ｚ４４ +T Ｚ６６ ) > 2.00

[0049] In the glass substrate of the present invention, it is also preferable that the following formula (6A-1) is satisfied, in that the error during correction is further reduced. (6A-1) (T Ｚ３３ +T Ｚ７７ ) - 2 × T Ｚ５５ >0.50

[0050] In the glass substrate of the present invention, it is also preferable that the following formula (6A-2) is satisfied, in that the error during correction is further reduced. (6A-2) (T Ｚ３３ +T Ｚ７７ ) - 2 × T Ｚ５５ >1.00

[0051] Furthermore, in the glass substrate of the present invention, it is also preferable that it satisfies one or more of the above formulas (2A), (2A-1), and (2A-2), one or more of the above formulas (5A), (5A-1), and (5A-2), and one or more of the above formulas (6A), (6A-1), and (6A-2), in that the error during correction becomes smaller.

[0052] In the glass substrate of the present invention, it is also preferable that the following formula (5A-3) is satisfied. (5A-3) (TＺ３３ +T Ｚ７７ )-(T Ｚ４４ +T Ｚ６６ ) < 5.00

[0053] In the glass substrate of the present invention, it is also preferable that the following formula (6A-3) is satisfied. (6A-3) (T Ｚ３３ +T Ｚ７７ ) - 2 × T Ｚ５５ <6.00

[0054] Furthermore, according to the method described above, T in each rectangular region ＺＣ The following is required: In other words, in the group of rectangular regions mentioned above, the T in the rectangular region whose center is located on the diagonal of the principal plane passing through the fourth vertex (fourth vertex P4), which is the intersection point of the fourth side (fourth side S4) opposite the second side (second side S2) and the first side (first side S1). ＺＣ This is what is required. Specifically, in Figure 2, the rectangular region A is determined in order from closest to the fourth vertex P4. １９ , rectangular area A ２８ , rectangular area A ３７ , rectangular area A ４６ , rectangular area A ５５ , rectangular area A ６４ , rectangular area A ７３ , rectangular area A ８２ , and rectangular area A ９１ T ＺＣ Each of these can be calculated. Here, each T ＺＣ In degrees Celsius, in order from the fourth vertex closest to T Ｚ１９ , T Ｚ２８ , T Ｚ３７ , T Ｚ４６ , T Ｚ５５ , T Ｚ６４ , T Ｚ７３ , T Ｚ８２ , and, T Ｚ９１ In this case, it is also preferable that the following requirements 1, 2, 3, and 4 are met, as this reduces the error during correction. Requirement 1: The above zero crossover temperature T Ｚ１１ , T Ｚ１９ , T Ｚ９１ , and, T Ｚ９９ The maximum temperature difference within the range is 2.00°C or less. Requirement 2: The above zero crossover temperature T Ｚ２２ , TＺ２８ , T Ｚ８２ , and, T Ｚ８８ The maximum temperature difference within the range is 2.00°C or less. Requirement 3: The above zero crossover temperature T Ｚ３３ , T Ｚ３７ , T Ｚ７３ , and, T Ｚ７７ The maximum temperature difference within the range is 2.00°C or less. Requirement 4: The above zero crossover temperature T Ｚ４４ , T Ｚ４６ , T Ｚ６４ , and, T Ｚ６６ The maximum temperature difference within is 2.00°C or less. Note that in requirements 1 to 4, the maximum temperature difference refers to the four T ＺＣ This refers to the value obtained by subtracting the smallest value from the largest value among them.

[0055] The glass substrate of the present invention is also preferable to satisfy the following requirements 1-1, 2-1, 3-1, and 4-1, in that the error during correction is smaller. Requirement 1-1: The above zero crossover temperature T Ｚ１１ , T Ｚ１９ , T Ｚ９１ , and, T Ｚ９９ The maximum temperature difference within the range is 1.00°C or less. Requirement 2-1: The above zero crossover temperature T Ｚ２２ , T Ｚ２８ , T Ｚ８２ , and, T Ｚ８８ The maximum temperature difference within the range is 1.00°C or less. Requirement 3-1: The above zero crossover temperature T Ｚ３３ , T Ｚ３７ , T Ｚ７３ , and, T Ｚ７７ The maximum temperature difference within is 1.00°C or less. Requirement 4-1: The above zero crossover temperature T Ｚ４４ , T Ｚ４６ , T Ｚ６４ , and, T Ｚ６６ The maximum temperature difference within is 1.00°C or less. Note that in requirements 1-1 to 4-1, the maximum temperature difference refers to the four T ＺＣ This refers to the value obtained by subtracting the smallest value from the largest value among them.

[0056] Also, the T of the rectangular regionＺＣ It is also preferable that the distribution of is point-symmetric with respect to the intersection of the diagonals of the principal plane. ＺＣ The distribution of is point-symmetric with respect to the intersection of the diagonals of the principal plane, for example, in the rectangular region A in Figure 2. １１ and rectangular area A ９９ T ＺＣ T is Ｚ１１ and T Ｚ９９ One necessary condition is that the values ​​of are equal, but strictly speaking, T Ｚ１１ and T Ｚ９９ This does not require the values ​​to be equal, but rather that the temperature is within a range of ±1.00°C in a rectangular region that is point-symmetric with respect to the intersection of its diagonals.

[0057] Furthermore, as described above, T in the rectangular region whose center is located on the diagonal of the principal plane passing through the second vertex (second vertex P2) ＺＣ In degrees Celsius, in order from the fourth vertex closest to T Ｚ１９ , T Ｚ２８ , T Ｚ３７ , T Ｚ４６ , T Ｚ５５ , T Ｚ６４ , T Ｚ７３ , T Ｚ８２ , and, T Ｚ９１ In this case, it is also preferable that the following equation (1B) is satisfied. (1B) (T Ｚ１９ +T Ｚ９１ )-(T Ｚ２８ +T Ｚ８２ ) < 0.00 In other words, it is preferable that the same equation as equation (1A) is satisfied not only in the rectangular region where the center is located on the diagonal line passing through the first vertex P1, but also in the rectangular region where the center is located passing through the second vertex P2.

[0058] Furthermore, in the glass substrate of the present invention, it is also preferable that the following formula (2B) is satisfied, in that the error during correction is further reduced. (2B) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ３７ +T Ｚ７３ ) > -1.00 T in equation (2B) Ｚ２８ , T Ｚ８２ , T Ｚ３７ and T Ｚ７３This can be determined using the method described above.

[0059] Furthermore, in the glass substrate of the present invention, it is also preferable that the following formula (3B) is satisfied, in that the error during correction is further reduced. (3B) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ４６ +T Ｚ６４ ) > 0.00 T in equation (3B) Ｚ２８ , T Ｚ８２ , T Ｚ４６ and T Ｚ６４ This can be determined using the method described above.

[0060] Furthermore, in the glass substrate of the present invention, it is also preferable that the following formula (4B) is satisfied, in that the error during correction is further reduced. (4B) (T Ｚ２８ +T Ｚ８２ ) - 2 × T Ｚ５５ >0.00 T in equation (4B) Ｚ２８ , T Ｚ８２ and T Ｚ５５ This can be determined using the method described above.

[0061] Furthermore, in the glass substrate of the present invention, it is also preferable that the above formulas (2B), (3B), and (4B) are satisfied, in that the error during correction is reduced.

[0062] In the glass substrate of the present invention, it is also preferable that the following formula (1B-1) is satisfied. (1B-1) (T Ｚ１９ +T Ｚ９１ )-(T Ｚ２８ +T Ｚ８２ ) < -0.50

[0063] In the glass substrate of the present invention, it is also preferable that the following formula (1B-2) is satisfied. (1B-2) (T Ｚ１９ +T Ｚ９１ )-(T Ｚ２８ +T Ｚ８２ ) < -1.00

[0064] In the glass substrate of the present invention, it is also preferable that the following formula (2B-1) is satisfied, in that the error during correction is further reduced. (2B-1) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ３７ +TＺ７３ ) > 0.10

[0065] In the glass substrate of the present invention, it is also preferable that the following formula (2B-2) is satisfied, in that the error during correction is further reduced. (2B-2) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ３７ +T Ｚ７３ ) > 0.20

[0066] In the glass substrate of the present invention, it is also preferable that the following formula (3B-1) is satisfied, in that the error during correction is further reduced. (3B-1) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ４６ +T Ｚ６４ ) > 1.00

[0067] In the glass substrate of the present invention, it is also preferable that the following formula (3B-2) is satisfied, in that the error during correction is further reduced. (3B-2) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ４６ +T Ｚ６４ ) > 2.00

[0068] In the glass substrate of the present invention, it is also preferable that the following formula (4B-1) is satisfied, in that the error during correction is further reduced. (4B-1) (T Ｚ２８ +T Ｚ８２ ) - 2 × T Ｚ５５ >2.00

[0069] In the glass substrate of the present invention, it is also preferable that the following formula (4B-2) is satisfied, in that the error during correction is further reduced. (4B-2) (T Ｚ２８ +T Ｚ８２ ) - 2 × T Ｚ５５ >4.00

[0070] Furthermore, in the glass substrate of the present invention, it is also preferable that one or more of the above formulas (2B), (2B-1), and (2B-2), one or more of the above formulas (3B), (3B-1), and (3B-2), and one or more of the above formulas (4B), (4B-1), and (4B-2) be satisfied, in that the error during correction is further reduced.

[0071] In the glass substrate of the present invention, it is also preferable that the following formula (1B-3) is satisfied. (1B-3) (T Ｚ１９ +T Ｚ９１ )-(T Ｚ２８ +T Ｚ８２ ) > -6.00

[0072] In the glass substrate of the present invention, it is also preferable that the following formula (1B-4) is satisfied. (1B-4) (T Ｚ１９ +T Ｚ９１ )-(T Ｚ２８ +T Ｚ８２ ) > -5.00

[0073] In the glass substrate of the present invention, it is also preferable that the following formula (2B-3) is satisfied. (2B-3) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ３７ +T Ｚ７３ ) < 4.00

[0074] In the glass substrate of the present invention, it is also preferable that the following formula (2B-4) is satisfied. (2B-4) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ３７ +T Ｚ７３ ) < 2.00

[0075] In the glass substrate of the present invention, it is also preferable that the following formula (3B-3) is satisfied. (3B-3) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ４６ +T Ｚ６４ ) < 7.00

[0076] In the glass substrate of the present invention, it is also preferable that the following formula (3B-4) is satisfied. (3B-4) (T Ｚ２８ +T Ｚ８２ )-(T Ｚ４６ +T Ｚ６４ ) < 5.00

[0077] In the glass substrate of the present invention, it is also preferable that the following formula (4B-3) is satisfied. (4B-3) (T Ｚ２８ +T Ｚ８２ ) - 2 × T Ｚ５５ <12.00

[0078] In the glass substrate of the present invention, it is also preferable to satisfy the following formula (4B-4). (4B-4) (T Ｚ２８ +T Ｚ８２ ) - 2×T Ｚ５５ <10.00

[0079] In the glass substrate of the present invention, in terms of reducing the error during correction, it is also preferable to satisfy the following formula (SB). (5B) (T Ｚ３７ +T Ｚ７３ ) - (T Ｚ４６ +T Ｚ６４ [[ID=])>0.00 T in formula (5B Ｚ３７ , T Ｚ７３ , T Ｚ４６ and T Ｚ６４ are obtained by the method described above.

[0080] In the glass substrate of the present invention, in terms of reducing the error during correction, it is also preferable to satisfy the following formula (6B). (6B) (T Ｚ３７ +T Ｚ７３ ) - 2×T Ｚ５５ >0.00 T in formula (6B Ｚ３７ , T Ｚ７３ and T Ｚ５５ are obtained by the method described above.

[0081] Furthermore, in the glass substrate of the present invention, in terms of reducing the error during correction, it is also preferable to satisfy the above formula (2B), the above formula (5B), and the above formula (6B).

[0082] In the glass substrate of the present invention, in terms of reducing the error during correction, it is also preferable to satisfy the following formula (5B-1). (5B-1) (T Ｚ３７ +T Ｚ７３ ) - (T Ｚ４６ +T Ｚ６４ )>0.50

[0083] In the glass substrate of the present invention, in terms of reducing the error during correction, it is also preferable to satisfy the following formula (5B-2). (5B-2) (T Ｚ３７ +T Ｚ７３ ) - (T Ｚ４６ +T Ｚ６４ )>1.00

[0084] In the glass substrate of the present invention, it is also preferable to satisfy the following formula (6B-1) in that the error during correction becomes smaller. (6B-1) (T Ｚ３７ + T Ｚ７３ ) - 2 × T Ｚ５５ > 1.00

[0085] In the glass substrate of the present invention, it is also preferable to satisfy the following formula (6B-2) in that the error during correction becomes smaller. (6B-2) (T Ｚ３７ + T Ｚ７３ ) - 2 × T Ｚ５５ > 2.00

[0086] Furthermore, in the glass substrate of the present invention, in that the error during correction becomes smaller, any one or more of the above formulas (2B), (2B-1) and (2B-2), any one or more of the above formulas (5B), (5B-1) and (5B-2), and any one or more of the above formulas (6B), (6B-1) and (6B-2) are preferably satisfied.

[0087] In the glass substrate of the present invention, it is also preferable to satisfy the following formula (5B-3). (5B-3) (T Ｚ３７ + T Ｚ７３ ) - (T Ｚ４６ + T Ｚ６４ ) < 5.00

[0088] In the glass substrate of the present invention, it is also preferable to satisfy the following formula (6B-3). (6B-3) (T Ｚ３７ + T Ｚ７３ ) - 2 × T Ｚ５５ < 6.00

[0089] Also, in terms of being more likely to reduce the error during correction, it is also preferable that the maximum temperature difference of T ＺＣ in each of the above rectangular regions of the rectangular region group is 1.00 °C or more. The maximum temperature difference means the value obtained by subtracting the value of the lowest T ＺＣ from the value of the highest T ＺＣ . The maximum temperature difference of the above T ＺＣ is more preferably 1.50 °C or more, and even more preferably 2.20 °C or more. Also, the above T ＺＣThe maximum temperature difference is often 10.00°C or less, preferably 8.00°C or less, more preferably 6.00°C or less, and even more preferably 5.00°C or less.

[0090] Furthermore, T in each of the above rectangular regions of the group of rectangular regions ＺＣ It is also preferable that the average value is 18.00°C or higher. ＺＣ The average value is calculated from T obtained in each of the 81 rectangular regions mentioned above. ＺＣ This refers to the arithmetic mean of the above T. ＺＣ The average value is more preferably 20.00°C or higher, and even more preferably 21.00°C or higher. ＺＣ The average temperature is preferably 30.00°C or lower, more preferably 28.00°C or lower, and even more preferably 26.00°C or lower.

[0091] Furthermore, in the glass substrate of the present invention, the above T Ｚ１１ , T Ｚ２２ , T Ｚ３３ , T Ｚ４４ , T Ｚ５５ , T Ｚ６６ , T Ｚ７７ , T Ｚ８８ , and, T Ｚ９９ , and also, T Ｚ１９ , T Ｚ２８ , T Ｚ３７ , T Ｚ４６ , T Ｚ５５ , T Ｚ６４ , T Ｚ７３ , T Ｚ８２ , and, T Ｚ９１ In this regard, it is also preferable that the following equation (1C) is satisfied. (1C) (T Ｚ１１ +T Ｚ１９ +T Ｚ９１ +T Ｚ９９ ) / 4-(T Ｚ２２ +T Ｚ２８ +T Ｚ８２ +T Ｚ８８ +T Ｚ３３ +T Ｚ３７ +T Ｚ７３ +T Ｚ７７ ) / 8 < 0.00

[0092] [Composition] The glass substrate of the present invention is silicon dioxide (SiO ２Preferably, it contains SiO. ２ In addition, it is preferable to include other components, such as titanium dioxide (TiO ２ It is more preferable that the material constituting the glass substrate of the present invention contains SiO ２ -TiO ２ It is preferable that the material constituting the glass substrate of the present invention is SiO ２ -TiO ２ If it is a system, SiO ２ and TiO ２ It may also contain trace amounts of other components. The material constituting the glass substrate of the present invention is SiO ２ -TiO ２ In the case of a system, TiO ２ The content of is preferably 6.0% or more, and more preferably 7.0% or more, expressed as a mass percentage based on oxides. ２ The content is preferably 9.0% or less, and more preferably 8.5% or less, expressed as a mass percentage based on oxides. Generally, SiO ２ -TiO ２ When manufacturing glass, the above formula (1A) is often not satisfied, but the manufacturing method described later makes it easier to manufacture glass that satisfies the above formula (1A).

[0093] Furthermore, it is preferable that the material constituting the glass substrate of the present invention contains a low amount of moisture. The amount of moisture contained in the glass substrate of the present invention can be measured using known methods. For example, the amount of moisture can be determined from the absorption peak at a wavelength of 2.7 μm by measurement using an infrared spectrophotometer (see J.P. Williams et al., American Ceramics Society Bulletin, 55(5), 524, 1976). The detection limit by the above method is 0.1 ppm. The moisture content in the material constituting the glass substrate of the present invention is preferably 1000 ppm by mass or less, and more preferably 600 ppm by mass or less, relative to the total mass of the material constituting the glass substrate. There is no particular lower limit to the moisture content, but it is preferably 50 ppm by mass or more, and more preferably 100 ppm by mass or more.

[0094] Furthermore, the Young's modulus of the obtained glass substrate of the present invention is preferably 65 GPa or higher.

[0095] [Shape] The shape of the glass substrate of the present invention is not particularly limited, but for example, it may be 153 mm square with a thickness of 0.25 inches (6.35 mm). In addition, the lengths of the first side S1 and the second side S2 may be, for example, 3 inches (76.2 mm) to 18 inches (457.2 mm), respectively. Furthermore, the shape of the first main surface MS1 of the glass substrate of the present invention may be rectangular. Furthermore, each side of the glass substrate of the present invention may be chamfered.

[0096] <Method for manufacturing a glass substrate> The glass substrate of the present invention is preferably manufactured by the soot method. The following describes how to manufacture a glass substrate by the soot method using SiO ２ -TiO ２ A method for manufacturing the glass substrate of the present invention, which is a SiO2-based glass, will be described. ２ -TiO ２ One method for producing glass is to first decompose the Si precursor and Ti precursor to obtain SiO ２ -TiO ２ Glass nanoparticles are deposited and grown on a substrate, and SiO ２ -TiO ２A porous glass material is obtained. Next, the obtained SiO ２ -TiO ２ A porous glass material is heated to create transparent SiO ２ -TiO ２ A glass system is obtained. Then, transparent SiO ２ -TiO ２ The glass is heated and shaped, then heat-treated to produce SiO ２ -TiO ２ Obtain a glass block of SiO. ２ -TiO ２ From a glass block, cut into a plate shape, SiO ２ -TiO ２ A glass substrate of the present invention, composed of a glass system, is obtained. Details and preferred conditions are described below.

[0097] SiO obtained by decomposing Si precursors and Ti precursors ２ -TiO ２ One method for depositing SiO2 glass nanoparticles onto a substrate is to introduce Si precursors and Ti precursors into a flame and perform flame hydrolysis. A suitable substrate is, for example, a seed rod made of quartz glass. ２ -TiO ２ The Si precursor used when obtaining a porous glass system is preferably a gaseous raw material, for example, SiCl ４ SiHCl ３ SiH ２ Cl ２ SiH ３ Chlorides such as Cl, SiF ４ SiHF ３ SiH ２ F ２ Fluorides such as SiBr ４ SiHBr ３ Bromides such as SiI ４ Silicon halide compounds such as iodides, and R ｎ Si (OR) ４－ｎ Examples of alkoxysilanes are those represented by (where R is an alkyl group having 1 to 4 carbon atoms, and n is an integer from 0 to 3). The Ti precursor is preferably a gaseous raw material, for example, TiCl ４ TiBr ４Titanium halogen compounds such as, and R ｎ Ti(OR) ４－ｎ Examples of alkoxytitaniums include those represented by (where R is an alkyl group having 1 to 4 carbon atoms, and n is an integer from 0 to 3). In addition, Si and Ti compounds such as silicon titanium double alkoxide can be used as Si precursors and Ti precursors.

[0098] SiO ２ -TiO ２ As a method for depositing glass nanoparticles onto the above substrate, the gasified Si precursor and Ti precursor are introduced into the flame of a burner, and the Si precursor and Ti precursor are subjected to flame hydrolysis to form SiO ２ -TiO ２ One method involves generating SiO2 glass nanoparticles and depositing them on the substrate. More specifically, one method involves using a multi-tube burner as the burner, supplying hydrogen gas and oxygen gas to the multi-tube burner to generate an oxyhydrogen flame, and supplying the Si precursor and Ti precursor into the resulting oxyhydrogen flame. ２ -TiO ２ When depositing glass microparticles, it is preferable to deposit them while rotating the substrate (e.g., seed rod).

[0099] While rotating the above substrate, SiO ２ -TiO ２ When depositing the glass nanoparticles, the Si precursor and Ti precursor are supplied along the direction from which the burner flame is emitted. Figure 3 shows the SiO2 process while rotating the substrate. ２ -TiO ２ This is a cross-sectional view showing the positional relationship when depositing glass nanoparticles. In Figure 3, the substrate 30 is rotated around the rotational axis SA, and SiO ２ -TiO ２ SiO2 glass nanoparticles are deposited on the surface of the substrate 30. ２ -TiO ２ The glass nanoparticles are generated by the heat of the flame FL of the burner 32, which contains the Si precursor and Ti precursor. These Si precursor and Ti precursor are supplied towards the substrate 30 along the flame radiation axis BA. Here, the surface of the substrate 30 (SiO ２ -TiO２ Consider a virtual plane VS that is in contact with the surface on which the glass nanoparticles are deposited and is perpendicular to the rotational axis SA of the substrate 30. The virtual plane VS has a point P1 which is the intersection with the rotational axis SA of the substrate 30. In the embodiment shown in Figure 3, the burner 32 is positioned such that the flame radiation axis BA passes through point P1. Then, SiO ２ -TiO ２ The glass nanoparticles are deposited around the center of the substrate 30. Here, if the swing angle θ of the burner 32 is adjusted around the burner fixing point MP within the plane of the paper, the flame radiation axis BA will no longer pass through point P1, and SiO ２ -TiO ２ The central position where the glass nanoparticles are deposited shifts from the center of the substrate 30 towards the outer periphery of the substrate 30.

[0100] Here, the Si precursor and Ti precursor are decomposed by the flame FL of the burner 32 to form SiO ２ -TiO ２ Although glass nanoparticles are formed, the reaction rates of the Si precursor and Ti precursor are often different. As a result, the precursor with the slower reaction rate (e.g., the Si precursor) is more likely to reach the substrate 30 in a gaseous state without being decomposed, and the precursor with the slower reaction rate (e.g., the Si precursor) tends to move outward from the flame radiation axis BA. Consequently, SiO deposits on the substrate 30. ２ -TiO ２ In glass nanoparticles, the concentration of the element (e.g., Si) contained in the precursor with the slower reaction rate (e.g., Si precursor) tends to increase outward from the flame radiation axis BA. In other words, the concentration of the element (e.g., Ti) contained in the precursor with the faster reaction rate (e.g., Ti precursor) tends to be higher near the flame radiation axis BA. Furthermore, since the reactions of the Si precursor and Ti precursor often have different activation energies, it is understood that the difference in reaction rates changes when the temperature is changed. Consequently, the temperature distribution in the flame FL of the burner 32 also affects the deposition of SiO on the substrate 30. ２ -TiO ２ The distribution of elemental concentrations in the glass nanoparticles may change.

[0101] Therefore, in the embodiment shown in Figure 3, the concentration of the element (e.g., Ti) contained in the precursor with the faster reaction rate (e.g., Ti precursor) is higher around the rotational axis SA. ２ -TiO ２ A porous glass material is easily obtained. Here, it is understood that by adjusting the swing angle θ of the burner 32, the intersection point of the flame radiation axis BA and the substrate 30 shifts towards the outer periphery of the substrate 30, and thus the position where the concentration of the element (e.g., Ti) in the precursor with the faster reaction rate (e.g., Ti precursor) becomes higher changes.

[0102] Furthermore, in Figure 3, the distance from the burner 32 to the surface of the substrate 30 is shown as the substrate-burner distance d. The Si precursor and Ti precursor supplied into the flame FL are supplied to the substrate 30 while being decomposed, but as the substrate-burner distance d shortens, the proportion of precursors that reach the substrate 30 without being decomposed increases. Among the precursors that reach the substrate 30 without being decomposed, the proportion of the precursor with the slower reaction rate tends to increase. Therefore, it is thought that shortening the substrate-burner distance d tends to increase the bias in the elemental concentrations mentioned above. Note that the substrate-burner distance d refers to the distance from the tip of the burner 32 to the surface of the substrate 30.

[0103] Furthermore, when a multi-tube burner is used as the burner 32, the temperature distribution in the flame FL of the burner 32 can be adjusted by adjusting the gas flow rate distribution. Figure 4 is a perspective view showing an example of a multi-tube burner. The burner 32 shown in Figure 4 is a multi-tube burner, having a central nozzle 34 in the center, and a triple-tube structure in which a first outer peripheral nozzle 36 and a second outer peripheral nozzle 38 are arranged concentrically with respect to the central nozzle 34. In the burner 32 shown in Figure 4, a shield 40 is provided at the opening of the first outer peripheral nozzle 36. The shield 40 is arranged to cover 1 / 3 of the opening area of ​​the first outer peripheral nozzle 36. In the area where the shield 40 is located, the gas supplied to the first outer peripheral nozzle 36 is not supplied from the tip of the first outer peripheral nozzle 36, and a distribution can be created in the amount of gas supplied. When using the burner 32 shown in Figure 4, supplying oxygen or hydrogen to the first outer nozzle 36 reduces the amount of gas supplied in the area where the shield 40 is placed, and it is understood that a temperature distribution of the flame FL occurs according to the distribution of the amount of gas supplied. Therefore, when using the burner 32 shown in Figure 4, a temperature distribution of the flame FL occurs according to the arrangement of the shield 40, and according to that temperature distribution, the distribution of elemental concentrations changes through the mechanism described above. Furthermore, it is easily understood that the temperature distribution of the flame FL (i.e., the distribution of elemental concentrations) can be adjusted by the arrangement of the shield 40.

[0104] As described above, the distribution of elemental concentrations is adjusted by the swing angle θ of the burner 32 shown in Figure 3, the distance d between the substrate and the burner, and the arrangement of the shielding 40 shown in Figure 4. SiO ２ -TiO ２ The distribution of elemental concentrations in a porous glass material tends to remain unchanged when obtaining the glass substrate of the present invention through the procedure described later. Therefore, as a method for obtaining the glass substrate of the present invention, SiO ２ -TiO ２A preferred method is to adjust the elemental concentration in the porous glass body. In terms of facilitating the acquisition of the glass substrate of the present invention, the swing angle θ of the burner 32 is preferably 2.0° or more, more preferably 3.0° or more, and even more preferably 3.2° or more. Furthermore, the swing angle θ of the burner 32 is preferably 6.0° or less, more preferably 5.0° or less, and even more preferably 4.5° or less. Furthermore, in terms of facilitating the acquisition of the glass substrate of the present invention, the distance d between the substrate and the burner is preferably 205 mm or less, more preferably 200 mm or less, and even more preferably 195 mm or less. Furthermore, the distance d between the substrate and the burner is often 150 mm or more. Furthermore, in terms of facilitating the acquisition of the glass substrate of the present invention, the shielding 40 preferably covers 1 / 4 or more of the opening area of ​​the nozzle in which the shielding 40 is placed, and preferably covers 1 / 3 or more. Furthermore, the shielding 40 preferably covers 3 / 4 or less of the opening area of ​​the nozzle in which the shielding 40 is placed, and even more preferably covers 2 / 3 or less. Preferably, the shield 40 is positioned such that its center of gravity is on the opposite side of the flamethrower axis BA from the rotational axis SA of the base material 30. Alternatively, the center of gravity of the shield 40 may be positioned so as to rotate around the flamethrower axis BA. Specifically, with reference to a straight line located on the plane including the opening of the first outer peripheral nozzle 36 and the plane including the rotational axis SA of the base material 30 and the flamethrower axis BA, it is preferable that the center of gravity of the shield 40 is located within a range of ±30°, where the position furthest from the rotational axis SA is defined as 0° on the plane including the opening of the first outer peripheral nozzle 36.

[0105] The diameter of the burner 32 is preferably φ50 to 100 mm. Also, although the burner 32 (multi-tube burner) shown in Figure 4 has a triple-tube configuration, a quadruple-tube or higher configuration is also acceptable.

[0106] SiO obtained by the above method ２ -TiO ２ A porous glass material is heated to its densification temperature under reduced pressure or in a helium atmosphere, and SiO ２ -TiO ２A dense body is obtained. The densification temperature is usually 1250 to 1550°C, and preferably 1300 to 1500°C. In this specification, the densification temperature is defined as the temperature at which voids can no longer be observed with an optical microscope. ２ -TiO ２ This refers to the temperature at which a porous glass material can be densified. ２ -TiO ２ Further heating of the dense material to make transparent SiO ２ -TiO ２ A glass system is obtained by heating SiO. ２ -TiO ２ To make a dense material transparent. In this specification, SiO ２ -TiO ２ Making a dense material transparent means that the crystals can no longer be seen under an optical microscope, resulting in a transparent, glass-like state. ２ -TiO ２ The temperature at which the dense material becomes transparent is preferably 1500 to 1750°C, and more preferably 1550 to 1700°C. SiO ２ -TiO ２ For heating the porous glass material, an atmosphere consisting of 100% inert gas such as helium, or an atmosphere mainly composed of inert gas such as helium, is preferred. The pressure of the atmosphere is preferably reduced pressure or atmospheric pressure. In particular, when the atmosphere pressure is atmospheric pressure, helium gas is preferably used. Furthermore, when the atmosphere pressure is reduced, an absolute pressure of 13,000 Pa or less is preferred.

[0107] Next, the transparent SiO obtained by the above method ２ -TiO ２ The glass is heated and shaped, then heat-treated to produce SiO ２ -TiO ２ A glass block is obtained. The heating temperature during molding is SiO ２ -TiO ２It is preferable that the temperature is above the softening point of the glass. Specifically, the heating temperature during molding is preferably 1500 to 1800°C. When performing the above heating, the heating rate from 1100 to 1500°C is preferably 0.5°C / min or more, more preferably 1°C / min or more, and even more preferably 2°C / min or more, in that it is easier to obtain the glass substrate of the present invention. Furthermore, when performing the above heating, it is preferable to heat at 1600°C or higher, and more preferably at 1650°C or higher. When heating from 1500°C to the above temperature (for example, 1650°C), the heating rate is preferably less than 15°C / min. Transparent SiO ２ -TiO ２ When heating and shaping glass, transparent SiO is placed inside the mold. ２ -TiO ２ It is preferable to install a glass frame. Examples of suitable formwork include carbon fiber formwork.

[0108] Here, the size of the molded body obtained by molding is preferably 185 mm square or less, and more preferably 180 mm square or less, in the plane perpendicular to the rotational axis SA of the base material 30, in order to make it easier to obtain the glass substrate of the present invention. The size of the molded body is often 159 mm square or larger.

[0109] The above process is performed by SiO ２ -TiO ２ A molded body of SiO2 is obtained. Next, the obtained molded body is ground to remove SiO2. ２ -TiO ２ A system block is obtained. Furthermore, the obtained SiO ２ -TiO ２ A glass plate of the desired shape is cut from a glass block of SiO to obtain the glass substrate of the present invention. ２ -TiO ２ The size of the molded glass body is preferably adjusted according to the size of the glass substrate of the present invention to be cut. ２ -TiO ２ The molded glass body is preferably 3 mm or more larger than the size of the glass substrate of the present invention to be cut, and may be 5 mm or more larger. ２ -TiO ２The difference between the size of the molded glass body and the size of the glass substrate of the present invention to be cut is preferably 8 mm or less, and more preferably 7 mm or less, in terms of the ease with which the glass substrate of the present invention can be obtained. More specifically, when the size of the glass substrate of the present invention to be cut is 153 mm in length and 153 mm in width, ２ -TiO ２ The size of the molded glass body is preferably 185 mm or less in length and 185 mm or less in width. ２ -TiO ２ The size of the molded glass body is more preferably 180 mm or less in length and 180 mm or less in width. ２ -TiO ２ The size of the molded glass body can be adjusted by the size of the mold used during molding. ２ -TiO ２ When cutting a glass substrate from a glass block, SiO ２ -TiO ２ It is preferable to cut the glass porous material such that the surface parallel to the virtual surface (the surface perpendicular to the rotation center of the substrate) becomes the first main surface of the glass substrate of the present invention.

[0110] Glass substrate SiO ２ -TiO ２ After cutting the glass block, it is preferable to perform a slow cooling treatment. The slow cooling treatment is preferably carried out by maintaining the temperature in the range of 600 to 1200°C for 5 hours or more, and then cooling it to 870°C or below at a cooling rate of 1°C / hour or less. The atmosphere during the slow cooling treatment is preferably an atmosphere containing 100% inert gas such as helium gas, argon gas, and nitrogen gas, or an atmosphere in which these inert gases are the main component. The pressure of the atmosphere is preferably reduced pressure or atmospheric pressure. If the pressure of the atmosphere is reduced pressure, it is preferably 13000 Pa or less in absolute pressure.

[0111] According to the method described above, a glass substrate of the present invention satisfying formula (1A) can be obtained. Furthermore, according to the method described above, the amount of moisture contained in the material constituting the glass substrate of the present invention tends to fall within the range described above. According to the method described above, a glass substrate satisfying formulas (2A) to (6A) can be easily obtained. According to the method described above, a glass substrate satisfying formulas (1B) to (6B) can be easily obtained. Furthermore, according to the method described above, a glass substrate satisfying requirements 1 to 4 can be easily obtained.

[0112] The cut glass substrate of the present invention may be processed as appropriate. For example, the first main surface may be polished to achieve a predetermined flatness and surface roughness.

[0113] <Mask Blank> The EUV lithography mask blank of the present invention has a glass substrate of the present invention. Processing the EUV lithography mask blank of the present invention yields a reflective mask for EUV lithography. The glass substrate of the present invention has a small error when correcting for thermal deformation, so it is easy to transfer a desired pattern using the resulting reflective mask. The configuration of the EUV lithography mask blank of the present invention (hereinafter also referred to as "this mask blank") may include, for example, a glass substrate of the present invention and, on the first main surface side of the glass substrate of the present invention, a multilayer reflective film, a protective film, and an absorber film in order from the first main surface side, and further, a conductive film on the second main surface side of the glass substrate of the present invention. Alternatively, this mask blank may have a multilayer reflective film, a protective film, and an absorber film in order from the second main surface side, and further, a conductive film on the first main surface side of the glass substrate of the present invention. The configuration of this mask blank will be described below.

[0114] [Multilayer Reflective Film] One embodiment of this mask blank has a multilayer reflective film. The multilayer reflective film is not particularly limited as long as it has the desired properties as a reflective film for the EUV mask blank. The multilayer reflective film preferably has a high reflectivity to EUV light. Specifically, when EUV light is incident on the surface of the multilayer reflective film at an incident angle of 6°, the maximum reflectivity of EUV light around a wavelength of 13.5 nm is preferably 60% or more, and more preferably 65% ​​or more. Similarly, even when a protective film is laminated on the multilayer reflective film, the maximum reflectivity of EUV light around a wavelength of 13.5 nm is preferably 60% or more, and more preferably 65% ​​or more.

[0115] Since multilayer reflective films can achieve high reflectivity of EUV light, a multilayer reflective film is usually used in which a high refractive index layer exhibiting a high refractive index for EUV light and a low refractive index layer exhibiting a low refractive index for EUV light are alternately stacked multiple times. The multilayer reflective film may be stacked in multiple periods, with one period consisting of a stacked structure in which the high refractive index layer and the low refractive index layer are stacked in this order from the substrate side, or it may be stacked in multiple periods, with one period consisting of a stacked structure in which the low refractive index layer and the high refractive index layer are stacked in this order. A layer containing Si can be used as the high refractive index layer. As a material containing Si, in addition to pure Si, a Si compound containing Si and one or more elements selected from the group consisting of B, C, N, and O can be used. By using a high refractive index layer containing Si, a reflective mask with excellent reflectivity of EUV light can be obtained. As a low refractive index layer, a layer containing a metal selected from the group consisting of Mo, Ru, Rh, and Pt, or an alloy thereof, can be used. Si is widely used for the high refractive index layer, and Mo is widely used for the low refractive index layer. In other words, Mo / Si multilayer reflective coatings are the most common. However, multilayer reflective coatings are not limited to this, and Ru / Si multilayer reflective coatings, Mo / Be multilayer reflective coatings, Mo compound / Si compound multilayer reflective coatings, Si / Mo / Ru multilayer reflective coatings, Si / Mo / Ru / Mo multilayer reflective coatings, Si / Ru / Mo multilayer reflective coatings, and Si / Ru / Mo / Ru multilayer reflective coatings can also be used.

[0116] The film thicknesses of the respective layers constituting the multilayer reflective film and the number of repeating units of the layers can be appropriately selected according to the film materials used and the reflectance of EUV light required for the reflective layer. Taking a Mo / Si multilayer reflective film as an example, in order to obtain a multilayer reflective film with a maximum reflectance of EUV light of 60% or more, a Mo film with a film thickness of 2.3 ± 0.1 nm and a Si film with a film thickness of 4.5 ± 0.1 nm may be laminated so that the number of repeating units is 30 to 60.

[0117] In addition, each layer constituting the multilayer reflective film can be formed to a desired thickness by using a known film-forming method such as a magnetron sputtering method or an ion beam sputtering method. For example, when producing a multilayer reflective film using the ion beam sputtering method, ion particles are supplied from an ion source to a target of a high refractive index material and a target of a low refractive index material. When the multilayer reflective film is a Mo / Si multilayer reflective film, by the ion beam sputtering method, for example, first, a Si layer with a predetermined film thickness is formed on the glass substrate of the present invention using a Si target. Thereafter, a Mo layer with a predetermined film thickness is formed using a Mo target. By laminating 30 to 60 cycles with this Si layer and Mo layer as one cycle, a Mo / Si multilayer reflective film is formed.

[0118] [Protective Film] One aspect of this mask blank may have a protective film between the multilayer reflective film and the absorber film. The protective film is provided for the purpose of protecting the multilayer reflective film so that the multilayer reflective film is not damaged by the etching process when patterning the absorber film by an etching process (usually a dry etching process). Examples of materials that can achieve the above object include materials containing at least one element selected from the group consisting of Ru and Rh. That is, the protective film preferably contains at least one element selected from the group consisting of Ru and Rh. The protective film may further contain one or more elements selected from the group consisting of Si, Ti, Nb, Ru, Ta, and Zr. Also, examples of materials that can achieve the above object include Al and nitrides containing these metals and nitrogen, and Al ２ O ３ etc.

[0119] The thickness of the protective film is not particularly limited as long as it can perform its function as a protective film. In order to maintain the reflectance of EUV light reflected by the multilayer reflective film, the thickness of the protective film is preferably 1 to 10 nm, more preferably 1.5 to 6 nm, and even more preferably 2 to 5 nm.

[0120] The protective film may be a single layer or a multilayer film consisting of multiple layers. If the protective film is a multilayer film, it is preferable that each layer constituting the multilayer film is made of the preferred material described above. Furthermore, if the protective film is a multilayer film, it is also preferable that the total thickness of the multilayer film is within the preferred range described above.

[0121] The protective film can be deposited using known deposition methods such as magnetron sputtering and ion beam sputtering. When depositing a Ru film by magnetron sputtering, it is preferable to use a Ru target as the target and Ar gas as the sputtering gas.

[0122] [Absorber Film] In one embodiment of the mask blank of the present invention, the absorber film is required to have high contrast between the EUV light reflected by the multilayer reflective film and the EUV light absorbed by the absorber film when the absorber film is patterned. The patterned absorber film (absorber film pattern) may function as a binary mask by absorbing EUV light, or it may function as a phase-shift mask that reflects EUV light and interferes with the EUV light from the multilayer reflective film to produce contrast.

[0123] When an absorber film pattern is used as a binary mask, the absorber film must absorb EUV light and have a low reflectivity of EUV light. Specifically, when EUV light is irradiated onto the surface of the absorber film, the maximum reflectivity of EUV light at a wavelength of around 13.5 nm is preferably 2% or less. The absorber film may contain one or more metals selected from the group consisting of Ta, Ti, Sn, and Cr, as well as one or more components selected from the group consisting of O, N, B, Hf, and H. Among these, it is preferable that the absorber film contains Ta and also contains N or B. The crystalline state of the absorber film is preferably amorphous. This improves the smoothness and flatness of the absorber film. Furthermore, when the smoothness and flatness of the absorber film are high, the edge roughness of the absorber film pattern is reduced, and the dimensional accuracy of the absorber film pattern can be improved. When using an absorber membrane pattern as a binary mask, the thickness of the absorber membrane is preferably 40 to 70 nm, and more preferably 50 to 65 nm.

[0124] When an absorber film pattern is used as a phase shift mask, the reflectivity of the absorber film for EUV light is preferably 2% or more. To obtain a sufficient phase shift effect, the reflectivity of the absorber film is preferably 9 to 15%. When an absorber film is used as a phase shift mask, the contrast of the optical image on the wafer is improved and the exposure margin is increased. Examples of materials for forming the phase shift mask include materials containing Ru and materials containing Ta, and these materials may contain one or more elements selected from the group consisting of B, N, and O. When an absorber film pattern is used as a phase shift mask, the film thickness of the absorber film is preferably 30 to 60 nm, and more preferably 35 to 55 nm.

[0125] The absorber film may be a single layer or a multilayer film consisting of multiple layers. If the absorber film is a single layer, the number of steps in mask blank manufacturing can be reduced, improving production efficiency. If the absorber film is a multilayer film, the layer located on the side opposite the protective film side of the absorber film may be an anti-reflective film used when inspecting the absorber film pattern using inspection light (for example, wavelength 193-248 nm). Examples of materials for forming the anti-reflective film include materials containing Ta and O.

[0126] Absorber films can be formed using known film deposition methods such as magnetron sputtering and ion beam sputtering. For example, when forming a Ta nitride film as an absorber film using magnetron sputtering, a Ta target is used, and sputtering is performed by supplying a gas containing Ar gas and nitrogen gas to form the absorber film.

[0127] [Hard Mask Film] This mask blank may have a hard mask film. The hard mask film is preferably positioned on the side of the absorber film opposite to the glass substrate side of the present invention. As the hard mask film, it is preferable to use a material that has high resistance to dry etching, such as a Cr-based film or a Si-based film. Examples of Cr-based films include materials containing Cr and one or more elements selected from the group consisting of Cr and O, N, C, and H. Specifically, examples include CrO and CrN. Examples of Si-based films include materials containing Si and one or more elements selected from the group consisting of Si and O, N, C, and H. Specifically, SiO ２ Examples include SiO, SiN, SiO, SiC, SiCO, SiCN, and SiCON. When a hard mask film is formed on the absorber film, dry etching can be performed even if the minimum line width of the absorber film pattern becomes small. Therefore, it is effective for miniaturizing the absorber film pattern.

[0128] [Conductive Film] One embodiment of this mask blank has a conductive film. By having a conductive film, the reflective mask blank can be handled with an electrostatic chuck.

[0129] The conductive film preferably contains one or more elements selected from the group consisting of Ta and Cr. Furthermore, the conductive film preferably contains at least one element selected from the group consisting of B, N, and O. The sheet resistance of the conductive film is preferably 250 Ω / sq. or less. The surface hardness of the conductive film is preferably 10.0 GPa or more.

[0130] The method for patterning the absorber film of this mask blank to form a mask pattern is not particularly limited, and known methods can be applied. For example, one method is to form a resist pattern on the absorber film of this mask blank and then dry etch the absorber film using the resist pattern as a mask. Alternatively, if this mask blank has a hard mask film on the side opposite to the multilayer reflective film side of the absorber film, one method is to first form a resist pattern on the hard mask film and then etch and pattern the hard mask film using the resist pattern as a mask. Next, one method is to etch the absorber film using the patterned hard mask film as a mask.

[0131] The present invention will be described in more detail below based on examples. The materials, amounts used, proportions, processing content, and processing procedures shown in the following examples can be modified as appropriate without departing from the spirit of the present invention. Therefore, the scope of the present invention should not be interpreted as being limited by the examples shown below. Examples 1 to 4 described later are examples, and Examples 5 to 7 are comparative examples.

[0132] <Example 1>

[0133] [Fabrication of glass substrates] The procedure for obtaining the glass substrate of Example 1 will be explained. The glass substrate of Example 1 is made of SiO ２ -TiO ２ It is made of glass, SiO ２ -TiO ２ The glass was obtained by the soot process (see Figure 3). First, the Ti precursor, TiCl ４ And, SiCl, which is a Si precursor. ４ Next, an oxyhydrogen flame was generated from the tip of the multi-tube burner, and TiCl was added to the oxyhydrogen flame. ４ and SiCl ４ The gases of each were introduced. TiCl was introduced into the oxyhydrogen flame. ４ and SiCl ４ It is heated and hydrolyzed, SiO ２ -TiO ２Glass microparticles were generated. The multi-tube burner used was the one shown in Figure 5. Figure 5 is a top view of the multi-tube burner used to obtain the glass substrate in the embodiment, as seen from the flame radiation axis side. The 11-tube burner 32a shown in Figure 5 is an 11-tube burner in which the first outer peripheral nozzle 36a to the tenth outer peripheral nozzle 36j are arranged in order around the central nozzle 34a. A shield 40a (shaded area in Figure 5) is placed at the opening of the first outer peripheral nozzle 36a, covering two-thirds of the opening. The center of gravity of the shield 40a was located on the left side of the plane of the paper relative to the flame radiation axis of the 11-tube burner 32a. Here, the rotational axis of the substrate is located on the right side of the plane of Figure 5 (the side indicated by the black arrow in Figure 5).

[0134] The following gases were supplied from each nozzle of the 11-tube burner 32a shown in Figure 5 above: Central nozzle 34a: TiCl ４ (Ti precursor), SiCl ４ (Si precursor), hydrogen, nitrogen First outer nozzle 36a: hydrogen Second outer nozzle 36b: nitrogen Third outer nozzle 36c: oxygen Fourth outer nozzle 36d: oxygen Fifth outer nozzle 36e: nitrogen Sixth outer nozzle 36f: hydrogen Seventh outer nozzle 36g: nitrogen Eighth outer nozzle 36h: hydrogen Ninth outer nozzle 36i: nitrogen Tenth outer nozzle 36j: oxygen The ratio of each gas to the total supply amount of all gases supplied from the 11-tube burner 32a was as follows: TiCl ４ :0.1mol% SiCl ４ Hydrogen: 2.0 mol% Oxygen: 46.2 mol% Nitrogen: 36.1 mol%

[0135] Using the above 11-tube burner 32a, SiO ２ -TiO ２ Glass nanoparticles are deposited onto the tip of a quartz glass seed rod that rotates at 25 revolutions per minute, and SiO ２ -TiO ２ A porous glass material was obtained. ２ -TiO ２ When obtaining the porous glass material, the substrate-burner distance d, as explained in Figure 3, was set to 190 mm. The swing angle θ, also as explained in Figure 3, was set to 4.2°.

[0136] The obtained SiO ２ -TiO ２ The porous glass material was left deposited on the seed rod and held in the air at 1280°C for 6 hours before being removed from the seed rod. Next, SiO ２ -TiO ２ A porous glass material is placed in an electric furnace with a controllable atmosphere, the pressure is reduced to 10 Pa or less at room temperature, and then the temperature is raised to 1360°C while maintaining the reduced pressure, and held at that temperature for 2 hours to extract SiO2. ２ -TiO ２ A dense material was obtained. ２ -TiO ２ The dense material was cut by approximately 50 mm from both ends along its long axis (the axis of rotation of the seed rod), and then the outer circumference was ground down by approximately 1 mm. The resulting SiO ２ -TiO ２ The dense material is heated to 1700°C in an argon atmosphere using a carbon furnace, and transparent SiO ２ -TiO ２ A glassy material was obtained.

[0137] Transparent SiO obtained using the above procedure ２ -TiO ２ The glass was placed in a carbon container and heated to 1680°C in an argon atmosphere for 60 hours. The heating rate in the range of 1100-1500°C was 5°C / min. The heating rate in the range of 1500-1680°C was 0.5°C / min. The inner bottom surface of the carbon container was a square with sides of 190 mm, and the height of the carbon container was approximately 1000 mm. After the heat treatment, a SiO₂ sample measuring 190 mm in length, 190 mm in width, and 220 mm in height was obtained. ２ -TiO ２ A molded glass body was obtained.

[0138] The above SiO ２ -TiO ２ A glass molded body is uniformly ground from the outer edge using a surface grinding machine, resulting in a SiO2 sieve measuring 153 mm in length, 153 mm in width, and 220 mm in height. ２ -TiO ２ A glass block was obtained. The obtained SiO ２ -TiO２ A glass block was cut perpendicular to its height, and the cut surface was polished to obtain a glass substrate with a thickness of 0.25 inches (6.3 mm). The obtained glass substrate was subjected to a slow cooling process. Specifically, it was held at 950°C for 24 hours, then cooled to 870°C over 40 days, and then the heater output was turned off and it was cooled to room temperature to obtain the glass substrate of Example 1.

[0139] [Measurement] Using the method described above, the T of each of the 81 rectangular regions was measured. ＺＣ The following was measured. The specific method is as described above.

[0140] [Evaluation] T of each obtained rectangular region ＺＣBased on the values, a simulation of thermal deformation of the glass substrate was performed, and the degree of error after correction was evaluated. More specifically, the thermal deformation was simulated under temperature distribution conditions where the temperature of the exposure area (132 mm × 104 mm) was 35°C and the other areas were 18°C, and under constraint conditions that simulated the fixed position when mounted on the actual device. Based on the shape after thermal deformation, thermal deformation correction was performed using a virtual marker placed outside the exposure area as a reference. The table shown later shows the maximum displacement after the above thermal deformation correction. Specifically, the displacement is defined as the difference between the position of the center of the 81 rectangular areas before thermal deformation and the position of the center of each rectangular area after thermal deformation correction, and the largest displacement is shown as the maximum displacement. The maximum displacement is shown decomposed into the first side direction (X direction in the table) and the second side direction (Y direction in the table). In addition, the same simulation was performed by rotating each glass substrate by 90°, and the same maximum displacement was obtained as above. For glass substrates, it is preferable that the obtained maximum displacement is small. Table 1 shows the maximum displacement in the direction in which the larger of the maximum displacement values ​​in the X direction and the Y direction becomes smaller. The larger of the two maximum displacement values ​​was used to evaluate the magnitude of the error when correcting for thermal deformation according to the following criteria. The evaluation results are shown in the table below. A to C evaluations are preferred, A or B evaluations are more preferred, and A evaluation is even more preferred. ・A: The larger of the two maximum displacement values ​​is less than 0.19 nm ・B: The larger of the two maximum displacement values ​​is 0.19 nm or more and less than 0.20 nm ・C: The larger of the two maximum displacement values ​​is 0.20 nm or more and less than 0.21 nm ・D: The larger of the two maximum displacement values ​​is 0.21 nm or more

[0141] <Examples 2-7> Using the suit method to obtain SiO ２ -TiO ２ A glass substrate was obtained in the same manner as in Example 1, except that the conditions for obtaining the porous glass body and the conditions for obtaining the molded body were changed as shown in the table below. Measurement and evaluation were also performed in the same manner as in Example 1.

[0142] <Results> The manufacturing conditions, measurement results, and evaluation results for the glass substrates of Examples 1 to 7 are summarized in Table 1. In Table 1, "First diagonal" refers to the diagonal passing through the first vertex, and "Second diagonal" refers to the diagonal passing through the second vertex. In Table 1, the values ​​listed in the "(1C) Left Side" column are the values ​​calculated from the left side of the above equation (1C). In Table 1, for example, "Maximum temperature difference (T Ｚ１１ , T Ｚ１９ , T Ｚ９１ , T Ｚ９９ The number in the column is T Ｚ１１ , T Ｚ１９ , T Ｚ９１ and T Ｚ９９ This shows the maximum temperature difference within the given area.

[0143]

[0144] From the results shown in Table 1, it was confirmed that the glass substrates of Examples 1 to 4, in which the value of the left side of equation (1A) is less than 0.00°C, exhibit a smaller maximum displacement and a smaller error when correcting for thermal deformation compared to the glass substrates of Examples 5 to 7, in which the value of the left side of equation (1A) is 0.00°C or greater. From a comparison between Example 1 and Examples 2 to 4, it was confirmed that the error when correcting for thermal deformation is even smaller when one or more of equations (2A), (3A), and (4A) are satisfied. Furthermore, it was confirmed that the error when correcting for thermal deformation is even smaller when equations (2A), (5A), and (6A) are satisfied. The entire contents of the specification, claims, drawings, and abstract of Japanese Patent Application No. 2024-173174, filed on October 2, 2024, are incorporated herein by reference as disclosure of the present invention.

[0145] 10 Glass substrate MS1 First main surface MS2 Second main surface S1 First side S2 Second side S3 Third side S4 Fourth side 30 Base material 32 Burner (multi-tube burner) 32a 11-tube burner 34 Central nozzle 36 First outer nozzle 38 Second outer nozzle 36a First outer nozzle 36b Second outer nozzle 36c Third outer nozzle 36d Fourth outer nozzle 36e Fifth outer nozzle 36f Sixth outer nozzle 36g Seventh outer nozzle 36h Eighth outer nozzle 36i Ninth outer nozzle 36j Tenth outer nozzle FL Flame

Claims

1. A glass substrate having a rectangular main surface, wherein the main surface is divided into nine equal parts in a direction perpendicular to a first side which is one side of the main surface, and the main surface is divided into nine equal parts in a direction perpendicular to a second side which is a side adjacent to the first side, thereby dividing the main surface into a rectangular region group composed of 81 rectangular regions. Among the rectangular region group, the zero-crossing temperature at which the thermal expansion coefficient of the glass substrate in the rectangular region whose center is located on the diagonal of the main surface passing through a first vertex which is an intersection of the first side and the second side becomes 0 ppb / K, in units of °C, in order from the side closer to the first vertex, T Ｚ１１ , T Ｚ２２ , T Ｚ３３ , T Ｚ４４ , T Ｚ５５ , T Ｚ６６ , T Ｚ７７ , T Ｚ８８ , and, T Ｚ９９ When it is set as, a glass substrate that satisfies the following formula (1A). (1A) (T Ｚ１１ + T Ｚ９９ ) - (T Ｚ２２ + T Ｚ８８ ) < 0.00 2. A glass substrate according to claim 1, satisfying the following formula (2A). (2A) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ３３ +T Ｚ７７ ) > -1.00 3. A glass substrate according to claim 1 or 2, satisfying the following formula (3A). (3A) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ４４ +T Ｚ６６ ) > 0.00 4. A glass substrate according to claim 1 or 2, satisfying the following formula (4A). (4A) (T Ｚ２２ +T Ｚ８８ ) - 2 × T Ｚ５５ >0.00 5. A glass substrate according to claim 1 or 2, satisfying the following formulas (2A), (5A), and (6A). (2A) (T Ｚ２２ +T Ｚ８８ )-(T Ｚ３３ +T Ｚ７７ )>-1.00 (5A) (T Ｚ３３ +T Ｚ７７ )-(T Ｚ４４ +T Ｚ６６ )>0.00 (6A) (T Ｚ４４ +T Ｚ６６ ) - 2 × T Ｚ５５ >0.00 6. The glass substrate according to claim 1 or 2, wherein the distribution of the zero crossover temperature in the rectangular region is point-symmetric with respect to the intersection of the diagonals of the main surface.

7. Among the group of rectangular regions, the zero crossover temperature in the rectangular region whose center is located on the diagonal of the main plane passing through the fourth vertex, which is the intersection point of the fourth side opposite the second side and the first side, is determined in order from the one closest to the fourth vertex as follows: T Ｚ１９ , T Ｚ２８ , T Ｚ３７ , T Ｚ４６ , T Ｚ５５ , T Ｚ６４ , T Ｚ７３ , T Ｚ８２ , and, T Ｚ９１ The glass substrate according to claim 1 or 2, which satisfies the following requirements 1, 2, 3, and 4. Requirement 1: The zero crossover temperature T Ｚ１１ , T Ｚ１９ , T Ｚ９１ , and, T Ｚ９９ The maximum temperature difference within is 2.00°C or less. Requirement 2: The zero crossover temperature T Ｚ２２ , T Ｚ２８ , T Ｚ８２ , and, T Ｚ８８ The maximum temperature difference within is 2.00°C or less. Requirement 3: The zero crossover temperature T Ｚ３３ , T Ｚ３７ , T Ｚ７３ , and, T Ｚ７７ The maximum temperature difference within is 2.00°C or less. Requirement 4: The zero crossover temperature T Ｚ４４ , T Ｚ４６ , T Ｚ６４ , and, T Ｚ６６ The maximum temperature difference within the area is 2.00°C or less.

8. Of the group of rectangular regions, the zero crossover temperature in the rectangular region whose center is located on the diagonal of the main plane passing through the fourth vertex, which is the intersection point of the fourth side opposite the second side and the first side, is expressed in units of °C, starting from the region closest to the fourth vertex, as follows: Ｚ１９ , T Ｚ２８ , T Ｚ３７ , T Ｚ４６ , T Ｚ５５ , T Ｚ６４ , T Ｚ７３ , T Ｚ８２ , and, T Ｚ９１ The glass substrate according to claim 1 or 2, wherein the following formula (1B) is satisfied. (1B) (T Ｚ１９ +T Ｚ９１ )-(T Ｚ２８ +T Ｚ８２ ) < 0.00 9. The glass substrate according to claim 1 or 2, wherein the maximum temperature difference of the zero crossover temperature in each of the rectangular regions of the group of rectangular regions is 1.00°C or more.

10. The glass substrate according to claim 1 or 2, wherein the average value of the zero crossover temperature in each of the rectangular regions of the group of rectangular regions is 18.00°C or higher.

11. A mask blank for EUV lithography having a glass substrate according to claim 1 or 2.

Images