Homogeneous silica-titanium oxide glass

Abstract

Glass comprising titanium oxide and silica is disclosed. A relationship diagram of an average hydroxyl concentration of each of the plurality of segments to a distance along the glass provides y = Ax2 + Bx + C where A (in ppm / mm2) ranges from about 0.0 to about-0.1, B (in ppm / mm) ranges from about-10 to about 10, C (in ppm) is about 450 or less, y is the average hydroxyl concentration (in ppm), and x is the distance (in mm), where B is the average hydroxyl concentration (in ppm), and C is the distance (in mm). The pattern extends along the glass such that the hydroxyl concentration of each section is measured using transmitted Fourier transform infrared spectroscopy, and the pattern extends a distance of about 50 mm or greater along the glass.

Description

[0001] This application claims the benefit of priority to Netherlands Patent Application No. 2033057 filed on September 16, 2022, which claims the benefit of priority to U.S. Provisional Application Serial No. 63 / 401,334 filed on August 26, 2022, the contents of which are relied upon herein and are incorporated herein by reference in their entirety, respectively. Technical Field

[0002] The present disclosure pertains to titania-doped silica glass, and more particularly, to titania-doped silica glass with increased homogeneity to produce glass articles. The glass articles may be suitable for extreme ultraviolet lithography applications. Background Art

[0003] Extreme ultraviolet (EUV) lithography uses optics to illuminate, project, and reduce pattern images to form integrated circuit patterns. The benefit of using extreme ultraviolet radiation is that smaller integrated circuit features can be achieved. Currently, optics for EUV lithography are made from low thermal expansion glasses (e.g., silica-titania glasses). The glass is usually made by a flame hydrolysis process, in which a high-purity precursor is injected into a flame to form fine glass particles. The fine glass particles can then be formed into products by axial pressing, radial pressing, or cold isostatic pressing. In such flame hydrolysis processes, the glass is formed into fine glass particles.

[0004] In EUV lithography systems, glass is often coated with a reflective surface to form a mirror. In addition, in EUV lithography systems, the glass must be able to meet the stringent thermal expansion requirements in the system. Specifically, the glass must be able to maintain its surface shape (called "figure") when subjected to temperature changes in the system. Temperature-stable glass is required to avoid any distortion induced in the wavefront characteristics of EUV projection optics. Summary of the invention

[0005] Embodiments of the present disclosure provide glass bodies that can advantageously maintain their profile during operation of an EUV lithography system.Thus, glass bodies according to embodiments of the present disclosure reduce or prevent any wavefront properties of EUV projection optics.

[0006] According to a first aspect, embodiments of the present disclosure are directed to a glass comprising titanium oxide and silicon dioxide. A plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is provided as follows: y=Ax 2 +Bx+C, where A (unit: ppm / mm 2) ranges from about 0.0 to about -0.1, B (in ppm / mm) ranges from about -10 to about 10, C (in ppm) is about 450 or less, y is the average hydroxyl concentration (in ppm), and x is the distance (in mm), thereby using transmission Fourier transform infrared spectroscopy to measure the hydroxyl concentration of each segment, and the graph extends along the glass for a distance of about 50 mm or more.

[0007] According to a second aspect, embodiments of the present disclosure are directed to a glass comprising titanium oxide and silicon dioxide. A plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is provided as follows: y=Ax 2 +Bx+C, where A (unit: ppm / mm 2 ) ranges from about 0.0 to about -0.1, B (in ppm / mm) ranges from about -10 to about 10, C (in ppm) is about 800 ppm or greater, y is the average hydroxyl concentration (in ppm), and x is the distance (in mm), thereby using transmission Fourier transform infrared spectroscopy to measure the hydroxyl concentration of each segment, and the graph extends along the glass for a distance of about 50 mm or greater.

[0008] According to a third aspect, embodiments of the present disclosure are directed to a glass comprising titanium oxide and silicon dioxide. A plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is provided as follows: y=Ax 2 +Bx+C, where A (unit: ppm / mm 2 ) ranges from about 0.0 to about -0.1, B (in ppm / mm) ranges from about -10 to about 10, C (in ppm) is not limited, y is the average hydroxyl concentration (in ppm), and x is the distance (in mm), thereby using transmission Fourier transform infrared spectroscopy to measure the hydroxyl concentration of each segment, and the graph extends along the glass for a distance of about 50 mm or more.

[0009] Additional features and advantages are set forth in the following detailed description, and in part will be readily apparent to those skilled in the art or may be learned by practicing the embodiments described in the written description and claims hereof as well as the accompanying drawings.

[0010] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework for understanding the nature and character of the claims.

[0011] The accompanying drawings provide a further understanding, and the drawings are incorporated in and constitute a part of this specification. The drawings are schematic of selected aspects of the specification and, together with the description, are used to explain the principles and operations of the methods, products and compositions pertaining to the specification. The features shown in the drawings are schematic of selected embodiments of the present invention and are not necessarily drawn to scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] While the specification and claims conclude and particularly point out and distinctly claim the subject matter of the present specification, it is believed that the following description will be better understood in conjunction with the accompanying drawings, wherein:

[0013] Figure 1 showing an exemplary glass body according to an embodiment disclosed herein;

[0014] Figure 2A Showing the embodiment disclosed in this article Figure 1 A cross section of a sample of a glass body;

[0015] Figure 2B Showing the embodiment disclosed in this article Figure 1 another cross-section of a sample of the glass body having a peripheral lip;

[0016] Figure 3 showing a graph of hydroxyl concentration versus length for the sample of FIG. 2 according to an embodiment disclosed herein;

[0017] Figure 4 shows a graph of titanium oxide concentration versus length for the sample of FIG. 2 according to an embodiment disclosed herein;

[0018] Figure 5 shows a zero temperature crossing versus length graph for the sample of FIG. 2 according to an embodiment disclosed herein;

[0019] Figure 6 shows a graph of refractive index versus length for the sample of FIG. 2 according to an embodiment disclosed herein;

[0020] Figure 7 shows a graph of coefficient of thermal expansion versus length for the sample of FIG. 2 according to embodiments disclosed herein;

[0021] Fig. 8A showing a cross-section of an exemplary sample of a glass body divided into a plurality of segments and the hydroxyl concentration of each segment according to embodiments disclosed herein;

[0022] Figure 8B show Fig. 8A The best-fit parabolic curve of the hydroxyl concentration in each segment;

[0023] Fig.9AAnother cross-section showing an exemplary sample of a glass body divided into a plurality of segments and the hydroxyl concentration of each segment according to embodiments disclosed herein;

[0024] Fig. 9B show Fig.9A The best-fit parabolic curve of the hydroxyl concentration in each segment;

[0025] Fig. 10A Another cross-section showing an exemplary sample of a glass body divided into a plurality of segments and the hydroxyl concentration of each segment according to embodiments disclosed herein;

[0026] Fig. 10B show Fig. 10A Two best-fit parabolic curves of hydroxyl concentration in each segment;

[0027] Fig.11 Showing a process for forming a glass body according to an embodiment disclosed herein;

[0028] Fig.12 Schematic representation of the adoption Fig.11 A system for producing a glass body using a process; and

[0029] Figure 13-16 A cross section of an exemplary sample of a glass body divided into a plurality of segments according to embodiments disclosed herein and a hydroxyl concentration of each segment are respectively shown. DETAILED DESCRIPTION

[0030] The present disclosure relates to glass with improved homogeneity and uniformity. Embodiments of the present disclosure provide glass having substantially uniform hydroxyl and titanium oxide concentrations across the length and width of the glass. The glass may be ultra-low expansion glass ( glass), manufactured by Corning Incorporated, and which is suitable for EUV applications.

[0031] EUV lithography relies on an optical projection system to expose a reflective photomask with EUV light so that the light reflected from the photomask is directed to a photosensitive thin layer deposited on the surface of a semiconductor wafer. This technology is commonly used in semiconductor device production processes. EUV lithography systems operate at a light wavelength of about 13.5nm. This extremely short wavelength presents many challenges for the design of EUV systems. For example, the reflective coating on the mirror substrate in the EUV system cannot reflect all light with such a low wavelength. About 30% of the light is absorbed by the reflective coating instead of being reflected. The absorbed light generates undesirable heat in the mirror substrate, causing the mirror substrate to thermally expand or contract. Such changes in the mirror substrate can in turn cause the reflective coating on the mirror substrate to deform, which causes distortion in the wavefront of the reflected light. Wavefront distortion may cause resolution degradation of the EUV system and errors in the pattern formed on the photosensitive layer.

[0032] Mirror substrates must therefore be able to maintain their shape and form, even when subjected to the harsh thermal loads of an EUV system. Currently, silica-titania glasses (e.g. Glass) is the material option for mirror substrates in EUV systems.

[0033] However, even for For glass, it is also necessary to reduce the coefficient of thermal expansion (CTE) of the glass substrate in the EUV system. A low CTE at room temperature is critical to achieving that the shape of the glass substrate remains substantially constant when heated in the EUV system. Modifiers can be added to the glass substrates to reduce their CTE. However, it is known that such modifiers reduce the homogeneity of the glass. Homogeneous glass with uniform composition is also important so that the glass can be easily polished and has favorable thermal expansion behavior throughout the glass body. For example, a glass substrate with localized areas of different titanium oxide concentrations will polish unevenly because areas with different titanium concentrations in the glass substrate polish at different rates.

[0034] Embodiments of the present disclosure provide homogeneous glass substrates having uniform composition while maintaining an overall low CTE value. Specifically, the glass substrates provided by embodiments of the present disclosure have a uniform hydroxyl concentration. In addition or alternatively, the glass substrates provided by embodiments of the present disclosure have a uniform titanium oxide concentration. Such uniform concentrations provide glass substrates that can be easily polished while maintaining an overall low CTE value.

[0035] Another important characteristic of the glass substrate in an EUV system is the temperature at which the CTE of the glass substrate is exactly equal to zero. This temperature is called the zero crossing temperature and is denoted as Tzc. The glass substrate in an EUV system should ideally have a Tzc value close to the temperature of the glass substrate when it is exposed to the EUV light of the EUV system. When the Tzc value matches (or is close to) this temperature, the glass substrate will experience minimal expansion (and therefore minimal shape distortion) during operation of the EUV system.

[0036] It is also noted that (at the typical fictive temperature range) Tzc is directly related to the hydroxyl and titania concentrations in the glass substrate. Thus, as the titania concentration increases, Tzc also increases. However, hydroxyl is negatively correlated to Tzc, so that as the hydroxyl concentration increases, Tzc decreases. It is also noted that the hydroxyl concentration has a greater effect on Tzc than the titania concentration.

[0037] As used herein, "ppm" means parts per million by weight.

[0038] As used herein, unless otherwise specified, the term "hydroxyl" or OH means a radical consisting of an oxygen atom and a hydrogen atom (11 As used herein, n(OH) represents the total number of OH or hydroxyl moieties in a material.

[0039] Figure 1 An exemplary glass body 10 is shown having a length (L), a width (W), and a height (H). In some embodiments, the length and the width may be respectively greater than the height (H). For example, the length (L) and the width (W) may be respectively about 2000 mm or less, or about 1700 mm or less, or about 1500 mm or less, or about 1200 mm or less, or about 1000 mm or less, or 700 mm or less, or about 500 mm or less, or about 450 mm or less, or about 400 mm or less, or about 350 mm or less, or about 300 mm or less, or about 250 mm or less, or about 200 mm or less, or about 150 mm or less, or about 100 mm or less, or about 75 mm or less, or about 50 mm or less, or about 25 mm or less, or about 20 mm or less, or about 15 mm or less. Additionally or alternatively, the length and width of the glass body 10 are respectively about 15 mm or more, or about 20 mm or more, or about 25 mm or more, or about 50 mm or more, or about 75 mm or more, or about 100 mm or more, or about 150 mm or more, or about 200 mm or more, or about 250 mm or more, or about 300 mm or more, or about 350 mm or more, or about 400 mm or more, or about 450 mm or more, or about 500 mm or more, or about 700 mm or more, or about 1000 mm or more, or about 1200 mm or more, or about 1500 mm or more, or about 1700 mm or more, or about 2000 mm or more. In some embodiments, both the length and the width are about 150 mm, about 152 mm, or about 179 mm, or about 530 mm, or about 1200 mm. However, it is contemplated that in some embodiments the length may be different than the width.

[0040] In addition, the height (H) can be less than each of the length and width. In some embodiments, the height is: about 400 mm or less, or about 350 mm or less, or about 300 mm or less, or about 250 mm or less, or about 200 mm or less, or about 150 mm or less, or about 100 mm or less, or about 75 mm or less, or about 50 mm or less, or about 25 mm or less, or about 20 mm or less, or about 15 mm or less, or about 10 mm or less, or about 5 mm or less. In addition or alternatively, the height is: about 5mm or more, or about 10mm or more, or about 15mm or more, or about 20mm or more, or about 25mm or more, or about 50mm or more, or about 75mm or more, or about 100mm or more, or about 150mm or more, or about 200mm or more, or about 250mm or more, or about 300mm or more, or about 350mm or more, or about 400mm or more. In some embodiments, the height is: about 63mm, or about 150mm, or about 152mm.

[0041] In some embodiments, the glass body 10 has a mass of 2.0 kg or more, or about 2.5 kg or more, or about 5 kg or more, or about 15 kg or more, or about 20 kg or more, or about 30 kg or more, or about 50 kg or more, or about 100 kg or more, or about 150 kg or more, or about 200 kg or more, or about 300 kg or more, or about 400 kg or more, or about 500 kg or more.

[0042] The glass body 10 may be a substrate to which one or more additional layers or coatings may be applied. Figure 1 As shown, the body 10 includes at least one sub-portion, such as a sample 15, having a length and a width that are respectively equal to the length and the width of the body 10. However, the height (h) of the sample 15 can be less than the height (H) of the body 10. In some embodiments, the height of the sample 15 is: about 200 mm or less, or about 150 mm or less, or about 100 mm or less, or about 75 mm or less, or about 50 mm or less, or about 25 mm or less, or about 20 mm or less, or about 15 mm or less, or about 10 mm or less, or about 5 mm or less. In some embodiments, the height (h) is about 7.62 mm. In some embodiments, it is also contemplated that the height (h) of the sample 15 can be equal to the height (H) of the body 10.

[0043] Sample 15 can be a glass body and / or a glass substrate. Body 10 (and also sample 15) can be a titanium oxide doped silica glass. In some embodiments, body 10 can be produced by a precursor comprising, for example, octamethylcyclotetrasiloxane and titanium tetraisopropoxide. It is also contemplated that body 10 can include one or more additional modifiers and / or additives.

[0044] The silicon dioxide (SiO2) concentration in the body 10 can be: about 80 weight % or greater, or about 85 weight % or greater, or about 90 weight % or greater, or about 92 weight % or greater, or about 95 weight % or greater, or about 97 weight % or greater, or about 98 weight % or greater, or about 99 weight % or greater, or about 85 weight % to about 97 weight %, or about 90 weight % to about 95 weight %.

[0045] As discussed above and with reference to Figure 1 , the body 10 includes at least one sample 15, which forms a sub-portion of the body 10. Figure 1 In the embodiment of the present invention, the sample 15 is a cross-sectional sub-portion of the body 10, so that the height (h) of the sample 15 extends along the height (H) of the body 10. It is also noted that the height (H) of the body 10 is less than its width (W) and length (L), so that the sample 15 forms a cross-sectional sub-portion along the smallest dimension of the body 10 (along its height (H)). The smallest dimension of the body 10 can also be referred to as the characteristic length of the body, as discussed further below, so that the sample 15 extends along the characteristic length of the body 10. Figure 1 In some embodiments, the body 10 includes multiple samples along its height (H). However, in other embodiments, it is also considered that one sample 15 extends the entire height (H) of the body 10. In these embodiments, the body 10 only includes one sample 15 so that the one sample 15 forms the entire body 10.

[0046] although Figure 1 The main body 10 and the sample 15 are shown as square components with flat surfaces, but it is also considered in embodiments that the main body 10 and / or the sample 15 include other shapes. For example, the outer contour of the main body 10 and / or the sample 15 can be circular or oval or asymmetrical. In addition, the main body 10 and / or the sample 15 can be bent to form a concave or convex structure. In an exemplary embodiment, the main body 10 is formed by a single sample 15 (so that the single sample 15 extends the entire length, width and height of the main body 10) and the main body 10 has a concave structure. The sample 15 can be a photomask, a photomask, a mirror and / or a photomask or photomask holder.

[0047] Each sample 15 has a substantially uniform concentration of hydroxyl (OH) and titanium oxide (TiO2) across the length and width of the sample. To determine the uniformity of the sample in the body, each sample is divided into a plurality of sections across the length and width of the sample. For example, Figure 2A The sample 15 is shown divided into a plurality of sections 20 across the cross-sectional length (L) and width (W) of the sample 15. The concentration of one or more components (e.g., hydroxyl, titanium oxide) can then be determined for each section 20, thereby determining the uniformity of each of these components along the sample 15. For example, the hydroxyl concentration can be measured for each section 20, thereby determining the hydroxyl concentration uniformity across the cross section of the sample 15. Additionally, the titanium oxide concentration can be determined for each section 20, thereby determining the titanium oxide concentration uniformity across the cross section of the sample 15. As discussed further below, the concentration of the one or more components is determined throughout the full thickness (h) of each section 20.

[0048] although Figure 2A The segments 20 are shown extending along the entire length (L) and width (W) of the sample 15, but it is also contemplated that portions of the sample 15 include segments 20 that may extend along less than the entire cross-sectional length (L) and width (W). Figure 2B As shown, the sample 15 may include a peripheral lip 17 on which no segment 20 is formed. Therefore, the peripheral lip 17 can be the clearance between the end of the segment 20 and the outer edge of the sample 15. In an embodiment, the peripheral lip can extend to a length (L") of about 2 mm to about 20 mm, or about 4 mm to about 16 mm, or about 5 mm to about 16 mm, or about 8 mm to about 14 mm, or about 10 mm to about 12 mm. In some embodiments, the length (L") is about 12.5 mm or about 12.7 mm.

[0049] The section 20 can be a contiguous section on a specific length and width of the sample 15, so that the section 20 spans the entire area formed by the specific length and width. As discussed above, the specific length and width can be equal to or less than the length (L) and width (W) of the sample 15. In an embodiment, the segments 20 are adjacent segments in the length and width of the sample 15 (with no gaps therebetween) such that the length and width are, respectively, about 25 mm or more, or about 30 mm or more, or about 40 mm or more, or about 50 mm or more, or about 60 mm or more, or about 75 mm or more, or about 100 mm or more, or about 125 mm or more, or about 150 mm or more, or about 175 mm or more, or about 180 mm or more, or about 190 mm or more, or about 200 mm or more, or about 250 mm or more, or about 500 mm or more, or about 700 mm or more, or about 800 mm or more, or about 900 mm or more, or about 1000 mm or more, or about 1100 mm or more, or about 1200 mm or more, or about 1500 mm or more, or about 1700 mm or more, or about 2000 mm or more. In some embodiments, section 20 is a contiguous section of the length and width of sample 15, such that the length and width are approximately 530 mm or approximately 1200 mm, respectively.

[0050] When the sample 15 comprises a flat surface, the segment 20 is formed along the flat surface, such as Figure 2A However, when the sample 15 includes a concave or convex surface, the segment 20 is formed along the curved surface of the sample 15 .

[0051] like Figure 2A As shown, each segment 20 has a length (L') and a width (W') of approximately 12.7 mm, respectively. However, embodiments of the present disclosure encompass other length (L') and width (W") values ​​and are not limited to 12.7 mm. It is also contemplated that in embodiments the length (L') is not equal to the width (W'). Further, it is noted that in some embodiments, the (L') and width (W') of the segment 20 may be equal to the length (L") of the peripheral lip 17.

[0052] The height of each section 20 is the height (h) of the sample 15, as discussed above. Thus, in an embodiment, the height h is about 7.62 mm.

[0053] As discussed above, the concentration of one or more components in each segment 20 can be determined. Thus, for example, the hydroxyl concentration and / or titanium oxide concentration can be determined for each adjacent segment 20 in the sample 15. When each segment 20 has a length and width of 12.7 mm, the concentration of the component is determined at a frequency of 12.7 mm across the cross section of the sample 15. For example, the hydroxyl concentration is measured at a frequency of 12.7 mm across the cross section of the sample 15.

[0054] The hydroxyl concentration of each segment 20 is measured using transmission Fourier transform infrared spectroscopy ("FTIR"). As used herein, "transmission" means that light is directed through the glass body to be measured to determine the hydroxyl concentration (rather than using light reflected from the body to be measured to determine the hydroxyl concentration). Therefore, "transmission" requires a non-scattering surface. Once the sample 15 is loaded into the FTIR for measurement, beam alignment and background measurements can be performed first. The FTIR then measures the basic absorption peak of hydroxyl, which measures the peak height relative to the background signal, which is a straight line between points around the absorption peak. The absorption peak height is then divided by the thickness (h) of the sample 15 to obtain the absorption coefficient β OH Then, the absorption coefficient β is calculated using the following equation: OH The hydroxyl concentration is obtained:

[0055] C=β OH / εx MW OH / D Glass x106

[0056] Where C is the hydroxyl concentration (in ppm) for a particular segment 20, β OH is the absorption coefficient of glass, ε is the absorption coefficient of hydroxyl group at 3670 cm -1 The molar absorption coefficient of the absorption peak at the wave number, MW OH is the molecular weight of the hydroxyl group (g / mole), and D is the density of the hydroxyl group (g / cm 3 ). KM Davis et al., "Quantitative infrared spectroscopic measurement of hydroxyl concentration in silica glass", Journal of Non-Crystalline Solids, 203 (1996) 27-36, further discloses the FTIR analysis disclosed above, which is incorporated herein by reference. As discussed above, the hydroxyl concentration of each section 20 of the sample 15 is measured and the measurement is performed throughout the entire thickness (h) of each section 20. The hydroxyl concentration measurement is then repeated on all sections 20 of the sample 15.

[0057] The titanium oxide concentration of each segment 20 is calculated based on the refractive index measured for each segment 20. More specifically, the refractive index is measured using an optical interferometer operating at a wavelength of 633 nm. Specifically, the optical interferometer is a Zygo Verifire HD purchased from Zygo Corporation, equipped with a 270 micron pixel size resolution and operating at a wavelength of 633 nm. The optical interferometer is set so that the pixel is a square with a size of 270 microns x 270 microns, and each pixel extends through the entire thickness (h) of the sample 15. The refractive index is measured for each pixel in the segment 20 and through the entire thickness of the pixel. Then, the refractive indices measured for each pixel in the segment 20 are averaged together to determine the average refractive index of each segment 20. The refractive index measurement is then repeated on all segments 20 of the sample 15.

[0058] Then, the average titanium oxide concentration of each segment 20 is determined based on the average refractive index of each segment 20 using the following relationship:

[0059] 55ppm RI=0.0125% C Ti

[0060] Where RI is the average refractive index of each segment 20, and C Ti is the average concentration of titanium oxide (in weight %) per segment 20. Note that the above relationship assumes that the only contribution to the change in refractive index is from titanium oxide.

[0061] Furthermore, the average CTE of each segment 20 is determined from the average refractive index of each segment 20 using the following relationship:

[0062] 55ppm RI=1ppb / K CTE

[0063] Where RI is the average refractive index of each segment 20, and CTE is the average coefficient of thermal expansion (in ppb / K) of each segment 20. Note that the above relationship assumes that the only influence on the refractive index change comes from CTE.

[0064] Furthermore, the Tzc of each segment 20 is determined from the CTE of each segment 20 using the following relationship:

[0065] ΔCTE / CT slope = ΔTzc

[0066] Where ΔCTE is the deviation of the CTE of a particular segment 20 from the average CTE of all segments 20 (in ppb / K), and CTE slope is the slope of the CTE of all segments 20 as a function of temperature (in ppb / K). 2), and ΔTzc is the deviation (°C) of the Tzc of the particular segment 20 compared to the average Tzc of all segments 20. Note that the above relationship assumes that the only influence on the change in Tzc comes from CTE. In the embodiments disclosed herein, the CTE slope is: about 1.0 ppb / K 2 To about 2.5ppb / K 2 , or about 1.15ppb / K 2 To about 2.0ppb / K 2 , or about 1.2ppb / K 2 to about 1.9ppb / K 2 , or about 1.3ppb / K 2 to about 1.7ppb / K 2 .

[0067] One or more segments 20 may have different concentrations of one or more components than one or more other segments 20. For example, one or more segments 20 may have a different average concentration of hydroxyl groups than one or more other segments 20. Additionally or alternatively, one or more segments 20 may have a different average concentration of titanium oxide than one or more other segments 20. In some embodiments, segments 20 closer to the center point 18 of the sample 15 may have a higher concentration of hydroxyl groups than segments 20 closer to the perimeter edge of the sample 15. As illustrative examples, segments A, B, and C in FIG. 2 may each have a higher concentration of hydroxyl groups than segments X, Y, and Z.

[0068] In some embodiments, the hydroxyl concentration can be a gradient extending radially outward along the sample 15, with the highest hydroxyl concentration near the center point 18, such that the hydroxyl concentration of the segment gradually decreases radially outward from the center point 18. In these embodiments, the segment near the center point 18 has the highest hydroxyl concentration, while the segment near the peripheral edge of the sample 15 has the lowest hydroxyl concentration.

[0069] In other embodiments, a segment 20 closer to the perimeter edge of the sample 15 may have a higher hydroxyl concentration than other segments. For example, segments Q, R, and S in FIG. 2 may each have a higher hydroxyl concentration than segments A, B, and C and higher than segments X, Y, and Z.

[0070] It is also contemplated that in some embodiments, segments 20 all have the same (or substantially the same) hydroxyl concentration.

[0071] In addition, one or more sections 20 may have the same or different titanium oxide concentrations. In some embodiments, the titanium oxide concentrations on multiple sections 20 may be the same (or substantially the same). Thus, in some embodiments, the titanium oxide concentration may be uniformly distributed across multiple sections 20.

[0072] The average concentrations for each segment 20 may be averaged together to determine the average concentration across a cross section of the sample 15. For example, the average hydroxyl concentration for each segment 20 may be measured (as described above) and these concentrations may be averaged together to determine the average hydroxyl concentration across the entire sample 15. More specifically, in an embodiment, when the sample 15 includes 144 segments 20, the hydroxyl concentrations for these 144 segments 20 are averaged together to determine the average hydroxyl concentration across the entire sample 15. It is also noted that the average concentration across the sample 15 may extend over a particular length and width across the sample, which may be less than the entire length (L) and width (W) of the sample.

[0073] According to embodiments disclosed herein, the average hydroxyl concentration on sample 15 can be about 5 ppm or greater, or about 10 ppm or greater, or about 20 ppm or greater, or about 30 ppm or greater, or about 40 ppm or greater, or about 50 ppm or greater, or about 75 ppm or greater, or about 100 ppm or greater, or about 125 ppm or greater, or about 150 ppm or greater, or about 175 ppm or greater, or about 200 ppm or greater, or about 250 ppm or greater, or about 300 ppm or greater. Or about 300 ppm or greater, or about 400 ppm or greater, or about 500 ppm or greater, or about 600 ppm or greater, or about 700 ppm or greater, or about 800 ppm or greater, or about 900 ppm or greater, or about 1000 ppm or greater, or about 1100 ppm or greater, or about 1200 ppm or greater, or about 1300 ppm or greater, or about 1400 ppm or greater, or about 1500 ppm or greater, or about 2000 ppm or greater. Additionally or alternatively, the average hydroxyl concentration on sample 15 can be about 2000 ppm or less, or about 1500 ppm or less, or about 1400 ppm or less, or about 1300 ppm or less, or about 1200 ppm or less, or about 1100 ppm or less, or about 1000 ppm or less, or about 900 ppm or less, or about 800 ppm or less, or about 700 ppm or less, or about 600 ppm or less, or about 500 ppm or less, or about 1000 ppm or less. Or about 400 ppm or less, or about 300 ppm or less, or about 250 ppm or less, or about 200 ppm or less, or about 175 ppm or less, or about 150 ppm or less, or about 125 ppm or less, or about 100 ppm or less, or about 75 ppm or less, or about 50 ppm or less, or about 40 ppm or less, or about 30 ppm or less, or about 20 ppm or less, or about 10 ppm or less, or about 5 ppm or less.In an embodiment, the average hydroxyl concentration is in the range of about 0 ppm to about 2000 ppm, or about 200 ppm to about 1900 ppm, or about 300 ppm to about 1800 ppm, or about 400 ppm to about 1700 ppm, or about 500 ppm to about 1750 ppm, or about 600 ppm to about 1600 ppm, or about 700 ppm to about 1500 ppm, or about 800 ppm to about 1400 ppm, or about 900 ppm to about 1300 ppm, or about 1000 ppm to about 2000 ppm, or about 1000 ppm to about 1500 ppm, or about 1000 ppm to about 1 ppm, or about 1000 ppm to about 1100 ppm, or about 600 ppm to about 1500 ppm, or about 600 ppm to about 1400 ppm, or about 600 ppm to about 1300 ppm, or about 700 ppm to about 1000 ppm, or about 20 ppm to about 450 ppm, or about 50 ppm to about 200 ppm, or about 75 ppm to about 150 ppm, or about 80 ppm to about 125 ppm, or about 80 ppm to about 500 ppm, or about 80 ppm to about 400 ppm, or about 80 ppm to about 300 ppm, or about 80 ppm to about 200 ppm.

[0074] In some specific embodiments, the maximum hydroxyl concentration in the plurality of sections 20 may be in the range of about 1000 ppm to about 1400 ppm, or about 1000 ppm to about 1300 ppm, or about 1000 ppm to about 1200 ppm, or about 1000 ppm to about 1100 ppm, or about 1050 ppm to about 1100 ppm, or about 1060 ppm to about 1090 ppm. In some specific embodiments, the minimum hydroxyl concentration in the plurality of sections 20 may be in the range of about 900 ppm to about 1300 ppm, or about 900 ppm to about 1200 ppm, or about 900 ppm to about 1100 ppm, or about 1000 ppm to about 1100 ppm, or about 1050 ppm to about 1100 ppm, or about 1060 ppm to about 1080 ppm.

[0075] The average titanium oxide concentration on sample 15 can be: about 1.0 wt % to about 15.0 wt %, or about 6.0 wt % to about 12.0 wt %, or about 6.0 wt % to about 8.5 wt %, or about 6.5 wt % to about 8.0 wt %, or about 7.0 wt % to about 7.7 wt %, or about 6.5 wt % to about 7.8 wt %.

[0076] The difference between the highest and lowest average concentrations of the one or more components in the different sections 20 is also determined. More specifically, the sections 20 having the highest average concentration of a particular component (e.g., hydroxyl or titanium oxide) are compared to the sections 20 having the lowest average concentration of the particular component. The difference between the highest and lowest average concentrations of the particular component is then calculated. This difference between the highest and lowest average concentrations in the sample 15 is referred to as the peak-to-valley (PV) difference in average concentration.

[0077] Figure 3 An example graph 100 is shown showing the average hydroxyl concentration for each segment radially outward from the center of a sample 15 according to an embodiment of the present disclosure. Figure 3 is a graph extending radially outward from the center point 18 along the length of the sample 15. Figure 3 As shown in the exemplary embodiment of FIG. 1 , the position of the segment 20 having the highest average hydroxyl concentration is close to the center point 18, while the position of the segment having the lowest average hydroxyl concentration is at the radial circumferential end of the sample 15. Specifically, at Figure 3 In the example shown, the average hydroxyl concentration is Max OH The highest position and Min OH Therefore, the PV difference is at the Max OH With Min OH However, as also discussed above, the distribution of hydroxyl groups may be changed in other embodiments so that, for example, Max OH The location may be at the perimeter edge of the sample 15 and / or at the Min OH The location may be located close to the center point 18 .

[0078] The PV difference in hydroxyl concentration of section 20 in sample 15 may be about 70 ppm or less, or about 60 ppm or less, or about 55 ppm or less, or about 50 ppm or less, or about 45 ppm or less, or about 40 ppm or less, or about 35 ppm or less, or about 30 ppm or less, or about 25 ppm or less, or about 20 ppm or less, or about 15 ppm or less, or about 10 ppm or less, or about 5.0 ppm or less, or about 2.5 ppm or less, or about 1.0 ppm or less, or about 0.0 ppm. Additionally or alternatively, the PV difference in hydroxyl concentration of the segment 20 may be about 0.0 ppm or greater, or about 1.0 ppm or greater, or about 2.5 ppm or greater, or about 5.0 ppm or greater, or about 10 ppm or greater, or about 15 ppm or greater, or about 20 ppm or greater, or about 25 ppm or greater, or about 30 ppm or greater, or about 35 ppm or greater, or about 40 ppm or greater, or about 45 ppm or greater, or about 50 ppm or greater. In some embodiments, the PV difference in the average hydroxyl concentration of the segment 20 is in the range of about 0.0 ppm to about 60 ppm, or about 10 ppm to about 50 ppm, or about 15 ppm to about 45 ppm, or about 20 ppm to about 40 ppm, or about 10 ppm to about 30 ppm.

[0079] In an embodiment, the PV difference in the hydroxyl concentration of the segment 20 in the sample 15 is related to the size of the sample 15 according to the following expression: PV OH =Y x L c , where PV OH is the PV of hydroxyl groups in the sample (in ppm), and L c is the characteristic length of the sample (in cm). As used, the characteristic L c is the smallest of the length L and width W of the sample 15. Therefore, if the sample 15 contains a length L that is less than the width W, its length L is the characteristic length L c Conversely, if the sample 15 includes a width W that is less than the length L, then its width W is the characteristic length L cIn the above expression, Y (in ppm / cm2) is about 1 or more, or about 2 or more, or about 5 or more, or about 10 or more, or about 20 or more, or about 30 or more, or about 40 or more, or about 50 or more, or about 60 or more, or about 70 or more, or about 80 or more, or about 90 or more, or about 100 or more, or about 110 or more, or about 120 or more, or about 130 or more, or about 140 or more, or about 150 or more. Additionally or alternatively, Y is about 150 or less, or about 140 or less, or about 130 or less, or about 120 or less, or about 110 or less, or about 100 or less, or about 90 or less, or about 80 or less, or about 70 or less, or about 60 or less, or about 50 or less, or about 40 or less, or about 30 or less, or about 20 or less, or about 15 or less, or about 10 or less, or about 5 or less, or about 2 or less, or about 1 or less. In an embodiment, Y is in the range of about 1 to about 150, or about 2 to about 250, or about 2 to about 120, or about 3 to about 100, or about 4 to about 80, or about 5 to about 60, or about 6 to about 30, or about 7 to about 20, or about 1 to about 30, or about 2 to about 25, or about 3 to about 20, or about 1 to about 15, or about 2 to about 10, or about 5 to about 10.

[0080] Figure 4 An example graph 200 is shown showing titanium oxide concentration for each segment 20 radially outward from the center of a sample 15 in accordance with an embodiment of the present disclosure. Figure 4 is a graph extending radially outward from the center point 18 along the length of the sample 15 (similar to Figure 3 If Figure 4 As shown, the titanium oxide concentration of the segments 20 is approximately equal near the center point 18, and there is a small change in the titanium oxide concentration at the radial peripheral ends of the sample 15. However, even a small change in the titanium oxide concentration still produces a Max. Ti The maximum titanium oxide concentration at the position and the Min Ti The minimum titanium oxide concentration at the position. Therefore, the PV difference is Max Ti With Min Ti The difference in titanium oxide concentration at the position.

[0081] The PV difference in titanium oxide concentration of multiple sections 20 in sample 15 can be: about 0.0040 wt. % or less, or about 0.0035 wt. % or less, or about 0.0030 wt. % or less, or about 0.0025 wt. % or less, or about 0.0020 wt. % or less, or about 0.0015 wt. % or less, or about 0.0010 wt. % or less. In an embodiment, the PV difference in titanium oxide concentration of the plurality of segments 20 is in the range of about 0.0010 wt % to about 0.0050 wt %, or about 0.0015 wt % to about 0.0045 wt %, or about 0.0020 wt % to about 0.0040 wt %, or about 0.0025 wt % to about 0.0035 wt %, or about 0.0030 wt % to about 0.0050 wt %, or about 0.0010 wt % to about 0.0030 wt %, or about 0.0010 wt % to about 0.0025 wt %, or about 0.0010 wt % to about 0.0020 wt %.

[0082] As discussed above, the PV difference in concentration of both hydroxyl and titanium oxide is very low, thereby providing a homogenous glass body 10. With such a low PV difference, the glass body 10 can be efficiently polished to provide a uniform surface with a high degree of flatness.

[0083] Additionally, as discussed above, the average Tzc, average refractive index, and average CTE are determined for each segment 20. These properties of one or more segments 20 may differ from one or more other segments 20. Thus, for example, the average Tzc and / or average refractive index of a first segment 20 may differ from that of a second segment 20.

[0084] Figure 5 An example graph 300 is shown showing the average Tzc for each segment 20 radially outward from the center of the sample 15 according to an embodiment of the present disclosure. Figure 4 is a graph 300 extending radially outward from the center point 18 along the length of the sample 15 (similar to Figure 3 and Figure 4 If Figure 5 As shown in the exemplary embodiment of FIG. 1 , the position of the segment 20 with the lowest average Tzc is close to the center point 18, while the position of the segment with the highest average Tzc is at the perimeter end of the sample 15. Specifically, at Figure 5 In the exemplary graph 300 shown, the average Tzc is at Max Tzc The highest position and Min TZC The position is the lowest. Therefore, the PV difference is Max Tzc With Min TZCHowever, the distribution of average Tzc may be changed in other embodiments, so that, for example, Max TZC The location may be at the perimeter edge of the sample 15 and / or at the Min TZC The position may be located at a center point 18 .

[0085] The PV difference of the average Tzc in multiple sections 20 on the sample 15 can be: about 0.050°C to about 0.300°C, or about 0.075°C to about 0.250°C, or about 0.080°C to about 0.200°C, or about 0.100°C to about 0.190°C, or about 0.120°C to about 0.180°C, or about 0.140°C to about 0.160°C, or about 0.050°C to about 0.180°C, or about 0.100°C to about 0.140°C.

[0086] Due to the low PV difference in the average Tzc among the plurality of segments 20, the glass body 10 is able to maintain its surface shape ("profile") when subjected to temperature changes in an EUV lithography system.

[0087] Also note that when comparing Figure 3 and 5 , Max OH Min position on sample 15 Tzc Therefore, in these embodiments, the segment 20 (segments 20) having the maximum hydroxyl concentration also has the minimum Tzc. In addition, in these embodiments, the segment 20 having a relatively high hydroxyl concentration has a relatively low Tzc.

[0088] The average Tzc of the plurality of zones 20 on the sample 15 may be in the range of about 20°C to about 60°C, or about 25°C to about 55°C, or about 30°C to about 50°C, or about 35°C to about 45°C, or about 40°C to about 45°C, or about 20°C to about 45°C, or about 20°C to about 40°C, or about 10°C to about 50°C.

[0089] Figure 6 An example graph 400 is shown of the average refractive index of a plurality of segments 20 radially outward from the center of a sample 15 in accordance with an embodiment of the present disclosure. Figure 6 is a graph 400 extending radially outward from the center point 18 along the length of the sample 15 (similar to Figure 3-5 In addition, when (such as Figure 4 Compared with the graph 200 shown in FIG. 1 , the average refractive index of the plurality of segments 20 on the sample 15 is similar to the average concentration of titanium oxide in the plurality of segments 20 on the sample 15. Figure 6As shown, the average refractive index is approximately equal near the center point 18, and has a small change in the average refractive index at the radial peripheral ends of the sample 15. However, the small change in the average refractive index still produces a Max RI The maximum amount at the position and the Min RI Therefore, the PV difference is the Max RI With Min RI The difference in average refractive index at each location.

[0090] The PV difference of the average refractive index of the plurality of segments 20 on the sample 15 may be: about 1x10 -4 or smaller, or about 5x10 -5 or smaller, or about 1x10 -5 or smaller, or about 5x10 -6 or smaller, or about 1x10 -6 or smaller, or about 5x10 -7 or smaller, or about 1x10 -7 or smaller, or about 1x10 -6 About 1x10 -4 , or about 6x10 -6 About 9x10 -5 , or about 10x10 -6 About 6x10 -5 , or about 1x10 -6 About 1x10 -5 , or about 1x10 -5 About 1x10 -4 The refractive index distribution in a glass body is an indicator of the titanium oxide concentration distribution of the glass body. Therefore, a glass body having a smaller PV difference of refractive index will also have a smaller PV difference of titanium oxide. As discussed above, a smaller PV difference of titanium oxide enables the glass body to be polished more uniformly.

[0091] Figure 7 An example graph 500 is shown showing the average CTE of a plurality of segments 20 radially outward from the center of a sample 15 in accordance with an embodiment of the present disclosure. Figure 7 is a graph 500 (similar to Figure 3-6 In addition, when (such as Figure 4 200 and (as shown in FIG. Figure 6 Compared with the graph 400 shown in FIG. 4A , the average CTE of the plurality of segments 20 on the sample 15 is similar to the average concentration of titanium oxide in the plurality of segments 20 and is similar to the average refractive index of the plurality of segments 20 on the sample 15. Figure 7As shown, the average CTE is approximately equal near the center point 18, and there is a small change in the average CTE at the radial circumferential ends of the sample 15. However, the small change in the average CTE still produces a Max. CTE The maximum amount at the position and the Min CTE Therefore, the PV difference is the Max CTE With Min CTE The difference in average CTE at the locations.

[0092] The PV difference of the average CTE of the plurality of sections 20 on the sample 15 may be about 0.30 ppb / K or less, or about 0.25 ppb / K or less, or about 0.20 ppb / K or less, or about 0.15 ppb / K or less, or about 0.12 ppb / K or less, or about 0.10 ppb / K or less, or about 0.05 ppb / K or less. In an embodiment, the PV difference of the average CTE of the plurality of sections 20 on the sample is in the range of about 0.05 ppb / K to about 0.25 ppb / K, or about 0.07 ppb / K to about 0.20 ppb / K, or about 0.08 ppb / K to about 0.18 ppb / K, or about 0.09 ppb / K to about 0.16 ppb / K, or about 0.10 ppb / K to about 0.15 ppb / K.

[0093] The average CTE of each segment 20 at a temperature of 288K to 303K is about -30ppb / K to about +30ppb / K. In some embodiments, the CTE is about -10ppb / K to about +10ppb / K at a temperature of 288K to 303K, or about -5ppb / K to about +5ppb / K at a temperature of 288K to 303K, or about -2ppb / K to about +2ppb / K at a temperature of 288K to 303K.

[0094] See again Figure 3 , the average hydroxyl concentration of the plurality of sections 20 along the sample 15 plotted as a function of distance along the sample 15 forms a parabolic curve. Figure 3 In a particular embodiment of the parabolic curve, the parabolic curve is centered at a center point 18, such that the slope of the curve begins downward from this center point. However, in other embodiments, it is also contemplated that the average hydroxyl concentration along multiple sections 20 of the sample 15 can form a parabolic curve with other profiles and shapes.

[0095] In an embodiment, the average hydroxyl concentration of the plurality of sections 20 along the length of the sample 15 forms a parabolic curve represented by the following equation:

[0096] y=Ax 2 +Bx+C,

[0097] Where y represents the average hydroxyl concentration in a particular segment 20 (in ppm), x represents the distance along the sample 15 (in mm), and A is a quadratic term and has units of ppm / mm 2 , B is a linear term and has a unit of ppm / mm, and C is a constant and has a unit of ppm. In some embodiments, the parabolic curve has a Gaussian distribution symmetrical about the point x=0. Thus, the parabolic curve can be a bell-shaped curve. In other embodiments, the parabolic curve is asymmetric and can have other distribution functions.

[0098] In an embodiment, A defines the slope and steepness of the parabolic curve and is in the range of: about -20 ppm / mm 2 To about 20ppm / mm 2 , or about -15ppm / mm 2 To about 15ppm / mm 2 , or about -10ppm / mm 2 To about 10ppm / mm 2 , or about -5ppm / mm 2 To about 5ppm / mm 2 , or about -2.5ppm / mm 2 To about 2.5ppm / mm 2 , or about -20ppm / mm 2 To about 5ppm / mm 2 , or about -20ppm / mm 2 To about 2ppm / mm 2 , or about -20ppm / mm 2 To about 0.5ppm / mm 2 , or about -20ppm / mm 2 To about 0ppm / mm 2 , or about -20ppm / mm 2 To about -0.1ppm / mm 2 , or about -20ppm / mm 2 To about -0.25ppm / mm 2 , or about -20ppm / mm 2 To about -0.5ppm / mm 2 , or about -10ppm / mm 2 To about -0.1ppm / mm 2 , or about -5ppm / mm 2 To about -0.1ppm / mm 2 , or about -2ppm / mm 2 To about -0.1ppm / mm 2, or about -1.8ppm / mm 2 To about -0.2ppm / mm 2 , or about -1.6ppm / mm 2 To about -0.4ppm / mm 2 , or about -1.2ppm / mm 2 To about -0.8ppm / mm 2 , or about -1.8ppm / mm 2 To about -1.0ppm / mm 2 , or about -1.6ppm / mm 2 To about -1.0ppm / mm 2 , or about -1.0ppm / mm 2 To about 1.0ppm / mm 2 , or about -0.5ppm / mm 2 To about 0.5ppm / mm 2 , or about -0.25ppm / mm 2 To about 0.25ppm / mm 2 , or about -0.2ppm / mm 2 To about 0.2ppm / mm 2 , or about -0.2ppm / mm 2 To about -0.1ppm / mm 2 , or about -0.2ppm / mm 2 To about -0.8ppm / mm 2 , or about -0.2ppm / mm 2 To about 0.6ppm / mm 2 , or about 0.0ppm / mm 2 To about -0.1ppm / mm 2 , or about 0.0ppm / mm 2 To about -0.04ppm / mm 2 , or about 0.0ppm / mm 2 To about -0.02ppm / mm 2 , or about 0.0ppm / mm 2 To about -0.01ppm / mm 2 , or about -0.01ppm / mm 2 To about -0.04ppm / mm 2 , or about -0.01ppm / mm 2 To about -0.02ppm / mm 2 , or about -0.02ppm / mm 2 To about -0.04ppm / mm 2In some embodiments, A is: about -0.2 ppm / mm 2 , or about -1.5ppm / mm 2 , or about -1.6ppm / mm 2 , or about -1.9ppm / mm 2 .

[0099] In an embodiment, B is in the range of about -50 ppm / mm to about 50 ppm / mm, or about -40 ppm / mm to about 40 ppm / mm, or about -30 ppm / mm to about 30 ppm / mm, or about -20 ppm / mm to about 20 ppm / mm, or about -15 ppm / mm to about 15 ppm / mm, or about -10 ppm / mm to about 10 ppm / mm, or about -5 ppm / mm to about 5 ppm / mm, or about -2 ppm / mm to about 2 ppm / mm, or about -1 ppm / mm to about In some embodiments, B is: about -21ppm / mm, or about -0.1ppm / mm, or about 0.05ppm / mm, or about 4.8ppm / mm.

[0100] In an embodiment, C is: about 2000 ppm or less, or about 1750 ppm or less, or about 1500 ppm or less, or about 1250 ppm or less, or about 1000 ppm or less, or about 750 ppm or less, or about 500 ppm or less, or about 450 ppm or less, or about 400 ppm or less, or about 350 ppm or less, or about 300 ppm or less, or about 250 ppm or less, or about 200 ppm or less, or about 150 ppm or less, or about 100 ppm or less, or about 75 ppm or less, or about 50 ppm or less, or about 25 ppm or less, or about 0 ppm. In an embodiment, C is: about 500 ppm or greater, or about 600 ppm or greater, or about 700 ppm or greater, or about 800 ppm or greater, or about 850 ppm or greater, or about 900 ppm or greater, or about 950 ppm or greater, or about 1000 ppm or greater, or about 1500 ppm or greater, or about 2000 ppm or greater.In embodiments, C is in the range of about 0 ppm to about 2000 ppm, or about 200 ppm to about 1900 ppm, or about 300 ppm to about 1800 ppm, or about 400 ppm to about 1700 ppm, or about 500 ppm to about 1750 ppm, or about 600 ppm to about 1600 ppm, or about 700 ppm to about 1500 ppm, or about 800 ppm to about 1400 ppm, or about 800 ppm to about 1300 ppm, or about 900 ppm to about 1300 ppm, or about 1000 ppm to about 1200 ppm, or about 1000 ppm to about 1100 ppm, or about 600 ppm to about 1500 ppm, or about 600 ppm to about 1400 ppm, or about 600 ppm to about 1300 ppm, or about 700 ppm to about 1000 ppm, or about 700 ppm to about 1300 ppm, or or about 800 ppm to about 1200 ppm, or about 900 ppm to about 1100 ppm, or about 1000 ppm to about 1200 ppm, or about 1000 ppm to about 1100 ppm, or about 40 ppm to about 1300 ppm, or about 40 ppm to about 1100 ppm, or about 40 ppm to about 900 ppm, or about 50 ppm to about 200 ppm, or about 75 ppm to about 150 ppm, or about 80 ppm to about 125 ppm, or about 50 ppm to about 250 ppm, or about 75 ppm to about 200 ppm, or about 100 ppm to about 175 ppm, or about 100 ppm to about 150 ppm, or about 75 ppm to about 450 ppm, or about 80 ppm to about 400 ppm, or about 80 ppm to about 300 ppm, or about 80 ppm to about 200 ppm, or about 80 ppm to about 150 ppm. In some embodiments, C is: about 1030 ppm, or about 1078 ppm, or about 1080 ppm, or about 1140 ppm, or about 80 ppm, or about 50 ppm. In the embodiments disclosed herein, it is also contemplated that C may be unlimited, such that C may be any value not limited to any specific range.

[0101] In the above parabolic curve, x is the distance (in mm) along the sample 15 from the point x=0. Therefore, x is anywhere along the length of the sample 15 such that the above parameters of A, B, and C are satisfied. Figure 3 In the exemplary graph 100 of FIG. 1 , the x=0 point is at the center point 18 of the sample 15 . However, in other exemplary embodiments, the x=0 point may be located at other locations on the sample 15 .

[0102] In some embodiments, the parabolic curve extends a distance of at least about 50 mm or more along the sample 15. Thus, when the parabolic curve is plotted on x and y coordinates, the parabolic curve extends a length of at least 50 mm along the x-axis. In other embodiments, the parabolic curve extends along the sample 15 for a distance of about 60 mm or more, or about 70 mm or about, or about 75 mm or more, or about 80 mm or more, or about 90 mm or more, or about 100 mm or more, or about 125 mm or more, or about 150 mm or more, or about 175 mm or more, or about 200 mm or more, or about 250 mm or more, or about 300 mm or more, or about 400 mm or more, or about 500 mm or more, or about 600 mm or more, or about 700 mm or more, or about 800 mm or more, or about 900 mm or more, or about 1000 mm or more, or about 1100 mm or more, or about 1200 mm or more, or about 1500 mm or more, or about 2000 mm or more. The maximum distance that the parabolic curve extends along the x-axis is the longest length dimension (eg, the diagonal length) of the cross-section of the sample 15 .

[0103] In some embodiments, B is equal to zero so that the above equation simplifies to:

[0104] y=Ax 2 +C

[0105] The parabolic curve disclosed herein represents the best fit curve of the average hydroxyl concentration of the plurality of segments 20. The best fit value R 2 The different average hydroxyl concentrations of the multiple sections 20 can be quantified to determine how well they fit the resulting parabolic curve, calculated using the x and y discussed above and the following equation:

[0106]

[0107] The best fit value R of the parabolic curve disclosed in this paper 2 Is: greater than or equal to 0.3, or greater than or equal to 0.4, or greater than or equal to 0.5, or greater than or equal to 0.6, or greater than or equal to 0.7, or greater than or equal to 0.8, or greater than or equal to 0.9, or about 1.0.

[0108] Exemplary Embodiments

[0109] The following example shows the average hydroxyl concentration of a plurality of segments 20 and the corresponding parabolic curve for glass samples according to embodiments disclosed herein.

[0110] Fig. 8AAn exemplary embodiment of a sample 15-A is shown having a length (L) of 152.4 mm, a width (W) of 152.4 mm, and a height (h) of 7.62 mm. The sample 15-A is further divided into 100 segments 20. It is noted that the sample 15-A includes a peripheral lip having a length of 12.7 mm, where the sample is not divided into segments. The segments 20 of the sample 15-A each have a length (L') and width (W') of 12.7 mm and a height (h) of 7.62 mm. Fig. 8A The average hydroxyl concentration (in ppm) of each segment 20 is shown. Fig. 8A As shown, the segment 20 having the highest hydroxyl concentration is located near the center point 18 of the sample 15-A, while the segment having the lowest hydroxyl concentration is located closer to the peripheral edge of the sample.

[0111] Figure 8B The hydroxyl concentration for each section 20 of sample 15-A is plotted as a function of distance along sample 15-A. In this example, the point x=point is located at center point 18. The best fit parabolic curve for these data points is shown as Figure 8B It is shown and expressed as the following equation: y = -0.00235x 2 +-0.86x+1139.93. The best fit value R for this equation is 2 It is 0.73.

[0112] Fig.9A An exemplary embodiment of a sample 15-B is shown having a length (L) of 152.4 mm, a width (W) of 152.4 mm, and a height (h) of 7.62 mm. The sample 15-B is further divided into 100 segments 20. It is noted that the sample 15-B includes a peripheral lip having a length of 12.7 mm, in which the sample is not divided into segments. The segments 20 of the sample 15-B each have a length (L') and a width (W') of 12.7 mm and a height (h) of 7.62 mm. Fig.9A The hydroxyl concentration (in ppm) of each segment 20 is displayed. Fig.9A As shown, the segment 20 having the highest hydroxyl concentration is located near the lower left of sample 15-B, while the segment having the lowest hydroxyl concentration is located near the upper right of the sample.

[0113] Fig. 9B The hydroxyl concentration for each section 20 of sample 15-B is plotted as a function of distance along sample 15-B. In this example, the point x=point is located at center point 18. The best fit parabolic curve for these data points is shown in FIG. Figure 8B It is shown and expressed as the following equation: y = -0.000365x 2 +0.187x+1032.39. The best fit value R for this equation is2 is 0.11.

[0114] Fig. 10A An exemplary embodiment of a sample 15-C is shown having a length (L) of 152.4 mm, a width (W) of 152.4 mm, and a height (h) of 7.62 mm. The sample 15-C is further divided into 100 segments 20. It is noted that the sample 15-C includes a peripheral lip having a length of 12.7 mm, in which the sample is not divided into segments. The segments 20 of the sample 15-C each have a length (L') and a width (W') of 12.7 mm and a height (h) of 7.62 mm. Fig. 10A The hydroxyl concentration (in ppm) of each segment 20 is displayed. Fig. 10A As shown, the segment 20 having the highest hydroxyl concentration is located near but offset from the center 18 of the sample 15-C, while the segment having the lowest hydroxyl concentration is located closer to the peripheral edge of the sample.

[0115] Fig. 10B The hydroxyl concentration for each section 20 of sample 15-B is shown plotted as a function of distance along sample 15-C. More specifically, Fig. 10B A first graph showing the relationship between the hydroxyl concentration and the distance along the sample 15-C is shown. In this first graph, the point x=0 is at the center point 18, and the graph is represented by the following equation: y=-0.00251x 2 +-0.00568x+1077.54. The best fit value R for this equation is 2 is 0.46. Fig. 10B In the second graph shown, the point x=0 is at the center point 18', and the graph is represented by the following equation: y'=-0.00288x' 2 +0.00282x'+1079.02. The best fit value R for this equation is 2 is 0.94. Note that the point x=0 of the second graph is in the segment with the highest hydroxyl concentration (rather than at the center point 18 of sample 15), and the second graph has a better best fit value R than the first graph. 2 .

[0116] Figure 13-16 Exemplary samples of various sizes are shown, each sample having a low PV of hydroxyl concentration in a segment and thus having a uniform hydroxyl concentration along the sample. Specifically, Fig.13 Sample 15-D has a length (L) of 127 mm, a width (W) of 127 mm, and a height (h) of 7.62 mm. It should be noted that the hydroxyl concentration of sample 15-D is measured over the entire length (L) and width (W) of the sample. In addition, sample 15-D has a mass of 2.5 kg. Fig.13 As shown, sample 15-D is divided into 25 sections, each having a length (L') and width (W') of 25.4 mm. Fig.13 The average hydroxyl concentration (in ppm) is shown for each section 20. The average hydroxyl concentration in sample 15-D is 112 ppm, and the PV difference in hydroxyl concentration in sample 15-D is 4 ppm.

[0117] Fig.14 Sample 15-E has a length (L) of 127 mm, a width (W) of 127 mm, and a height (h) of 7.62 mm. It should be noted that the hydroxyl concentration of sample 15-E is measured over the entire length (L) and width (W) of the sample. In addition, sample 15-E has a mass of 4.5 kg. Fig.14 As shown, sample 15-E is divided into 25 sections, each having a length (L') and width (W') of 25.4 mm. Fig.14 The average hydroxyl concentration (in ppm) is shown for each section 20. The average hydroxyl concentration in sample 15-E is 171 ppm, and the PV difference in hydroxyl concentration in sample 15-E is 9 ppm.

[0118] Fig.15 Sample 15-F has a length (L) of 279.4 mm, a width (W) of 279.4 mm, and a height (h) of 7.62 mm. It should be noted that the hydroxyl concentration of sample 15-F is measured over the entire length (L) and width (W) of the sample. In addition, sample 15-F has a mass of 12 kg. Fig.15 As shown, sample 15-F was divided into 100 sections, each having a length (L') and a width (W') of 27.94 mm. Fig.15 The average hydroxyl concentration (in ppm) is shown for each section 20. The average hydroxyl concentration in sample 15-F is 155 ppm, and the PV difference in the average hydroxyl concentration in sample 15-F is 24 ppm.

[0119] Fig.16 Sample 15-G has a length (L) of 431.8 mm, a width (W) of 431.8 mm, and a height (h) of 7.62 mm. It should be noted that the hydroxyl concentration of sample 15-G is measured over the entire length (L) and width (W) of the sample. In addition, sample 15-G has a mass of 36.5 kg. Fig.16 As shown, sample 15-G is divided into 225 segments, each having a length (L') and width (W') of 27.79 mm. Fig.16The average hydroxyl concentration (in ppm) is shown for each section 20. The average hydroxyl concentration in sample 15-G is 225 ppm, and the PV difference in the average hydroxyl concentration in sample 15-G is 97 ppm. It is noted that, in particular, sample 15-G has such a uniform hydroxyl concentration throughout the sample including a sample with such a large mass.

[0120] Exemplary Process

[0121] Fig.11 A process 1100 for forming a glass body 10 according to an embodiment disclosed herein is shown. As discussed above, the unique steps of process 1100 form a glass body 10 having a hydroxyl concentration, titanium oxide concentration, Tzc, refractive index, and CTE profile as discussed above. Fig.11 As shown in the process 1100 of FIG. 1 , the glass body 10 may be prepared by burning and oxidizing a mixture of a silicon dioxide precursor and a titanium precursor to form loose soot particles at step 1110. Each soot particle contains SiO2 and TiO2.

[0122] Fig.12 A schematic representation of a system 1200 for producing loose soot particles is shown. Fig.12 , the system 1200 includes a first reservoir 1220 containing a silica precursor 1224 and a second reservoir 1230 containing a titanium oxide precursor 1234. The temperature of the first and second reservoirs 1220, 1230 can be monitored so that the precursor in each reservoir is uniform and constant throughout the reservoir (i.e., within + / - 0.5°C). The first reservoir 1220 includes an inlet 1222 for introducing a carrier gas (e.g., nitrogen) at the base of the reservoir or near the base of the reservoir. The carrier gas forms a gaseous stream with the silica precursor 1224. Similarly, the second reservoir 1230 includes an inlet 1232 for introducing a carrier gas (e.g., nitrogen) at the base of the reservoir or near the base of the reservoir. The carrier gas in the second reservoir 1230 forms a gaseous stream with the titanium oxide precursor 1234. The carrier gas flowing into the inlets 1222, 1232 flows into the respective reservoirs 1220, 1230 at a consistent and uniform flow rate, thereby avoiding introducing any disturbances into the system 1200. More specifically, the carrier gas flowing into the inlets 1222, 1232 flows at flow rates that are within 5% of each other.

[0123] The silicon dioxide precursor 1224 may include, for example, octamethylcyclotetrasiloxane, and the titanium oxide precursor 1234 may include titanium tetraisopropoxide, as discussed above.

[0124] A bypass stream of carrier gas is also introduced into the system 1200 at inlets 1226 and 1236 to prevent saturation of the gaseous silica stream and the gaseous titanium oxide stream. In an embodiment, the gaseous silica stream and the gaseous titanium oxide stream are heated by hot oil tracking to prevent hot spots and cold spots in the streams. It is noted that both hot spots and cold spots in the gaseous streams affect the concentration of precursors in the streams, thereby producing glass with suboptimal properties. The gaseous silica stream then passes through a distribution system 1242 to a manifold 1248, and the gaseous titanium oxide stream passes through a distribution system 1244 to a manifold 1248.

[0125] The silica and titania gaseous streams are then mixed in manifold 1248 to form a mixture of the two streams. Fig.12 As further shown, the mixture of the two streams flows to the furnace 1250. More specifically, the mixture of the two streams passes through the smoke line 1252 to the burner 1254 installed in the upper part of the furnace 1250. The two streams are further combined with the fuel / oxygen mixture in the burner 1254 so that the mixture is burned and oxidized. The fuel can be natural gas. The oxidation and combustion of the mixture forms loose soot particles 1260. The fuel / oxygen mixture is combined with the silica and titanium oxide gaseous streams in the burner 1254 so that the ratio of the amount of oxygen to the combined amount of silica and titanium oxide vapor (including any carrier gas) is at least 1:1. Therefore, the amount of oxygen is at least equal to the amount of silica and titanium oxide vapor (including any carrier gas), or 2 times, 3 times, 4 times, etc., the amount of silica and titanium oxide vapor (including any carrier gas).

[0126] At step 1120 of process 1100, the loose soot particles 1260 are then cooled and directed into a collection chamber. In some embodiments, the loose soot particles 1260 are directed into a collection chamber 1264. In other embodiments, the loose soot particles 1260 are directed vertically upward through a tube 1270 rather than downward into the collection chamber 1264. The tube 1270 may be a quartz tube that carries the soot particles 1260 in a gaseous stream to one or more filter bags 1272. The soot particles 1260 are removed from the gaseous stream by the filter bags 1272 and then deposited into one or more collection chambers 1264'. For example, the soot particles 1260 fall downward from the filter bags 1272 and into the collection chamber 1264'. N2 pulses are periodically applied to the filter bags 1272 to prevent excessive accumulation of soot particles 1260 on the bags. In some embodiments, the collection chamber 1264' is a stainless steel funnel.The soot particles 1260 may then be further collected from the collection chamber 1264' and deposited into a bucket where the soot particles 1260 may be stored for further use.

[0127] In an embodiment, the gas pressure around the system 1200 is precisely monitored to produce a glass body having the optimal properties disclosed herein (e.g., uniform concentrations of hydroxyl and titanium oxide). In addition, it has been found that frequent cleaning of the gas lines in the system 1200 and frequent replacement of the filter bags 1271 produce a glass body having the optimal properties disclosed herein. Before reaching the collection chamber 1264, 1264', the soot particles 1260 can also be cooled to: about 200°C or less, or about 175°C or less, or about 150°C or less, or about 125°C or less, or about 100°C or less, or about 75°C or less, or about 50°C or less, or about 25°C or less, or about 20°C or less, thereby producing the optical properties disclosed herein in the glass body.

[0128] In step 1130 of process 1100, Yantai particles are transferred from gallon buckets to molds to form a molded precursor body. The mold is graphite with a very high cleanliness level (i.e., less than 100ppm of impurity levels), thereby producing a glass body with excellent properties. Yantai particles are pressed in a mold by a pressing device to form a molded precursor body, which is then heat treated in the presence of steam or under vacuum pressure (i.e., less than 1 Torr) to form a consolidated molded precursor body. In an embodiment, the consolidated molded precursor body is opaque after the heat treatment step.

[0129] It is to be understood that in embodiments where the molded precursor body is heat treated under vacuum pressure, the body is not doped with hydroxide during step 1130 of process 1100. Thus, such embodiments may be referred to as "no OH doping". In contrast, when the molded precursor body is heated in the presence of steam (also referred to as steam doping, as discussed further below), the body is doped with hydroxide. The "no OH doping" process produces a glass body having a reduced hydroxyl concentration compared to the steam doping process.

[0130] In other embodiments, the molded precursor body can be actively dried during the heat treatment step to form a consolidated molded precursor body. During such active drying embodiments, the molded precursor body is exposed to a desiccant while being heated in a furnace. In embodiments, the desiccant can be a halide, such as chlorine and / or fluorine, or carbon monoxide. Active drying of the molded precursor body results in a reduced concentration of hydroxyl groups in the glass body, even less than that of a "no OH doping process".

[0131] Also note that in the "no OH doping" and vapor doping processes, the precursor body may not be exposed to a halide reagent. Therefore, in these embodiments, the final glass body may not contain halides such that the glass body is halide-free (i.e., may contain less than 100 ppm of halide).

[0132] Additionally, the molded precursor body is heated in the furnace at a heating rate of about 2.5° C. / hour or less during the consolidation heating process of step 1130. Such slow heating helps provide uniform hydroxyl and titanium oxide concentrations in the produced glass body.

[0133] Step 1140 of process 1100 includes melting the solidified molding precursor body into a melt, allowing the melt to flow into another mold, and then cooling the melt to form glass. Once the glass cools, it forms a glass body. This body no longer has the opacity created during the consolidation process of step 1130.

[0134] At step 1150, the body is then exposed to an environment of elevated temperature and elevated pressure for a period of time. In some embodiments, the environment having elevated temperature and elevated pressure comprises an inert gas. By "inert gas," it is meant a gas that does not chemically react with the body. In some embodiments, the elevated pressure is in the range of 0.5 kpsi to 15 kpsi. Further, in some embodiments, the elevated temperature is in the range of 1000° C. to 1800° C. The body may be subjected to the environment for a period of 1 hour to 120 hours. Step 1150 of subjecting the body to an environment having elevated pressure and elevated temperature may be referred to as "hot isostatic pressing."

[0135] Step 1160 of process 1100 includes an annealing step. During this step, internal stresses in the body are released, which provides better quality body cutting and machining. In addition, step 1160 of annealing the body reduces the average Tzc of the body.

[0136] Referring again to step 1110 of process 1100, samples 15-A through 15-G were prepared (as discussed above) in the following manner: a gaseous silica stream and a gaseous titanium oxide stream were flowed through distribution system 1242 at a flow rate of 9 standard liters per minute (SLPM). As discussed above, the two gaseous streams were mixed together and then directed to burner 1254 of furnace 1250, where the mixed gas was combusted in the presence of oxygen. The oxygen that caused the mixed gas to combust flowed from burner 1254 at a flow rate of 45 SLPM.

[0137] Steam doping

[0138] As discussed above, in embodiments, the glass body of the present disclosure includes a titanium oxide-silica glass having a high concentration of hydroxyl groups. Specifically, the glass body is modified to contain a high concentration of hydroxyl groups by consolidating the molded precursor glass body in a steam-containing atmosphere (during step 1130 of process 1100).

[0139] Processing the molded precursor glass body using a vapor doping process includes heat treating the glass body in a vapor-free atmosphere, exposing the heat treated glass body to vapor, and consolidating the heat treated glass body in a vapor-containing atmosphere.

[0140] Heat treating the glass body in a steam-free atmosphere achieves purging and removing gases from the body. The heat treatment process can be carried out in a steam-free atmosphere at a temperature ranging from about 100°C to about 900°C, or from about 200°C to about 700°C, or from about 300°C to about 600°C. The steam-free atmosphere can also contain an inert gas. In addition, the heat treatment can be carried out for an amount of time sufficient to increase the internal temperature of the body to at least 100°C, or at least 200°C, or in the range of about 100°C to about 600°C, or from about 100°C to about 500°C, or from about 150°C to about 600°C.

[0141] After heat treatment in a steam-free atmosphere, the main body is then exposed to a steam-containing atmosphere so that the main body is loaded with hydroxyl groups. The steam-containing atmosphere can contain only steam or a combination of steam and an inert gas. The pressure of the steam can be about 0.1atm to about 10atm, or about 0.5atm to about 5atm. The steam pressure in the furnace should be constant, and any pressure difference differs from the absolute pressure in the furnace by only + / -2%. The temperature at which the main body is exposed to the steam-containing atmosphere can be the following range: about 200°C to about 900°C, or about 300°C to about 700°C. The temperature is preferably less than the temperature that induces the densification or consolidation of the main body. The time at which the main body is exposed to the steam-containing atmosphere can be adjusted to control the concentration of the hydroxyl groups incorporated into the main body. Longer exposure times result in higher hydroxyl concentrations.

[0142] After the main body is exposed to the steam-containing atmosphere, the main body is consolidated in the presence of steam. The steam-containing consolidation atmosphere can have the same composition as the steam-containing load atmosphere (as described above). The consolidation of the main body in the steam-containing atmosphere occurs at a temperature that lasts enough to make the main body transform from a porous main body into a closed-cell main body. The temperature can be as follows: about 900°C to about 1850°C, or about 900°C to about 1700°C, or about 900°C to about 1500°C, or about 900°C to about 1300°C. The time that the main body is exposed to the steam-containing consolidation atmosphere can be: at least 0.5 hours, or at least 1 hour, or at least 2 hours, or at least 5 hours. The heating rate can be about 3°C / minute to about 100°C / minute, or about 5°C / minute to about 50°C / minute.

[0143] The steam consolidation step may include maintaining the body at a fixed temperature (holding temperature) for a predetermined amount of time. The holding temperature may be from about 1000°C to about 1250°C or from about 1150°C to about 1200°C, such that the temperature increases at a heating rate of about 2.5°C / hour or more. The peak holding temperature during the steam consolidation step is about 1250°C. The body may be maintained at the holding temperature for a duration of from about 1 hour to about 240 hours or from about 5 hours to about 20 hours.

[0144] The steam consolidation process disclosed above transforms the molded precursor body into a consolidated glass. Then, after the steam consolidation process, the glass melts, as discussed above with respect to step 1140 of process 1100.

[0145] The use of steam in the above disclosed vapor doping process provides a number of benefits including the advantage of having a high concentration of hydroxyl groups in the glass (which reduces viscosity and contributes to a low fictive temperature), and avoiding the formation of seeds in the glass.

[0146] Other embodiments of the steam consolidation process disclosed above are disclosed in US Pat. No. 9,580,350, which is incorporated by reference in its entirety.

[0147] Unless otherwise stated, it is not intended that any method described herein be construed as requiring that its steps be performed in a specific order. Therefore, when a method claim does not actually state that its steps follow a certain order or it does not specifically indicate in any other way in the claims or description that the steps are limited to a specific order, it is not intended to imply any particular order.

[0148] It will be apparent to those skilled in the art that various modifications and variations may be made without departing from the spirit or scope of the illustrated embodiments. Because those skilled in the art may conceive of various modifications, combinations, sub-combinations, and variations of the disclosed embodiments that incorporate the spirit and substance of the illustrated embodiments, this specification should be deemed to include all of the contents within the scope of the appended claims and their equivalents.

Claims

1. A glass comprising: Titanium oxide and silicon dioxide, in: A plot of the average hydroxyl concentration for each of the plurality of segments versus distance along the glass is provided below: y=Ax 2 +Bx+C, A(Unit: ppm / mm 2 ) is in the range of about 0.0 to about -0.1, B (in ppm / mm) is in the range of about -10 to about 10, C (in ppm) is about 450 or less, y is the average hydroxyl concentration (in ppm), and x is the distance (in mm), Transmission Fourier transform infrared spectroscopy was used to measure the hydroxyl concentration in each segment, and The relationship graph extends along the glass for a distance of about 50 mm or more.

2. The glass according to claim 1, wherein: The range of C is about 75 to about 450.

3. The glass according to claim 2, wherein: The range of C is about 80 to about 150.

4. The glass according to any one of claims 1 to 3, wherein: The range of B is about -5 to about 5.

5. The glass according to claim 4, wherein: B is approximately 0.

6. The glass according to any one of claims 1 to 5, wherein: A ranges from about 0.0 to about -0.

04.

7. The glass according to claim 6, wherein: A ranges from about 0.0 to about -0.

02.

8. The glass according to any one of claims 1 to 7, wherein: The best fit value R of the relationship graph 2 Greater than or equal to 0.

3.

9. The glass according to claim 8, wherein: The best fit value R of the relationship graph 2 Greater than or equal to 0.

5.

10. The glass according to any one of claims 1 to 9, wherein: The relationship graph extends along the glass for a distance of about 75 mm or more.

11. The glass according to claim 10, wherein: The relationship diagram extends along the glass for a distance of about 100 mm or more.

12. The glass according to any one of claims 1 to 11, wherein: The plurality of segments include each adjacent segment having a length and a width of the glass, the length being approximately 25 mm or greater and the width being 25 mm or greater.

13. The glass according to claim 12, wherein: The length is about 50 mm or more and the width is about 50 mm or more.

14. The glass according to claim 13, wherein: The length is about 150 mm or more and the width is about 150 mm or more.

15. The glass according to any one of claims 1 to 14, wherein: The glass is a photomask.

16. The glass according to any one of claims 1 to 15, wherein: A section having a relatively higher hydroxyl concentration has a relatively lower zero-temperature crossing point.

17. The glass according to claim 16, wherein: The segment with the maximum hydroxyl concentration has the minimum zero temperature crossing.

18. A glass comprising: Titanium oxide and silicon dioxide, in: A plot of the average hydroxyl concentration for each of the plurality of segments versus distance along the glass is provided below: y=Ax 2 +Bx+C, A(Unit: ppm / mm 2 ) is in the range of about 0.0 to about -0.1, B (in ppm / mm) is in the range of about -10 to about 10, C (in ppm) is about 800 or greater, y is the average hydroxyl concentration (in ppm), and x is the distance (in mm), Transmission Fourier transform infrared spectroscopy was used to measure the hydroxyl concentration in each segment, and The relationship graph extends along the glass for a distance of about 50 mm or more.

19. The glass according to claim 18, wherein: The range of C is about 800 to about 1300.

20. The glass according to claim 18, wherein: The range of B is about -5 to about 5.

21. The glass according to claim 20, wherein: B is approximately 0.

22. The glass according to any one of claims 18 to 21, wherein: A ranges from about 0.0 to about -0.

04.

23. The glass according to claim 22, wherein: A ranges from about 0.0 to about -0.

02.

24. The glass according to any one of claims 18 to 23, wherein: The best fit value R of the relationship graph 2 Greater than or equal to 0.

3.

25. The glass according to claim 24, wherein: The best fit value R of the relationship graph 2 Greater than or equal to 0.

5.

26. The glass according to any one of claims 18 to 25, wherein: The relationship graph extends along the glass for a distance of about 75 mm or more.

27. The glass according to any one of claims 18 to 26, wherein: The relationship diagram extends along the glass for a distance of about 100 mm or more.

28. The glass according to any one of claims 18 to 27, wherein: The plurality of segments include each adjacent segment having a length and a width of the glass, the length being approximately 25 mm or greater and the width being 25 mm or greater.

29. The glass according to claim 28, wherein: The length is about 50 mm or more and the width is about 50 mm or more.

30. The glass according to claim 29, wherein: The length is about 150 mm or more and the width is about 150 mm or more.

31. The glass according to any one of claims 18 to 30, wherein: The glass is a photomask.

32. The glass according to any one of claims 18 to 31, wherein: A section having a relatively higher hydroxyl concentration has a relatively lower zero-temperature crossing point.

33. The glass according to claim 32, wherein: The segment with the maximum hydroxyl concentration has the minimum zero temperature crossing.

34. A glass comprising: Titanium oxide and silicon dioxide, in: A plot of the average hydroxyl concentration for each of the plurality of segments versus distance along the glass is provided below: y=Ax 2 +Bx+C, A(Unit: ppm / mm 2 ) is in the range of about 0.0 to about -0.1, B (in ppm / mm) is in the range of about -10 to about 10, C (in ppm) is not limited, y is the average hydroxyl concentration (in ppm), and x is the distance (in mm), Transmission Fourier transform infrared spectroscopy was used to measure the hydroxyl concentration in each segment, and The relationship graph extends along the glass for a distance of about 50 mm or more.

35. The glass according to claim 34, wherein: The range of B is about -5 to about 5.

36. The glass according to claim 35, wherein: B is approximately 0.

37. The glass according to any one of claims 34 to 36, wherein: A ranges from about 0.0 to about -0.

04.

38. The glass according to claim 37, wherein: A ranges from about 0.0 to about -0.

02.

39. The glass according to any one of claims 34 to 38, wherein: The best fit value R of the relationship graph 2 Greater than or equal to 0.

3.

40. The glass according to claim 39, wherein: The best fit value R of the relationship graph 2 Greater than or equal to 0.

5.

41. The glass according to any one of claims 34 to 40, wherein: The relationship graph extends along the glass for a distance of about 75 mm or more.

42. The glass according to any one of claims 34 to 41, wherein: The relationship diagram extends along the glass for a distance of about 100 mm or more.

43. The glass according to any one of claims 34 to 42, wherein: The plurality of segments include each adjacent segment having a length and a width of the glass, the length being approximately 25 mm or greater and the width being 25 mm or greater.

44. The glass according to claim 43, wherein: The length is about 50 mm or more and the width is about 50 mm or more.

45. The glass according to claim 44, wherein: The length is about 150 mm or more and the width is about 150 mm or more.

46. ​​The glass according to any one of claims 34 to 45, wherein: The glass is a photomask.

47. The glass according to any one of claims 34 to 46, wherein: A section having a relatively higher hydroxyl concentration has a relatively lower zero-temperature crossing point.

48. The glass according to claim 47, wherein: The segment with the maximum hydroxyl concentration has the minimum zero temperature crossing.

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