Homogeneous silica-titania glass

Abstract

A glass comprising titania and silica is disclosed. A plot of the average hydroxyl concentration in each of a plurality of segments versus distance along the glass is given by y=Ax 2 + Bx + C, where the hydroxyl concentration of each segment is measured using transmission Fourier transform infrared spectroscopy and plotted over a distance of about 50 mm or more along the glass, A (ppm / mm 2 where A (expressed in ppm / mm) is in the range of about 0.0 to about −0.1, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is less than or equal to about 450, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm).

Description

Priority

[0001] This application claims the benefit of priority to Dutch Patent Application No. 2033057, filed September 16, 2022, which claims the benefit of priority to U.S. Provisional Patent Application No. 63 / 401334, filed August 26, 2022, the contents of which are relied upon and incorporated herein by reference in their entirety. [Technical Field]

[0002] This description relates to titania-doped silica glass, and more particularly to titania-doped silica glass with enhanced homogeneity for producing glass articles that may be suitable for use in extreme ultraviolet lithography applications. [Background technology]

[0003] Extreme ultraviolet (EUV) lithography uses optical elements to illuminate, project, and reduce pattern images to form integrated circuit patterns. The use of extreme ultraviolet light is beneficial because it allows for smaller integrated circuit features to be obtained. Optical elements for EUV lithography are currently made from low-thermal expansion glasses, such as silica-titania glasses. These glasses are traditionally produced by a flame hydrolysis process, in which high-purity precursors are injected into a flame to form fine glass particles. These fine glass particles can then be formed into articles by axial pressing, radial pressing, or cold isostatic pressing. In this flame hydrolysis process, the glass is formed as fine glass particles.

[0004] In EUV lithography systems, glass is typically coated with a reflective surface to form a reflective mirror. Furthermore, the glass must be able to meet the stringent thermal expansion requirements within the system. Specifically, the glass must be able to maintain its surface shape (known as "figure") when exposed to temperature changes within the system. Highly temperature-stable glass is required to avoid induced distortions in the wavefront characteristics of EUV projection optics. Summary of the Invention

[0005] Embodiments of the present disclosure provide glass bodies that can beneficially maintain their appearance during operation in an EUV lithography system, thus reducing or preventing distortion of the wavefront characteristics of EUV projection optics.

[0006] According to a first aspect, embodiments of the present disclosure relate to a glass comprising titania and silica. A plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is given by y=Ax 2 + Bx + C, where the hydroxyl concentration of each segment is measured using transmission Fourier transform infrared spectroscopy and plotted over a distance of about 50 mm or more along the glass, A (ppm / mm 2 where A (expressed in ppm / mm) is in the range of about 0.0 to about −0.1, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is less than or equal to about 450, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm).

[0007] According to a second aspect, embodiments of the present disclosure relate to a glass comprising titania and silica, wherein a plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is given by y=Ax 2+ Bx + C, where the hydroxyl concentration of each segment is measured using transmission Fourier transform infrared spectroscopy and plotted over a distance of about 50 mm or more along the glass, A (ppm / mm 2 where A (expressed in ppm / mm) is in the range of about 0.0 to about −0.1, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is greater than or equal to about 800, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm).

[0008] According to a third aspect, embodiments of the present disclosure relate to a glass comprising titania and silica, wherein a plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is given by y=Ax 2 + Bx + C, where the hydroxyl concentration of each segment is measured using transmission Fourier transform infrared spectroscopy and plotted over a distance of about 50 mm or more along the glass, A (ppm / mm 2 where A (expressed in ppm / mm) ranges from about 0.0 to about −0.1, B (expressed in ppm / mm) ranges from about −10 to about 10, C (expressed in ppm) is undefined, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm).

[0009] Additional features and advantages will be set forth in the following detailed description, and in part will become apparent to those skilled in the art from that description, or will be learned by practicing the embodiments as set forth in the written description and claims thereof, 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 characteristics and features of the claims.

[0011] The accompanying drawings are included to provide a further understanding, and are incorporated into and constitute a part of this specification. The drawings illustrate selected aspects of the present description and, together with the description, serve to explain the principles and operation of the methods, products, and compositions encompassed by the present description. The features illustrated in the drawings illustrate selected embodiments of the present description and are not necessarily drawn to scale. [Brief explanation of the drawings]

[0012] While the specification concludes with claims particularly pointing out and distinctly claiming the subject matter described, it is believed that the same will be better understood from the following specification when taken in conjunction with the accompanying drawings. [Figure 1] 1 is a schematic diagram of an exemplary glass body according to embodiments disclosed herein; [Figure 2A] 2 illustrates a cross-section of a sample of the glass body of FIG. 1 according to embodiments disclosed herein. [Figure 2B] 2 illustrates another cross-section of the sample glass body of FIG. 1 having a peripheral edge according to embodiments disclosed herein. [Figure 3] 3 is a plot of hydroxyl concentration versus sample length of FIG. 2 according to embodiments disclosed herein. [Figure 4] 3 is a plot of titania concentration versus sample length of FIG. 2 according to embodiments disclosed herein. [Figure 5] 3 is a plot of zero temperature crossing point versus length for the sample of FIG. 2 according to embodiments disclosed herein. [Figure 6] 3 is a plot of refractive index versus length for the sample of FIG. 2 according to embodiments disclosed herein. [Figure 7] 3 is a plot of the thermal expansion coefficient versus length for the sample of FIG. 2 according to embodiments disclosed herein. [Figure 8A] FIG. 1 illustrates a cross-section of an exemplary sample of a glass body divided into segments and the hydroxyl concentration of each segment, according to embodiments disclosed herein. [Figure 8B]Graph showing best-fit parabolic curves of hydroxyl concentration for each segment of FIG. 8A. [Figure 9A] FIG. 10 illustrates another cross-section of an exemplary sample of a glass body divided into segments, and the hydroxyl concentration of each segment, according to embodiments disclosed herein. [Figure 9B] Graph showing best-fit parabolic curves of hydroxyl concentration for each segment of FIG. 9A. [Figure 10A] FIG. 10 illustrates another cross-section of an exemplary sample of a glass body divided into segments, and the hydroxyl concentration of each segment, according to embodiments disclosed herein. [Figure 10B] Graph showing two best-fit parabolic curves of hydroxyl concentration for each segment of FIG. 10A. [Figure 11] FIG. 1 is a block diagram illustrating a process for forming a glass body according to embodiments disclosed herein. [Figure 12] Schematic of a system for producing glass bodies using the process of FIG. [Figure 13] FIG. 10 illustrates another cross-section of an exemplary sample of a glass body divided into segments, and the hydroxyl concentration of each segment, according to embodiments disclosed herein. [Figure 14] FIG. 10 illustrates another cross-section of an exemplary sample of a glass body divided into segments, and the hydroxyl concentration of each segment, according to embodiments disclosed herein. [Figure 15] FIG. 10 illustrates another cross-section of an exemplary sample of a glass body divided into segments, and the hydroxyl concentration of each segment, according to embodiments disclosed herein. [Figure 16] FIG. 10 illustrates another cross-section of an exemplary sample of a glass body divided into segments, and the hydroxyl concentration of each segment, according to embodiments disclosed herein. DETAILED DESCRIPTION OF THE INVENTION

[0013] The present disclosure relates to glasses with improved homogeneity and uniformity. Embodiments of the present disclosure provide glasses with substantially uniform hydroxyl and titania concentrations across the length and width of the glass. The glasses may be Ultra Low Expansion glasses (ULE® glasses) manufactured by Corning Incorporated that are suitable for EUV applications.

[0014] EUV lithography technology relies on an optical projection system to expose a reflective photomask to EUV light, which is then reflected by the photomask and directed onto a thin photosensitive layer deposited on the surface of a semiconductor wafer. This technology is commonly used in semiconductor device manufacturing processes. EUV lithography systems operate at a wavelength of approximately 13.5 nm. This extremely short wavelength poses numerous challenges to the design of EUV systems. For example, the reflective coating on the mirror substrate in an EUV system cannot reflect all of the light at such low wavelengths. Approximately 30 percent of the light is absorbed by the reflective coating rather than reflected. The absorbed light generates unwanted heat in the mirror substrate, causing it to thermally expand or contract. Such changes in the mirror substrate can, in turn, deform the reflective coating on the mirror substrate, resulting in a curvature in the wavefront of the reflected light. The curvature in the wavefront can reduce the resolution of the EUV system and result in errors in the pattern formed on the photosensitive layer.

[0015] Therefore, the mirror substrate must be able to maintain its shape and appearance even when exposed to the severe thermal loads of an EUV system. Silica-titania glasses, such as "ULE" glass, are currently the material of choice for mirror substrates in EUV systems.

[0016] However, even considering "ULE" glasses, the coefficient of thermal expansion (CTE) of glass substrates in EUV systems must be reduced. A low CTE at room temperature is important to ensure that the shape of the glass substrate remains substantially constant when heated in an EUV system. Modifiers can be added to the glass substrate to reduce the CTE. However, such modifiers are known to reduce the homogeneity of the glass. Homogeneous glass with a 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 titania concentrations will polish unevenly because areas of the glass substrate with different concentrations of titanium polish at different rates.

[0017] Embodiments of the present disclosure provide homogeneous glass substrates having uniform composition while maintaining an overall low CTE value. Specifically, embodiments of the present disclosure provide glass substrates having a uniform hydroxyl concentration. Additionally or alternatively, embodiments of the present disclosure provide glass substrates having a uniform titania concentration. Such a uniform concentration provides glass substrates that can be easily polished while maintaining an overall low CTE value.

[0018] Another important characteristic of glass substrates in EUV systems is the temperature at which the CTE of the glass substrate is exactly equal to zero. This temperature is known as the zero-crossing temperature and is denoted as Tzc. Glass substrates in EUV systems should ideally have a Tzc value that is close to the temperature of the glass substrate when exposed to the EUV light of the EUV system. If the Tzc value matches (or is close to) this temperature, the glass substrate will experience minimal expansion (and therefore minimal curvature) during operation of the EUV system.

[0019] Note also that Tzc is directly related (over a typical fictive temperature range) to the hydroxyl and titania concentrations in the glass substrate. Thus, as titania concentration increases, Tzc will also increase. However, hydroxyl is inversely related to Tzc; thus, as hydroxyl concentration increases, Tzc will decrease. Note further that hydroxyl concentration has a greater effect on Tzc than titania concentration.

[0020] As used herein, "ppm" refers to parts per million by mass.

[0021] As used herein, the term "hydroxyl," or OH, refers to an oxygen atom and a protium atom (1), respectively, unless otherwise specified. 1 H, herein referred to as "H"). As used herein, n(OH) refers to the total number of OH or hydroxyl moieties in a material.

[0022] 1 illustrates an exemplary glass body 10 having a length (L), a width (W), and a height (H). In some embodiments, the length and width can each be greater than the height (H). For example, the length (L) and width (W) can each be 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 about 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 each about 15 mm or greater, or about 20 mm or greater, or about 25 mm or greater, or about 50 mm or greater, or about 75 mm or greater, or about 100 mm or greater, or about 150 mm or greater, or about 200 mm or greater, or about 250 mm or greater, or about 300 mm or greater, or about 350 mm or greater, or about 400 mm or greater, or about 450 mm or greater, or about 500 mm or greater, or about 700 mm or greater, or about 1000 mm or greater, or about 1200 mm or greater, or about 1500 mm or greater, or about 1700 mm or greater, or about 2000 mm or greater. In some embodiments, both the length and width are about 150 mm, or 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 differ from the width.

[0023] Furthermore, 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. Additionally, or alternatively, the height is about 5 mm or more, or about 10 mm or more, or 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. In some embodiments, the height is about 63 mm, or about 150 mm, or about 152 mm.

[0024] In embodiments, the mass of glass body 10 is 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.

[0025] Glass body 10 may be a substrate onto which one or more additional layers or coatings may be applied. As also shown in FIG. 1 , glass body 10 includes at least one sub-portion, such as sample 15, having a length and width equal to the length and width, respectively, of glass body 10. However, the height (h) of sample 15 may be less than the height (H) of glass body 10. In some embodiments, the height of 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. It is also contemplated that in some embodiments, the height (h) of sample 15 may be equal to the height (H) of glass body 10.

[0026] Sample 15 can be a glass body and / or a glass substrate. Glass body 10 (and also sample 15) can be a titania-doped silica glass. In some embodiments, glass body 10 can be made from a precursor comprised of, for example, octamethylcyclotetrasiloxane and titanium tetraisopropoxide. It is also contemplated that glass body 10 can include one or more modifiers and / or additives up to the values ​​listed below.

[0027] The silicon dioxide (SiO2) concentration in glass body 10 can be about 80% by weight or more, or about 85% by weight or more, or about 90% by weight or more, or about 92% by weight or more, or about 95% by weight or more, or about 97% by weight or more, or about 98% by weight or more, or about 99% by weight or more, or about 85% by weight to about 97% by weight, or about 90% by weight to about 95% by weight.

[0028] As discussed above with reference to FIG. 1 , glass body 10 includes at least one sample 15 that forms a minor portion of glass body 10. In the embodiment of FIG. 1 , sample 15 is a minor cross-sectional portion of glass body 10, such that the height (h) of sample 15 extends along the height (H) of glass body 10. Note further that the height (H) of glass body 10 is less than the width (W) and length (L) of glass body 10, such that sample 15 forms a minor cross-sectional portion along the smallest dimension of glass body 10 (along the height (H)). The smallest dimension of glass body 10 is sometimes referred to as the characteristic length of the glass body, as further discussed below, such that sample 15 extends along the characteristic length of glass body 10. In the embodiment of FIG. 1 , glass body 10 includes multiple samples along its height (H). However, in other embodiments, it is contemplated that a single sample 15 may extend the entire height (H) of glass body 10. In these embodiments, the glass body 10 includes only one sample 15 such that one sample 15 forms the entire glass body 10.

[0029] While FIG. 1 depicts glass body 10 and sample 15 as square components with flat surfaces, in embodiments, glass body 10 and / or sample 15 may have other shapes. For example, the outer shape of glass body 10 and / or sample 15 may be circular, elliptical, or asymmetric. Additionally, glass body 10 and / or sample 15 may be curved to form a concave or convex structure. In one exemplary embodiment, glass body 10 is formed from a single sample 15 (such that the single sample 15 extends the entire length, width, and height of glass body 10), and glass body 10 has a concave structure. Sample 15 may be a reticle, photomask, mirror, and / or reticle or photomask holder.

[0030] Each sample 15 has substantially uniform hydroxyl (OH) and titania (TiO) concentrations across the length and width of the sample. To determine the uniformity of the sample within the glass body, each sample is divided into segments across the length and width of the sample. For example, FIG. 2A shows sample 15 divided into segments 20 across the length (L) and width (W) of a cross-section of sample 15. The concentration of one or more components (e.g., hydroxyl, titania) can then be determined for each segment 20 to determine the uniformity of each of these components along the sample 15. For example, the concentration of hydroxyl can be measured for each segment 20 to determine the uniformity of the hydroxyl concentration across the cross-section of sample 15. Additionally, the concentration of titania can be determined for each segment 20 to determine the uniformity of the titania concentration across the cross-section of sample 15. As described further below, the concentration of one or more components is determined throughout the entire thickness (h) of each segment 20.

[0031] While FIG. 2A depicts the segments 20 as extending along the entire length (L) and width (W) of the sample 15, it is contemplated that the portion of the sample 15 comprising the segments 20 may be less than the entire cross-sectional length (L) and width (W). For example, as shown in FIG. 2B, the sample 15 may include a peripheral edge 17 where no segments 20 are formed. Thus, the peripheral edge 17 may be the clearance between the end of the segment 20 and the outer edge of the sample 15. In embodiments, the peripheral edge may extend 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.

[0032] Segments 20 may be adjacent segments spanning a particular length and width of sample 15 such that segments 20 span the entire area defined by the particular length and width of sample 15. As previously mentioned, the particular length and width may be equal to or less than the length (L) and width (W) of sample 15. In embodiments, segments 20 are adjacent segments (with no gaps between them) spanning the length and width of sample 15 such that the length and width, respectively, are 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, segment 20 is a contiguous segment that spans the length and width of sample 15, such that the length and width are each about 530 mm or about 1200 mm.

[0033] If the sample 15 has a flat surface, the segments 20 are formed along that flat surface, as shown in Figure 2A. However, if the sample 15 has a concave or convex surface, the segments 20 are formed along the curved surface of the sample 15.

[0034] As shown in FIG. 2A , each segment 20 has a length (L′) and width (W′) that are each approximately 12.7 mm. However, embodiments of the present disclosure encompass other length (L′) and width (W′) values ​​and are not limited to 12.7 mm. It is contemplated that in embodiments, the length (L′) may not be equal to the width (W′). Additionally, it is noted that in some embodiments, the length (L′) and width (W′) of a segment 20 may be equal to the length (L”) of the perimeter 17.

[0035] As mentioned above, the height of each segment 20 is the height (h) of the sample 15. Therefore, in this embodiment, the height h is about 7.62 mm.

[0036] As previously discussed, the concentration of one or more components can be determined within each segment 20. Thus, for example, the concentration of hydroxyl and / or the concentration of titania can be determined for each adjacent segment 20 within sample 15. If each segment 20 has a length and width of 12.7 mm, the concentrations of those components are determined at a frequency of 12.7 mm across the cross-section of sample 15. For example, the concentration of hydroxyl is measured at a frequency of 12.7 mm across the cross-section of sample 15.

[0037] The concentration of hydroxyl for each segment 20 is measured using transmission Fourier transform infrared spectroscopy ("FTIR"). As used herein, "transmission" refers to directing light through the glass body to be measured to determine the hydroxyl concentration (as opposed to using light reflected from the glass body to determine the hydroxyl concentration). Thus, "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 base absorption peak for hydroxyl, which measures the peak height relative to the background signal, which is the straight line between the points surrounding the absorption peak. The absorption peak height is then divided by the height (h) of the sample 15 to determine the absorption coefficient β OH The hydroxyl concentration is then calculated using the formula: C=β OH / ε×MW OH / D ガラス ×106 Using the absorption coefficient β OH where C is the concentration of hydroxyl in ppm for a particular segment 20, and β OH is the absorption coefficient of the glass, and ε is 3670 cm -1is the molar extinction coefficient of hydroxyl for the absorption peak at wavenumber MW OH is the molecular weight of the hydroxyl (g / mol) and D is the density of the hydroxyl (g / cm 3 ) The FTIR analysis disclosed above is further disclosed in KM Vis et al., "Quantitative infrared spectroscopic measurement of hydroxyl concentration in silica glass," J. Non-Crystalline Solids, 203 (1996), pp. 27-36, which is incorporated herein by reference. As previously mentioned, the hydroxyl concentration is measured for each segment 20 of the sample 15 and is measured throughout the entire height (h) of each segment 20. The hydroxyl concentration measurement is then repeated across all segments 20 of the sample 15.

[0038] The titania concentration of each segment 20 is calculated based on the measured refractive index of 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 from Zygo Corporation, which has a pixel size resolution of 270 micrometers and operates at a wavelength of 633 nm. The optical interferometer is configured so that the pixels are square, measuring 270 micrometers by 270 micrometers, and each pixel spans the entire thickness (h) of the sample 15. The refractive index is measured at each pixel within the segment 20 throughout the entire thickness of the pixel. The measured refractive indices for each pixel within the segment 20 are then averaged together to determine the average refractive index for each segment 20. The refractive index measurement is then repeated across all segments 20 of the sample 15.

[0039] Next, the following relation: 55 ppm RI=0.0125%C Ti Determine the average titania concentration of each segment 20 based on the average refractive index of each segment 20 using the formula: where RI is the average refractive index of each segment 20 and C Tiis the average concentration (expressed in wt%) of titania in each segment 20. Note that the above relationship assumes that the only contribution to the refractive index change is from titania.

[0040] Furthermore, the following relation: 55ppm RI=1 ppb / K CTE Determine the average CTE of each segment 20 from the average refractive index of each segment 20 using: RI = CTE (where RI is the average refractive index of each segment 20 and CTE is the coefficient of thermal expansion (expressed in ppb / K) of each segment 20. Note that the above relationship assumes that the only contribution to the change in refractive index is from the CTE.

[0041] In addition, the following relation: ΔCTE / CTE slope = ΔT ZC Using the CTE of each segment 20, the T of each segment 20 ZC where ΔCTE is the deviation of the CTE for a particular segment 20 compared to the average CTE of all segments 20 (expressed in ppb / K), and CTE slope is the slope of the CTE of all segments 20 as a function of temperature (expressed in ppb / K 2 ) and ΔT ZC is the average T of all 20 segments ZC T for specific segments compared to ZC The above relation is the deviation (℃) of T ZC Note that we assume that the only contribution to the change in K is from the CTE. In the embodiments disclosed herein, the CTE gradient is approximately 1.0 ppb / K. 2 to approximately 2.5 ppb / K 2 , or about 1.15 ppb / K 2 to approximately 2.0 ppb / K 2 , or about 1.2 ppb / K 2 to approximately 1.9 ppb / K 2 , or about 1.3 ppb / K 2 to approximately 1.7 ppb / K 2 is.

[0042] One or more segments 20 may have a different concentration of one or more components from one or more other segments 20. For example, one or more segments 20 may have a different average concentration of hydroxyl than one or more other segments 20. Additionally or alternatively, one or more segments 20 may have a different average concentration of titania 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 than segments 20 closer to the periphery of the sample 15. As a representative example, segments A, B, and C in FIG. 2A may each have a higher concentration of hydroxyl than segments X, Y, and Z.

[0043] In some embodiments, the concentration of hydroxyl may be a gradient that extends radially outward along the sample 15, with the highest hydroxyl concentration near the center point 18, such that segments have gradually decreasing hydroxyl concentration moving radially outward from the center point 18. In these embodiments, the segments near the center point 18 have the highest concentration of hydroxyl, while the segments near the periphery of the sample 15 have the lowest concentration of hydroxyl.

[0044] In yet another embodiment, segments 20 near the periphery of sample 15 may have a higher concentration of hydroxyls than other segments. For example, Q, R, and S in FIG. 2A may each have a higher concentration of hydroxyls than segments A, B, and C, which in turn have a higher concentration of hydroxyls than segments X, Y, and Z.

[0045] In some embodiments, it is contemplated that all of the segments 20 have the same concentration (or substantially the same concentration) of hydroxyls.

[0046] Furthermore, one or more segments 20 may have the same or different titania concentrations. In some embodiments, the titania concentration may be the same (or substantially the same) throughout the segments 20. Thus, in some embodiments, the titania concentration may be uniformly distributed within the segments 20.

[0047] The average concentrations of each segment 20 can be averaged together to determine the average concentration across the cross-section of sample 15. For example, the average concentration of hydroxyl for each segment 20 can be measured (as described above), and each of these concentrations can be averaged together to determine the average hydroxyl concentration across the entire sample 15. More specifically, in embodiments where sample 15 includes 144 segments 20, the hydroxyl concentrations of the 144 segments 20 can be averaged together to determine the average hydroxyl concentration across the entire sample 15. Note also that the average concentration across sample 15 can be over a particular length and width across the sample that is less than the entire length (L) and width (W) of the sample.

[0048] According to embodiments disclosed herein, the average hydroxyl concentration across Sample 15 is 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 it can be about 300 ppm or more, or about 400 ppm or more, or about 500 ppm or more, or about 600 ppm or more, or about 700 ppm or more, or about 800 ppm or more, or about 900 ppm or more, or about 1000 ppm or more, or about 1100 ppm or more, or about 1200 ppm or more, or about 1300 ppm or more, or about 1400 ppm or more, or about 1500 ppm or more, or about 2000 ppm or more. Additionally, or alternatively, the average hydroxyl concentration across Sample 15 is 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 it may be 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 embodiments, the average hydroxyl concentration is from about 0 ppm to about 2000 ppm, or from about 200 ppm to about 1900 ppm, or from about 300 ppm to about 1800 ppm, or from about 400 ppm to about 1700 ppm, or from about 500 ppm to about 1750 ppm, or from about 600 ppm to about 1600 ppm, or from about 700 ppm to about 1500 ppm, or from about 800 ppm to about 1400 ppm, or from about 900 ppm to about 1300 ppm, or from about 1000 ppm to about 2000 ppm, or from about 1000 ppm to about 1500 ppm, or from about 1000 ppm to about 1200 ppm. ppm, or from about 1000 ppm to about 1100 ppm, or from about 600 ppm to about 1500 ppm, or from about 600 ppm to about 1400 ppm, or from about 600 ppm to about 1300 ppm, or from about 700 ppm to about 1000 ppm, or from about 20 ppm to about 450 ppm, or from about 50 ppm to about 200 ppm, or from about 75 ppm to about 150 ppm, or from about 80 ppm to about 125 ppm, or from about 80 ppm to about 500 ppm, or from about 80 ppm to about 400 ppm, or from about 80 ppm to about 300 ppm, or from about 80 ppm to about 200 ppm.

[0049] In some specific embodiments, the maximum hydroxyl concentration in segment 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 segment 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.

[0050] The average titania concentration across Sample 15 can be from about 1.0 wt.% to about 15.0 wt.%, or from about 6.0 wt.% to about 12.0 wt.%, or from about 6.0 wt.% to about 8.5 wt.%, or from about 6.5 wt.% to about 8.0 wt.%, or from about 7.0 wt.% to about 7.7 wt.%, or from about 6.5 wt.% to about 7.8 wt.%.

[0051] The difference between the highest and lowest average concentrations of one or more components among different segments 20 is also determined. More specifically, the segment 20 having the highest average concentration of a particular component (e.g., hydroxyl or titania) is compared to the segment 20 having the lowest average concentration of that particular component. The difference between the highest and lowest average concentrations of that 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.

[0052] FIG. 3 shows an exemplary plot 100 of the average hydroxyl concentration of each radially outward segment of sample 15 from the center, according to embodiments disclosed herein. The plot in FIG. 3 is taken along the length of sample 15, radially outward from center point 18. As shown in the exemplary embodiment of FIG. 3, the segment 20 having the highest average concentration of hydroxyl is located near center point 18, while the segment having the lowest average concentration of hydroxyl is located at the radially peripheral edge of sample 15. In particular, in the example shown in FIG. 3, the average concentration of hydroxyl is Max OH Highest and Min OH Therefore, the PV difference is Max OH Position and Min OH However, as also mentioned above, the distribution of hydroxyls may be varied in other embodiments, e.g., by varying the average hydroxyl concentration at each position. OH The location may be at the periphery of the sample 15 and / or OH The position may vary so that it may be located near the center point 18 .

[0053] The PV difference in hydroxyl concentration of segment 20 in sample 15 can 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 segment 20 can be about 0.0 ppm or more, or about 1.0 ppm or more, or about 2.5 ppm or more, or about 5.0 ppm or more, or about 10 ppm or more, or about 15 ppm or more, or about 20 ppm or more, or about 25 ppm or more, or about 30 ppm or more, or about 35 ppm or more, or about 40 ppm or more, or about 45 ppm or more, or about 50 ppm or more. In some embodiments, the PV difference in hydroxyl concentration of 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.

[0054] In embodiments, the PV difference in hydroxyl concentration of segment 20 in sample 15 is calculated using the following formula: PV OH = Y × L C is related to the size of the sample 15 according to the formula: OH is the PV of hydroxyl in the sample (expressed in ppm), and L C is the characteristic length of the sample (expressed in cm). As used herein, the characteristic length L C is the minimum of the length L and width W of the sample 15. Therefore, if the sample 15 has a length L that is smaller than the width W, the length L is the characteristic length L. C Conversely, if the sample 15 has a width W that is smaller than the length L, the width W is equal to the characteristic length L. CIn the above formula, Y (expressed in ppm / cm) 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 embodiments, Y is in the range of about 1 to about 150, about 2 to about 250, about 2 to about 120, about 3 to about 100, about 4 to about 80, about 5 to about 60, about 6 to about 30, about 7 to about 20, about 1 to about 30, about 2 to about 25, about 3 to about 20, about 1 to about 15, about 2 to about 10, or about 5 to about 10.

[0055] 4 shows an example plot 200 of titania concentration for each segment 20 radially outward from the center of sample 15, according to embodiments disclosed herein. The plot in FIG. 4 is taken along the length of sample 15 radially outward from center point 18 (similar to that in FIG. 3). As shown in FIG. 4, the titania concentration of segment 20 is approximately equal near center point 18 of sample 15 and at its radially peripheral edges, with little variation in titania concentration. However, even small variations in titania concentration can still result in a maximum titania concentration of 1000 MPa. Ti The highest titania concentration is at Min Ti The minimum titania concentration occurs at the position. Therefore, the PV difference is Max Ti Position and Min Ti is the difference between the titania concentrations at the positions.

[0056] The PV difference in titania concentration of segment 20 in sample 15 may be about 0.0040% by weight or less, or about 0.0035% by weight or less, or about 0.0030% by weight or less, or about 0.0025% by weight or less, or about 0.0020% by weight or less, or about 0.0015% by weight or less, or about 0.0010% by weight or less. In embodiments, the PV difference in titania concentration of segments 20 is in the range of about 0.0010% to about 0.0050% by weight, or about 0.0015% to about 0.0045% by weight, or about 0.0020% to about 0.0040% by weight, or about 0.0025% to about 0.0035% by weight, or about 0.0030% to about 0.0050% by weight, or about 0.0010% to about 0.0030% by weight, or about 0.0010% to about 0.0025% by weight, or about 0.0010% to about 0.0020% by weight.

[0057] As previously mentioned, the PV difference in both hydroxyl and titania concentrations is very small, thus providing a homogeneous glass body 10. Because the PV difference is so low, the glass body 10 can be efficiently polished to provide a flat surface with high flatness.

[0058] In addition, as mentioned above, the average T ZC , average refractive index, and average CTE are determined. One or more segments 20 may differ in these properties from one or more other segments 20. Thus, for example, a first segment 20 may have a different average T than a second segment 20. ZC and / or may have different average refractive indices.

[0059] FIG. 5 shows the average T for each radially outward segment 20 of the sample 15 according to embodiments disclosed herein. ZC 5 shows an example plot 300 of the lowest average T ZCThe segment 20 having the highest average T ZC The segment 20 having the average T ZC Max Tzc Highest and Min Tzc Therefore, the PV difference is Max Tzc Position and Min Tzc Average T at position ZC However, the average T ZC In other embodiments, the distribution of Tzc The location may be at the periphery of the sample 15 and / or Tzc The position may vary so that it may be located near the center point 18 .

[0060] Average T in 20 segments across 15 samples ZC The PV difference may be from about 0.050°C to about 0.300°C, or from about 0.075°C to about 0.250°C, or from about 0.080°C to about 0.200°C, or from about 0.100°C to about 0.190°C, or from about 0.120°C to about 0.180°C, or from about 0.140°C to about 0.160°C, or from about 0.050°C to about 0.180°C, or from about 0.100°C to about 0.140°C.

[0061] The vitreous body 10 has an average T ZC The small PV difference allows the surface shape ("appearance") to be maintained when exposed to temperature changes in an EUV lithography system.

[0062] Comparing Figures 3 and 5, Max OH The position is Min on sample 15 Tzc Thus, in these embodiments, the segment with the highest concentration of hydroxyls is located at the lowest T ZC Furthermore, in these embodiments, the segment 20 having a relatively high hydroxyl concentration also has a relatively low T ZCIt has.

[0063] Average T of 20 segments across 15 samples ZC 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.

[0064] FIG. 6 shows an example plot 400 of the average refractive index of each radially outward segment 20 of sample 15, according to embodiments disclosed herein. Plot 400 in FIG. 6 is taken from center point 18 along the length of sample 15 (similar to those in FIGS. 3-5). Furthermore, compared to plot 200 (shown in FIG. 4), the average refractive index of segments 20 across sample 15 is similar to the average titania concentration of segments 20 across sample 15. As shown in FIG. 6, the average refractive index is nearly equal near center point 18 and at the radially peripheral edges of sample 15, with little variation in the average refractive index. However, small variations in the average refractive index still result in a Max. RI Position the maximum amount, Min RI The minimum amount occurs at the position. Therefore, the PV difference is Max RI Position and Min RI is the difference between the average refractive index at a given position.

[0065] The PV difference in the average refractive index of segment 20 in sample 15 is approximately 1 × 10 -4 or less, or about 5 x 10 -5 or less, or about 1 x 10 -5 or less, or about 5 x 10 -6 or less, or about 1 x 10 -6 or less, or about 5 x 10 -7 or less, or about 1 x 10 -7 or less, or about 1 x 10 -6 to approximately 1 × 10 -4 , or approximately 6 × 10 -6 From about 9 x 10 -5 , or approximately 10 × 10 -6 From about 6 × 10 -5, or approximately 1 × 10 -6 to approximately 1 × 10 -5 , or approximately 1 × 10 -5 to approximately 1 × 10 -4 The refractive index distribution within a glass body is an indicator of the titania concentration distribution within that body. Therefore, a glass body with a smaller PV difference in refractive index will also have a smaller PV difference in titania. As mentioned earlier, a smaller PV difference in titania allows the glass body to be polished more uniformly.

[0066] FIG. 7 shows an example plot 500 of the average CTE of each radially outer segment 20 of sample 15 from the center, according to embodiments disclosed herein. Plot 500 in FIG. 7 is taken along the length of sample 15 from center point 18 (similar to those in FIGS. 3-6 ). Furthermore, compared to plot 200 (shown in FIG. 4 ) and plot 400 (shown in FIG. 6 ), the average CTE of segments 20 across sample 15 resembles the average concentration of titania in segments 20 across sample 15, which resembles the average refractive index of segments 20. As shown in FIG. 7 , the average CTE is nearly equal near center point 18 and at the radially peripheral edges of sample 15, with little variation in the average CTE. However, small variations in the average CTE still contribute to the Max CTE Position the maximum amount, Min CTE The minimum amount occurs at the position. Therefore, the PV difference is Max CTE Position and Min CTE is the difference between the mean CTE at the position.

[0067] The PV difference of the average CTE of segments 20 in 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 embodiments, the PV difference of the average CTE of segments 20 in a 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.

[0068] The average CTE of each segment 20 is from about −30 ppb / K to about +30 ppb / K at temperatures between 288 K and 303 K. In some embodiments, the CTE is from about −10 ppb / K to about +10 ppb / K at temperatures between 288 K and 303 K, or from about −5 ppb / K to about +5 ppb / K at temperatures between 288 K and 303 K, or from about −2 ppb / K to about +2 ppb / K at temperatures between 288 K and 303 K.

[0069] Referring again to Figure 3, the average hydroxyl concentration of a segment 20 along the sample 15 forms a parabolic curve when plotted as a function of distance along the sample 15. In the particular embodiment of Figure 3, the parabolic curve is centered about midpoint 18 such that the curve slopes downward from this midpoint. However, it is contemplated that in other embodiments, the average hydroxyl concentration of a segment 20 along the sample 15 may form a parabolic curve having other profiles and shapes.

[0070] In embodiments, the average hydroxyl concentration in a segment 20 along the length of the sample 15 is calculated according to the following formula: y=Ax 2 +Bx+C where y represents the average concentration of hydroxyl (expressed in ppm) for a particular segment 20, x represents the distance (expressed in mm) along the sample 15, and A is the quadratic term, expressed in ppm / mm. 2 where B is a linear term and has units of ppm / mm, and C is a constant and has units of ppm. In some embodiments, the parabolic curve has a Gaussian distribution that is symmetric about the point x=0. Therefore, the parabolic curve may be a bell curve. In other embodiments, the parabolic curve may not be symmetric and may have other distribution functions.

[0071] In an embodiment, A defines the slope or steepness of the parabolic curve and is approximately -20 ppm / mm 2 to about 20 ppm / mm 2 , or about -15 ppm / mm 2 to about 15 ppm / mm 2 , or about -10 ppm / mm 2 to about 10 ppm / mm 2 , or approximately -5 ppm / mm 2 to about 5 ppm / mm 2 , or about -2.5 ppm / mm 2 to approximately 2.5 ppm / mm 2 , or about -20 ppm / mm 2 to about 5 ppm / mm 2 , or about -20 ppm / mm 2 to approximately 2 ppm / mm 2 , or about -20 ppm / mm 2 to approximately 0.5 ppm / mm 2 , or about -20 ppm / mm 2 to approximately 0 ppm / mm 2 , or about -20 ppm / mm 2 to approximately -0.1 ppm / mm 2 , or about -20 ppm / mm 2 to approximately -0.25 ppm / mm 2 , or about -20 ppm / mm 2 to approximately -0.5 ppm / mm 2 , or about -10 ppm / mm 2 to approximately -0.1 ppm / mm 2, or approximately -5 ppm / mm 2 to approximately -0.1 ppm / mm 2 , or about -2 ppm / mm 2 to approximately -0.1 ppm / mm 2 , or about -1.8 ppm / mm 2 to approximately -0.2 ppm / mm 2 , or about -1.6 ppm / mm 2 to approximately -0.4 ppm / mm 2 , or about -1.2 ppm / mm 2 to approximately -0.8 ppm / mm 2 , or about -1.8 ppm / mm 2 to approximately -1.0 ppm / mm 2 , or about -1.6 ppm / mm 2 to approximately -1.0 ppm / mm 2 , or approximately -1.0 ppm / mm 2 to approximately 1.0 ppm / mm 2 , or approximately -0.5 ppm / mm 2 to approximately 0.5 ppm / mm 2 , or approximately -0.25 ppm / mm 2 to approximately 0.25 ppm / mm 2 , or approximately -0.2 ppm / mm 2 to approximately 0.2 ppm / mm 2 , or approximately -0.2 ppm / mm 2 to approximately -0.1 ppm / mm 2 , or approximately -0.2 ppm / mm 2 to approximately -0.8 ppm / mm 2 , or approximately -0.2 ppm / mm 2 to approximately 0.6 ppm / mm 2 , or approximately 0.0 ppm / mm 2 to approximately -0.1 ppm / mm 2 , or approximately 0.0 ppm / mm 2 to approximately -0.04 ppm / mm 2 , or approximately 0.0 ppm / mm 2 to approximately -0.02 ppm / mm 2 , or approximately 0.0 ppm / mm 2 to approximately -0.01 ppm / mm 2 , or approximately -0.01 ppm / mm 2to approximately -0.04 ppm / mm 2 , or approximately -0.01 ppm / mm 2 to approximately -0.02 ppm / mm 2 , or approximately -0.02 ppm / mm 2 to approximately -0.04 ppm / mm 2 In some embodiments, A is in the range of about −0.2 ppm / mm 2 , or about -1.5 ppm / mm 2 , or about -1.6 ppm / mm 2 , or approximately -1.9 ppm / mm 2 is.

[0072] In embodiments, B is from about -50 ppm / mm to about 50 ppm / mm, or from about -40 ppm / mm to about 40 ppm / mm, or from about -30 ppm / mm to about 30 ppm / mm, or from about -20 ppm / mm to about 20 ppm / mm, or from about -15 ppm / mm to about 15 ppm / mm, or from about -10 ppm / mm to about 10 ppm / mm, or from about -5 ppm / mm to about 5 ppm / mm, or from about -2 ppm / mm to about 2 ppm / mm, or from about -1 ppm / mm to about 1 ppm / mm, or about -30 ppm / mm to about 10 ppm / mm, or about -25 ppm / mm to about 5 ppm / mm, or about -20 ppm / mm to about 2.5 ppm / mm, or about -15 ppm / mm to about 0 ppm / mm, or about -10 ppm / mm to about 0 ppm / mm, or about -30 ppm / mm to about 0 ppm / mm, or about -20 ppm / mm to about 0 ppm / mm, or about 0 ppm / mm to about 5 ppm / mm, or about 0 ppm / mm to about 20 ppm / mm. In some embodiments, B is about -21 ppm / mm, or about -0.1 ppm / mm, or about 0.05 ppm / mm, or about 4.8 ppm / mm.

[0073] In embodiments, 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 embodiments, C is about 500 ppm or more, or about 600 ppm or more, or about 700 ppm or more, or about 800 ppm or more, or about 850 ppm or more, or about 900 ppm or more, or about 950 ppm or more, or about 1000 ppm or more, or about 1500 ppm or more, or about 2000 ppm or more.In embodiments, C is from about 0 ppm to about 2000 ppm, or from about 200 ppm to about 1900 ppm, or from about 300 ppm to about 1800 ppm, or from about 400 ppm to about 1700 ppm, or from about 500 ppm to about 1750 ppm, or from about 600 ppm to about 1600 ppm, or from about 700 ppm to about 1500 ppm, or from about 800 ppm to about 1400 ppm, or from about 800 ppm to about 1600 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 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 In some embodiments, C is about 1030 ppm, about 1078 ppm, about 1080 ppm, about 1140 ppm, about 80 ppm, or about 50 ppm. In some embodiments, C is 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. It is also contemplated that in embodiments disclosed herein, C may be undefined such that C can be any value and is not limited to any particular range.

[0074] In the parabolic curve, x is the distance (in mm) along the sample 15 from the point where x=0. Therefore, x can be anywhere along the length of the sample 15 such that the above parameters of A, B, and C are satisfied. In the example plot 100 of FIG. 3, the x=0 point is at the center point 18 of the sample 15. However, in other example embodiments, the x=0 point may be located at other locations on the sample 15.

[0075] In some embodiments, the parabolic curve extends a distance of at least about 50 mm or more along the sample 15. Thus, the parabolic curve spans a length of at least 50 mm along the x-axis when the parabolic curve is plotted in terms of x and y coordinates. In other embodiments, the parabolic curve extends a distance along the sample 15 of about 60 mm or more, or 70 mm or more, or about 75 mm or more, or 80 mm or more, or 90 mm or more, or 100 mm or more, or 125 mm or more, or 150 mm or more, or 175 mm or more, or 200 mm or more, or 250 mm or more, or 300 mm or more, or 400 mm or more, or 500 mm or more, or 600 mm or more, or 700 mm or more, or 800 mm or more, or 900 mm or more, or 1000 mm or more, or 1100 mm or more, or 1200 mm or more, or 1500 mm or more, or 2000 mm or more. The maximum distance that the parabolic curve extends along the x-axis is the longest linear dimension (eg, diagonal length) of the cross-section of sample 15 .

[0076] In some embodiments, B has the formula: y=Ax 2 +C is equal to zero so that it can be simplified to

[0077] The parabolic curves disclosed herein represent best-fit curves of the average hydroxyl concentrations of segment 20. A quantifiable analysis of how well different average hydroxyl concentrations of segment 20 fit the resulting parabolic curve is the best-fit value R 2 which can be expressed by the above-mentioned x and y and the following equation:

[0078]

number

[0079] The best fit value R of the parabolic curve disclosed herein is calculated using 2 is 0.3 or greater, or 0.4 or greater, or 0.5 or greater, or 0.6 or greater, or 0.7 or greater, or 0.8 or greater, or 0.9 or greater, or about 1.0.

[0080] Typical examples The following example shows the average hydroxyl concentration of segment 20 and the corresponding parabolic curve for glass samples according to embodiments disclosed herein.

[0081] FIG. 8A shows an exemplary embodiment of Sample 15-A, having a length (L) of 152.4 mm, a width (W) of 152.4 mm, and a height (h) of 7.62 mm. Sample 15-A is further divided into 100 segments 20. Note that Sample 15-A includes a perimeter edge having a length of 12.7 mm, where the sample is not divided into segments. Each of the segments 20 of Sample 15-A has a length (L') and width (W') of 12.7 mm and a height (h) of 7.62 mm. FIG. 8A shows the average hydroxyl concentration (expressed in ppm) for each segment 20. As shown in FIG. 8A, the segment 20 with the highest concentration of hydroxyl is located near the center point 18 of Sample 15-A, while the segment with the lowest concentration of hydroxyl is located near the perimeter edge of the sample.

[0082] FIG. 8B shows the hydroxyl concentration of each segment 20 of sample 15-A plotted as a function of distance along the sample 15-A. In this example, the x=0 point is at the center point 18. A best fit parabolic curve of these data points is shown in FIG. 8B and has the equation: y=-0.00235x 2 +(-0.86x)+1139.93. The best fit value for this equation is R 2 is 0.73.

[0083] FIG. 9A shows an exemplary embodiment of Sample 15-B, having a length (L) of 152.4 mm, a width (W) of 152.4 mm, and a height (h) of 7.62 mm. Sample 15-B is further divided into 100 segments 20. Note that Sample 15-B includes a perimeter edge having a length of 12.7 mm, where the sample is not divided into segments. The segments 20 of Sample 15-B each have a length (L') and width (W') of 12.7 mm and a height (h) of 7.62 mm. FIG. 9A shows the hydroxyl concentration (expressed in ppm) of each segment 20. As shown in FIG. 9A, the segment 20 with the highest concentration of hydroxyl is located near the left corner of Sample 15-B, while the segment with the lowest concentration of hydroxyl is located near the top right of the sample.

[0084] FIG. 9B shows the hydroxyl concentration of each segment 20 of Sample 15-B plotted as a function of distance along Sample 15-B. In this example, the x=0 point is at the center point 18. A best fit parabolic curve of these data points is shown in FIG. 9B and has the equation: y=-0.000365x 2 +0.187x+1032.39. The best fit value for this equation is R 2 is 0.11.

[0085] FIG. 10A shows an exemplary embodiment of Sample 15-C, which has a length (L) of 152.4 mm, a width (W) of 152.4 mm, and a height (h) of 7.62 mm. Sample 15-C is further divided into 100 segments 20. Note that Sample 15-C includes a perimeter edge having a length of 12.7 mm, where the sample is not divided into segments. The segments 20 of Sample 15-C each have a length (L') and width (W') of 12.7 mm and a height (h) of 7.62 mm. FIG. 10A shows the hydroxyl concentration (expressed in ppm) of each segment 20. As shown in FIG. 10A, the segment 20 with the highest concentration of hydroxyl is located near but offset from the center point 18 of Sample 15-C, while the segment with the lowest concentration of hydroxyl is located near the perimeter edge of the sample.

[0086] FIG. 10B shows the hydroxyl concentration of each segment 20 of Sample 15-C plotted as a function of distance along Sample 15-C. Most specifically, FIG. 10B shows a first plot of hydroxyl concentration versus distance along Sample 15-C. In this first plot, point x=0 is at center point 18, and the plot is calculated using the equation: y=−0.00251x 2 +(-0.00568x)+1077.54. The best fit value for this equation is R 2 In the second plot shown in FIG. 10B, point x=0 is at center point 18′, and this plot has the equation: y′=−0.00288x′ 2 +0.00282x'+1079.02. The best fit value for this equation is R 2 is 0.94. Point x=0 of the second plot is in the segment with the highest hydroxyl concentration (rather than the center point 18 of sample 15), and the second plot has a better best fit value R than the first plot. 2 Note that

[0087] Figures 13-16 show example samples of various sizes, each with a low hydroxyl concentration within a segment and therefore a uniform hydroxyl concentration along the sample. Specifically, Sample 15-D in Figure 13 has a length (L) of 127 mm, a width (W) of 127 mm, and a height (h) of 7.62 mm. Note that the hydroxyl concentration of Sample 15-D was measured across the entire length (L) and width (W) of the sample. Additionally, Sample 15-D has a mass of 2.5 kg. As shown in Figure 13, Sample 15-D is divided into 25 segments, each with a length (L') and width (W') of 25.4 mm. Figure 13 shows the average hydroxyl concentration (expressed in ppm) for each segment 20. The average hydroxyl concentration in Sample 15-D is 112 ppm, and the hydroxyl concentration PV difference across Sample 15-D is 4 ppm.

[0088] Sample 15-E in Figure 14 has a length (L) of 127 mm, a width (W) of 127 mm, and a height (h) of 7.62 mm. Note that the hydroxyl concentration of Sample 15-E was measured across the entire length (L) and width (W) of the sample. Additionally, Sample 15-E has a mass of 4.5 kg. As shown in Figure 14, Sample 15-E was divided into 25 segments, each of which had a length (L') and width (W') of 25.4 mm. Figure 14 shows the average hydroxyl concentration (expressed in ppm) for each segment 20. The average hydroxyl concentration in Sample 15-E was 171 ppm, and the PV difference in hydroxyl concentration in Sample 15-E was 9 ppm.

[0089] Sample 15-F in Figure 15 has a length (L) of 279.4 mm, a width (W) of 279.4 mm, and a height (h) of 7.62 mm. Note that the hydroxyl concentration of Sample 15-F was measured across the entire length (L) and width (W) of the sample. Additionally, Sample 15-F has a mass of 12 kg. As shown in Figure 15, Sample 15-F was divided into 100 segments, each of which had a length (L') and width (W') of 27.94 mm. Figure 15 shows the average hydroxyl concentration (expressed in ppm) for each segment 20. The average hydroxyl concentration in Sample 15-F was 155 ppm, and the PV difference in the average hydroxyl concentration in Sample 15-F was 24 ppm.

[0090] Sample 15-G in Figure 16 has a length (L) of 431.8 mm, a width (W) of 431.8 mm, and a height (h) of 7.62 mm. Note that the hydroxyl concentration of Sample 15-G was measured across the entire length (L) and width (W) of the sample. Additionally, Sample 15-G has a mass of 36.5 kg. As shown in Figure 16, Sample 15-G was divided into 225 segments, each of which has a length (L') and width (W') of 27.79 mm. Figure 16 shows the average hydroxyl concentration (expressed in ppm) for each segment 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. Note that Sample 15-G has such a uniform hydroxyl concentration across all of the sample, especially for such a large mass.

[0091] Typical Process 11 illustrates a process 1100 for forming a glass body 10 according to embodiments disclosed herein. As previously mentioned, specific steps of the process 1100 allow for the determination of the hydroxyl concentration, titania concentration, T ZCA glass body 10 is formed having a distribution of refractive indices, refractive indices, and CTEs. As shown in process 1100 of Figure 11, the glass body 10 can be prepared in step 1110 by combusting and oxidizing a mixture of silica and titanium precursors to form discrete soot particles. Each soot particle comprises SiO2 and TiO2.

[0092] FIG. 12 shows a schematic diagram of a system 1200 for producing discrete soot particles. Referring to FIG. 12, the system 1200 includes a first reservoir 1220 containing a silica precursor 1224 and a second reservoir 1230 containing a titania precursor 1234. The temperatures of the first and second reservoirs 1220, 1230 can be monitored to ensure that the precursors in each reservoir are uniform and constant (i.e., within ±0.5°C) throughout the reservoir. The first reservoir 1220 includes an inlet 1222 at or near the base of the reservoir for introducing a carrier gas, such as nitrogen. The carrier gas forms a vapor stream containing the silica precursor 1224. Similarly, the second reservoir 1230 includes an inlet 1232 at or near the base of the reservoir for introducing a carrier gas, such as nitrogen. The carrier gas in the second reservoir 1230 forms a vapor stream containing titania precursor 1234. The carrier gases flowing into the inlets 1222, 1232 flow into the respective reservoirs 1220, 1230 at a constant and uniform flow rate so as not to introduce any perturbations into the system 1200. More specifically, the carrier gases flowing into the inlets 1222, 1232 flow at flow rates within 5% of each other.

[0093] As discussed above, the silica precursor 1224 may include, for example, octamethylcyclotetrasiloxane, and the titania precursor 1234 may include titanium tetraisopropoxide.

[0094] A bypass flow of carrier gas is also introduced into system 1200 at inlets 1226 and 1236 to prevent saturation of the silica and titania vapor streams. In an embodiment, the silica and titania vapor streams are heated by thermal oil tracing to prevent the formation of hot and cold spots in the vapor streams. Note that both hot and cold spots in the vapor stream affect the precursor concentration in the vapor stream, thereby producing glass with suboptimal properties. The silica vapor stream then flows through distribution system 1242 to manifold 1248, and the titania vapor stream flows through distribution system 1244 to manifold 1248.

[0095] The silica and titania vapor streams then combine in manifold 1248 to form a two-stream mixture. As further shown in FIG. 12 , the two-stream mixture flows to furnace 1250. More specifically, the two-stream mixture flows through fume line 1252 to burner 1254, which is mounted on the top of furnace 1250. The two streams are further combined with a fuel / oxygen mixture at burner 1254 to combust and oxidize the mixture. The fuel may 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 titania vapor streams at burner 1254 such that the amount of oxygen is in a ratio of at least 1:1 to the amount of combined silica and titania vapor (including carrier gas). Thus, the amount of oxygen is at least equal to the amount of silica and titania vapor (including carrier gas), or is two times, or three times, or four times, etc. the amount of silica and titania vapor (including carrier gas).

[0096] In step 1120 of process 1100, the loose soot particles 1260 are then cooled and directed to a collection chamber. In some embodiments, the loose soot particles 1260 are directed to 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, which carries the soot particles in the vapor stream to one or more filter bags 1272. The soot particles 1260 are removed from the vapor 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 into the collection chambers 1264′. Pulses of N2 may be applied periodically to the filter bags 1272 to prevent excessive accumulation of soot particles 1260 on the bag. In some embodiments, the collection chamber 1264' is a stainless steel hopper. The soot particles 1260 can then be further collected from the collection chamber 1264' and placed into a barrel where they can be stored until further use.

[0097] In embodiments, the atmospheric pressure surrounding the system 1200 was precisely monitored to produce glass bodies with the optimal properties disclosed herein (e.g., uniform concentrations of hydroxyl and titania). It was further found that frequent cleaning of the gas lines within the system 1200 and frequent replacement of the filter bag 1272 produced glass bodies with the optimal properties disclosed herein. The soot particles 1260 may 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 before reaching the collection chamber 1264, 1264′ to produce the optimal properties disclosed herein in the glass body.

[0098] In step 1130 of process 1100, the soot particles are transported from the gallon barrel to a mold to form a shaped precursor. The mold is graphite with a very high level of cleanliness (i.e., impurity levels less than 100 ppm) to produce a glass body with excellent properties. The soot particles are pressed within the mold with a press to form a shaped precursor, which is then heat-treated in the presence of steam or under vacuum (i.e., pressure less than 1 Torr (about 133 Pa)) to form a consolidated shaped precursor. In embodiments, the consolidated shaped precursor is opaque after the heat-treatment step.

[0099] In embodiments in which the shaped precursor is heat-treated under vacuum, the precursor is not doped with hydroxide during step 1130 of process 1100. Thus, such embodiments can be referred to as "non-OH doped." Conversely, when the shaped precursor is heated in the presence of steam (also referred to as steam doped, as explained further below), the precursor is doped with hydroxide. The "non-OH doped" process produces a glass body with a reduced hydroxyl concentration compared to the steam doped process.

[0100] In yet another embodiment, the shaped precursor can be actively dried during the heat treatment step to form the consolidated shaped precursor. During such an active drying embodiment, the shaped precursor is exposed to a desiccant while the shaped precursor is 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 shaped precursor reduces the concentration of hydroxyls in the glass body, even lowering it compared to the "no OH doping" process.

[0101] It is further noted that in the "no OH doping" and vapor doping processes, the precursor may not be exposed to a halide reagent. Thus, in these embodiments, the final glass body may contain no halide (i.e., may contain less than 100 ppm halide) such that the glass body is halide-free.

[0102] Additionally, during the consolidation heating of step 1130, the shaped precursor is heated in a furnace at a heating rate of about 2.5° C. / hour or less. Such slow heating helps to uniform the hydroxyl and titania concentrations in the produced glass body.

[0103] Step 1140 of process 1100 includes melting the consolidated shaped precursor into a melt, pouring the melt into another mold, and then cooling the melt to form glass. Once the glass is cooled, a glass body is formed. This glass body no longer has the opacity that developed during the consolidation of step 1130.

[0104] In step 1150, the glass body is then exposed to an environment having high temperature and pressure for a period of time. In some embodiments, the environment having high temperature and pressure includes an inert gas. By "inert gas" is meant a gas that does not chemically react with the glass body. In some embodiments, the high pressure is in the range of 0.5 kpsi to 15 kpsi (about 3.4 MPa to about 103 MPa). Furthermore, in some embodiments, the high temperature is in the range of 1000°C to 1800°C. The glass body may be exposed to the environment for a period of time ranging from 1 hour to 120 hours. Step 1150, in which the glass body is exposed to an environment having high temperature and pressure, may be referred to as "hot isostatic pressing."

[0105] Step 1160 of process 1100 includes a slow cooling step. During this step, internal stresses within the glass body are relieved, which allows for better cutting and machining quality of the glass body. In addition, step 1160 of slow cooling the glass body reduces the average T ZC decreases.

[0106] Referring again to step 1110 of process 1100, Samples 15-A through 15-G (as previously described) were prepared by flowing a silica vapor stream and a titania vapor stream at a flow rate of 9 standard liters per minute (SLPM) into distribution system 1242. As previously described, the two vapor 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 for combusting the mixed gas flowed from burner 1254 at a flow rate of 45 SLPM.

[0107] Vapor doping As previously mentioned, in embodiments, the glass bodies of the present disclosure are comprised of titania-silica glasses having a high concentration of hydroxyl groups. Specifically, the glass bodies are modified to contain a high concentration of hydroxyl groups by consolidating a shaped precursor glass body in a steam-containing atmosphere (during step 1130 of process 1100).

[0108] Fabrication of shaped precursor glass bodies using the vapor doping process involves heat treating in a vapor-free atmosphere, exposing the heat-treated glass bodies to vapor, and consolidating the heat-treated glass bodies in a vapor-containing atmosphere.

[0109] Gases can be purged and removed from the glass body by heat treating the glass body in a steam-free atmosphere. This heat treatment process may 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 may further include an inert gas. Furthermore, this heat treatment may be carried out for a time sufficient to raise the internal temperature of the glass body to a temperature ranging from at least 100°C, or at least 200°C, or from about 100°C to 600°C, or from about 100°C to about 500°C, or from about 150°C to about 600°C.

[0110] After heat treatment in the steam-free atmosphere, the glass body is subsequently exposed to a steam-containing atmosphere to add hydroxyl groups to the glass body. The steam-containing atmosphere may contain steam alone or steam combined with an inert gas. The steam pressure may be about 0.1 atmospheres to about 10 atmospheres (about 10 kPa to about 1 MPa), or about 0.5 atmospheres to about 5 atmospheres (about 50 kPa to about 0.5 MPa). The steam pressure should be constant within the furnace, with a pressure difference of only ±2% of the absolute pressure within the furnace. The temperature at which the glass body is exposed to the steam-containing atmosphere may range from about 200°C to about 900°C, or from about 300°C to about 700°C. The temperature is preferably below the temperature that induces densification or consolidation of the glass body. The time the glass body is exposed to the steam-containing atmosphere can be adjusted to control the concentration of hydroxyl groups contained in the glass body. Longer exposure times result in higher hydroxyl concentrations.

[0111] After exposing the glass body to the steam-containing atmosphere, the glass body is consolidated in the presence of steam. This steam-containing consolidation atmosphere may have the same composition as the steam-containing additive atmosphere (as described above). Consolidation of the glass body in the steam-containing atmosphere is carried out at a temperature for a time sufficient to convert the glass body from a porous body to a closed-pore glass body. The temperature may range from about 900°C to about 1850°C, or from about 900°C to about 1700°C, or from about 900°C to about 1500°C, or from about 900°C to about 1300°C. The time for exposing the glass body to the steam-containing consolidation atmosphere may be at least 0.5 hours, or at least 1 hour, or at least 2 hours, or at least 5 hours. The heating rate may be from about 3°C / min to about 100°C / min, or from about 5°C / min to about 50°C / min.

[0112] The vapor consolidation process may include holding the glass body at a fixed temperature (hold temperature) for a predetermined time. The hold temperature may be from about 1000°C to about 1250°C, or from about 1150°C to about 1200°C, such that the temperature is increased at a heating rate of about 2.5°C / hour or greater. The peak hold temperature during the vapor consolidation process is about 1250°C. The glass body may be held at the hold temperature for a period of about 1 hour to about 240 hours, or between about 5 hours and about 20 hours.

[0113] The previously disclosed vapor consolidation process converts the shaped precursor into a consolidated glass, which, after the vapor consolidation process, is melted as described above with respect to step 1140 of process 1100.

[0114] The use of steam in the previously disclosed steam doping process offers numerous benefits, including the benefits of reduced viscosity, facilitated reduction of fictive temperature, high hydroxyl concentration in the glass, and avoidance of seed crystal formation in the glass.

[0115] Additional embodiments of the previously disclosed vapor consolidation process are disclosed in US Pat. No. 9,580,350, which is incorporated by reference in its entirety.

[0116] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a particular order. Thus, unless a method claim actually recites the order in which its steps should be followed, or unless the claim or description specifically states otherwise that the steps are limited to a particular order, no particular order is intended to be implied in any way.

[0117] It will be apparent to those skilled in the art that various modifications and changes can be made without departing from the spirit or scope of the illustrated embodiments. Since modifications, combinations, sub-combinations, and variations of the disclosed embodiments, which incorporate the spirit and substance of the illustrated embodiments, will occur to those skilled in the art, the description should be construed to include all within the scope of the appended claims and equivalents thereof.

[0118] Preferred embodiments of the present invention will be described below in detail.

[0119] Embodiment 1 It is glass, Titania and silica, Including, A plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is: y=Ax 2 +Bx+C is given by A (ppm / mm 2 (expressed in ppm / mm) is in the range of about 0.0 to about −0.1, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is less than or equal to about 450, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm); The hydroxyl concentration of each segment was measured using transmission Fourier transform infrared spectroscopy. The plot spans a distance of about 50 mm or more along the glass.

[0120] Embodiment 2 2. The glass of claim 1, wherein C is in the range of from about 75 to about 450.

[0121] Embodiment 3 3. The glass of embodiment 2, wherein C is in the range of from about 80 to about 150.

[0122] Embodiment 4 The glass of any one of the preceding claims, wherein B ranges from about -5 to about 5.

[0123] Embodiment 5 5. The glass of embodiment 4 wherein B is 0.

[0124] Embodiment 6 6. The glass of any one of claims 1 to 5, wherein A ranges from about 0.0 to about −0.04.

[0125] Embodiment 7 7. The glass of embodiment 6, wherein A is in the range of about 0.0 to about −0.02.

[0126] Embodiment 8 The best fit value R of the plot 2 8. The glass of any one of the preceding claims, wherein

[0127] Embodiment 9 The best fit value R of the plot 2 9. The glass of embodiment 8, wherein

[0128] Embodiment 10 10. The glass of any one of claims 1 to 9, wherein the plot spans a distance of about 75 mm or more along the glass.

[0129] Embodiment 11 11. The glass of claim 10, wherein the plot spans a distance of about 100 mm or more along the glass.

[0130] Embodiment 12 12. The glass of any one of claims 1-11, wherein the plurality of segments includes all adjacent segments across a length and width of the glass, the length being about 25 mm or greater and the width being 25 mm or greater.

[0131] Embodiment 13 13. The glass of claim 12, wherein the length is about 50 mm or greater and the width is about 50 mm or greater.

[0132] Embodiment 14 14. The glass of claim 13, wherein the length is about 150 mm or greater and the width is about 150 mm or greater.

[0133] Embodiment 15 15. The glass of any one of claims 1 to 14, wherein the glass is a photomask.

[0134] Embodiment 16 16. The glass of any one of claims 1 to 15, wherein the segment having a relatively high hydroxyl concentration has a relatively low zero temperature crossing point.

[0135] Embodiment 17 17. The glass of claim 16, wherein the segment having the highest hydroxyl concentration has the lowest zero temperature crossing point.

[0136] Embodiment 18 It is glass, Titania and silica, Including, A plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is: y=Ax 2 +Bx+C is given by A (ppm / mm 2 (expressed in ppm / mm) is in the range of about 0.0 to about −0.1, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is greater than or equal to about 800, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm); The hydroxyl concentration of each segment was measured using transmission Fourier transform infrared spectroscopy. The plot spans a distance of about 50 mm or more along the glass.

[0137] Embodiment 19 19. The glass of embodiment 18, wherein C is in the range of from about 800 to about 1300.

[0138] Embodiment 20 20. The glass of embodiment 18 or 19, wherein B is in the range of from about −5 to about 5.

[0139] Embodiment 21 21. The glass of embodiment 20, wherein B is 0.

[0140] Embodiment 22 22. The glass of any one of claims 18 to 21, wherein A ranges from about 0.0 to about −0.04.

[0141] Embodiment 23 23. The glass of embodiment 22, wherein A ranges from about 0.0 to about −0.02.

[0142] Embodiment 24 The best fit value R of the plot 2 24. The glass of any one of claims 18 to 23, wherein

[0143] Embodiment 25 The best fit value R of the plot 2 25. The glass of embodiment 24, wherein

[0144] Embodiment 26 26. The glass of any one of claims 18 to 25, wherein the plot spans a distance of about 75 mm or more along the glass.

[0145] Embodiment 27 27. The glass of any one of claims 18 to 26, wherein the plot spans a distance of about 100 mm or more along the glass.

[0146] Embodiment 28 28. The glass of any one of claims 18-27, wherein the plurality of segments includes all adjacent segments across the length and width of the glass, the length being at least about 25 mm, and the width being at least 25 mm.

[0147] Embodiment 29 29. The glass of claim 28, wherein the length is about 50 mm or greater and the width is about 50 mm or greater.

[0148] Embodiment 30 30. The glass of claim 29, wherein the length is about 150 mm or greater and the width is about 150 mm or greater.

[0149] Embodiment 31 31. The glass of any one of claims 18 to 30, wherein the glass is a photomask.

[0150] Embodiment 32 32. The glass of any one of claims 18 to 31, wherein the segment having a relatively high hydroxyl concentration has a relatively low zero temperature crossing point.

[0151] Embodiment 33 33. The glass of claim 32, wherein the segment having the highest hydroxyl concentration has the lowest zero temperature crossing point.

[0152] Embodiment 34 It is glass, Titania and silica, Including, A plot of the average hydroxyl concentration for each of a plurality of segments versus distance along the glass is: y=Ax 2 +Bx+C is given by A (ppm / mm 2 A (expressed in ppm / mm) is in the range of about 0.0 to about −0.1, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is undefined, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm); The hydroxyl concentration of each segment was measured using transmission Fourier transform infrared spectroscopy. The plot spans a distance of about 50 mm or more along the glass.

[0153] Embodiment 35 35. The glass of embodiment 34, wherein B ranges from about −5 to about 5.

[0154] Embodiment 36 36. The glass of embodiment 35, wherein B is 0.

[0155] Embodiment 37 37. The glass of any one of claims 34 to 36, wherein A ranges from about 0.0 to about −0.04.

[0156] Embodiment 38 38. The glass of embodiment 37, wherein A ranges from about 0.0 to about −0.02.

[0157] Embodiment 39 The best fit value R of the plot 2 39. The glass of any one of claims 34 to 38, wherein

[0158] Embodiment 40 The best fit value R of the plot 2 40. The glass of embodiment 39, wherein

[0159] Embodiment 41 41. The glass of any one of claims 34 to 40, wherein the plot spans a distance of about 75 mm or more along the glass.

[0160] Embodiment 42 42. The glass of any one of claims 34 to 41, wherein the plot spans a distance of about 100 mm or more along the glass.

[0161] Embodiment 43 43. The glass of any one of claims 34 to 42, wherein the plurality of segments includes all adjacent segments across the length and width of the glass, the length being at least about 25 mm and the width being at least 25 mm.

[0162] EMBODIMENT 44 44. The glass of claim 43, wherein the length is about 50 mm or greater and the width is about 50 mm or greater.

[0163] Embodiment 45 45. The glass of claim 44, wherein the length is about 150 mm or greater and the width is about 150 mm or greater.

[0164] Embodiment 46 46. ​​The glass of any one of claims 34 to 45, wherein the glass is a photomask.

[0165] Embodiment 47 47. The glass of any one of claims 34 to 46, wherein the segment having a relatively high hydroxyl concentration has a relatively low zero temperature crossing point.

[0166] Embodiment 48 48. The glass of claim 47, wherein the segment having the highest hydroxyl concentration has the lowest zero temperature crossing point. [Explanation of symbols]

[0167] 10. Vitreous body 15, 15-A to 15-G samples 17 outer edge 18 center point 20 segments 1200 System for generating discrete soot particles 1220 First Reservoir 1222, 1232, 1226, 1236 entrance 1224 Silica Precursor 1230 Second Reservoir 1234 Titania Precursor 1242, 1244 Distribution System 1248 Manifold 1250 Furnace 1252 Fume Line 1254 Burner 1260 Disjointed Soot Particles 1264 Collection Chamber 1270 tube 1272 filter bag

Claims

1. It is glass, Titania and silica, Including, A plot of the average hydroxyl concentration for each of the segments versus distance along the glass is: y=Ax ２ +Bx+C is given by A (ppm / mm ２ wherein B (expressed in ppm / mm) is in the range of about −0.1 to about 0.5, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is less than or equal to about 450, y is said average hydroxyl concentration (expressed in ppm), and x is distance (expressed in mm); The hydroxyl concentration of each segment was measured using transmission Fourier transform infrared spectroscopy. A glass, wherein the plot spans a distance of about 50 mm or more along the glass.

2. 10. The glass of claim 1, wherein C is in the range of from about 75 to about 450.

3. The glass of claim 1 wherein B is in the range of from about -5 to about 5.

4. The glass of claim 1, wherein A is in the range of from about 0.0 to about −0.

04.

5. The best fit value R of the plot ２ 5. The glass of claim 1, wherein .gtoreq.0.

3.

6. 5. The glass of claim 1, wherein the plot spans a distance of about 75 mm or more along the glass.

7. 5. The glazing of claim 1, wherein the plurality of segments includes all adjacent segments across a length and a width of the glazing, the length being at least about 25 mm and the width being at least 25 mm.

8. The glass of any one of claims 1 to 4, wherein the glass is a photomask.

9. 5. The glass of claim 1, wherein the plurality of segments has an average hydroxyl concentration of less than or equal to about 200 ppm.

10. It is glass, Titania and silica, Including, A plot of the average hydroxyl concentration for each of the segments versus distance along the glass is: y=Ax ２ +Bx+C is given by A (ppm / mm ２ wherein B (expressed in ppm / mm) is in the range of about −0.1 to about 0.5, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is greater than or equal to about 800, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm); The hydroxyl concentration of each segment was measured using transmission Fourier transform infrared spectroscopy. A glass, wherein the plot spans a distance of about 50 mm or more along the glass.

11. It is glass, Titania and silica, Including, A plot of the average hydroxyl concentration for each of the segments versus distance along the glass is: y=Ax ２ +Bx+C is given by A (ppm / mm ２ wherein A (expressed in ppm / mm) is in the range of about −0.1 to about 0.5, B (expressed in ppm / mm) is in the range of about −10 to about 10, C (expressed in ppm) is undefined, y is the average hydroxyl concentration (expressed in ppm), and x is the distance (expressed in mm); The hydroxyl concentration of each segment was measured using transmission Fourier transform infrared spectroscopy. A glass, wherein the plot spans a distance of about 50 mm or more along the glass.

12. The glass of claim 1, wherein A (expressed in ppm / mm 2 ) is in the range of from about −0.1 to about 0.

0.

13. The glass of claim 1, wherein A (expressed in ppm / mm 2 ) is in the range of about 0.0 to about 0.1.

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