METHOD FOR OPTIMIZING PROPERTY PROFILES IN SOLID SUBSTRATE PRECURSORS

Abstract

A method for producing a substrate precursor having a mass of more than 100 kg, comprising a TiO2-SiO2 mixed glass, comprising the steps including:

introducing a silicon dioxide raw material and a titanium dioxide raw material into a flame,

producing a glass body having a titanium dioxide content of 3 wt. % up to 10 wt. %, the glass body comprising:

a macroscopic, production-related titanium profile, and

a microscopic, production-related layer structure,

dividing the glass body into a plurality of rod-like glass body portions,

spatially measuring the titanium profile in each of the glass body portions,

connecting the glass body portions to form an elongate first glass component,

first homogenization treatment of the first glass component,

pushing together the first glass component to create a spherical glass system,

turning the glass system more than 70 degrees,

and stretching the glass system.

Claims

1. A method for producing a substrate precursor having a mass of more than 50 kg, comprising a TiO2-SiO2 mixed glass, comprising the steps of: introducing a silicon dioxide raw material and a titanium dioxide raw material into a flame, producing a glass body having a titanium dioxide content of 3 wt. % up to 10 wt. %, the glass body comprising: a macroscopic, production-related titanium profile, and a microscopic, production-related layer structure, dividing the glass body into a plurality of rod-like glass body portions, spatially measuring the titanium profile in each of the glass body portions, connecting the glass body portions to form an elongate first glass component, first homogenization treatment of the first glass component, pushing together the first glass component to create a spherical glass system, turning the glass system by more than 70 degrees, stretching the glass system to form an elongate second glass component, second homogenization treatment of the second glass component to create a substrate precursor, the substrate precursor being substantially free of layer structures, wherein the step of measuring comprises the following steps of: predetermining a desired spatial titanium distribution in the substrate precursor, providing a model of a titanium apportionment in the substrate precursor, the model being dependent on an arrangement of the plurality of glass body portions in the first glass component relative to one another, the spatial titanium profile in each of the glass body portions, and the effects of the step of pushing together and the step of turning on the spatial titanium profiles in the glass body portions, calculating an optimal arrangement of the glass body portions relative to one another by means of the model so that a difference between the titanium apportionment and titanium distribution is minimal, positioning the glass body portions so that, in the step of connecting, the glass body portions are connected according to the calculated optimal arrangement.

2. The method according to claim 1, wherein the substrate precursor has a mass of more than 100 kg, in particular more than 200 kg, in particular more than 300 kg.

3. The method according to claim 1, wherein the method comprises the following step of: producing a second glass body having a titanium dioxide content of 3 wt. % up to 10 wt. %, the second glass body comprising: a second, macroscopic, production-related titanium profile, and a second, microscopic, production-related layer structure, dividing the second glass body into a plurality of rod-like glass body portions.

4. The method according to claim 1, wherein at least three, in particular at least five, in particular at least eight, glass body portions are connected to form the first glass component.

5. The method according to claim 1, wherein the difference between the titanium apportionment and titanium distribution is less than 1.5% based on a maximum value of the titanium distribution, in particular less than 1.0%, in particular less than 0.5%.

6. The method according to claim 1, wherein the glass body comprises at least one of the following property profiles: a macroscopic, production-related OH profile, a macroscopic, production-related CTE profile, a macroscopic, production-related fluorine profile, a macroscopic, production-related bubble profile, a macroscopic, production-related ODC profile, a macroscopic, production-related Ti3+ profile, a macroscopic, production-related profile of metallic impurities.

7. The method according to claim 6, wherein, in the step of measuring, at least one of the property profiles is measured in each of the glass body portions.

8. The method according to claim 7, wherein the step of measuring comprises the following steps of: predetermining a desired spatial property distribution in the substrate precursor, providing a model of a property apportionment in the substrate precursor, the model being dependent on an arrangement of the plurality of glass body portions in the first glass component relative to one another, a spatial property profile in each of the glass body portions, and the effects of the step of pushing together and the step of turning on the spatial property profile in the glass body portions, calculating a best possible arrangement of the glass body portions relative to one another by means of the model so that a sum difference is minimal, the sum difference comprising the difference between the titanium apportionment and titanium distribution, and the second difference between the property apportionment and property distribution, positioning the glass body portions so that, in the step of connecting, the glass body portions are connected according to the calculated best possible arrangement.

9. The method according to claim 8, wherein the sum difference is less than 1.5% based on a sum of a maximum value of the titanium distribution and a maximum value of the property distribution, in particular less than 1.0%, in particular less than 0.5%.

10. The method according to claim 1, wherein the step of producing the glass body comprises at least the following steps of: creating a porous soot body, the macroscopic, production-related titanium profile extending substantially along a longitudinal axis, and the microscopic, process-related layer structure extending substantially along a growth axis, vitrifying the soot body to create the cylindrical glass body.

11. The method according to claim 1, wherein the first glass component is heated before the step of pushing together.

12. The method according to claim 1, wherein the connection takes place at a relevant contact surface of the glass body portions.

Description

FIGURES

[0271] Shown are:

[0272] FIG. 1 creation of a soot body,

[0273] FIG. 2 vitrification of the soot body into a glass body,

[0274] FIG. 3 the glass body,

[0275] FIG. 4 a glass body portion which was created from a division of the glass body,

[0276] FIG. 5 a representation of a two-dimensional, macroscopic, production-related titanium profile in a glass body portion,

[0277] FIG. 6 an arrangement of two glass body portions,

[0278] FIG. 7a a substrate precursor,

[0279] FIG. 7b a representation of a titanium profile of a plurality of glass body portions compared to a desired titanium distribution,

[0280] FIG. 8 a further illustration of a titanium profile of a plurality of glass body portions compared to a desired titanium distribution,

[0281] FIG. 9 a first homogenization treatment,

[0282] FIG. 10 a pushing together of the first glass component,

[0283] FIG. 11 a second homogenization treatment, and

[0284] FIG. 12 a representation of the method according to the invention.

DESCRIPTION OF THE FIGURES

[0285] FIG. 1 shows an apparatus 100 for producing a titanium-doped SiO2 soot body 200. A multiplicity of flame hydrolysis burners 220 arranged in a row is arranged along a carrier tube 210 made of aluminum oxide.

[0286] A silicon dioxide raw material and a titanium dioxide raw material are fed to the reaction zone of the flame hydrolysis burner 220 in gaseous form and are decomposed in the process by oxidation and/or hydrolysis and/or pyrolysis. In the reaction zone, both SiO2 particles and TiO2 particles are formed, both of which are deposited In layers on the carrier tube 210, forming the SiO2-TiO2 soot body 200. The SiO2-TiO2 particles themselves are present in the form of agglomerates or aggregates of SiO2 primary particles having particle sizes in the nanometer range.

[0287] In particular due to the layered construction, the soot body 200 can comprise a microscopic layer structure.

[0288] In particular in the production 1100 of large-volume cylindrical soot bodies 200, for producing a substrate precursor 900 having a mass of more than 50 kg, in particular more than 100 kg, in particular more than 200 kg, the flame hydrolysis burners 220 can be mounted on a common burner block which is moved back and forth, in parallel with a longitudinal axis of the carrier tube 210, between two turning points which are stationary with respect to the longitudinal axis.

[0289] This movement of the flame hydrolysis burners 220, mechanical inaccuracies in the feed lines of the raw materials or the burners 220, or also variations in the process temperatures can lead to the soot body 200 having a macroscopic, production-related spatial fluctuation in the physical properties, such as the TiO2 content.

[0290] FIG. 2 shows a vitrification of the soot body 200. The vitrification preferably takes place in a process chamber. Preferably, the vitrification temperature is in a range from 1200 to 1500 C., preferably 1250 to 1350 C. In order to avoid bubble formation in the later quartz glass, it has proven advantageous if, during the vitrification, the pressure within the process chamber is lower than outside the process chamber, i.e., the vitrification is carried out at reduced pressure. This furthermore has the advantage that the material of the process chamber is not affected by aggressive and corrosive gases and is therefore subject to reduced wear. Therefore, an embodiment is preferred in which the vitrification preferably takes place at a pressure of less than 1 mbar. Within the scope of the vitrification, the soot body 200 can be moved through a vitrification furnace 250 according to movement arrow 251.

[0291] As a result of the vitrification, a glass body 300 having a titanium dioxide content of 3 wt. % up to 10 wt. % results from the soot body 200. The production-related fluctuations in the physical properties which have already occurred in the soot body 200 are transferred to the glass body 300, so that the latter has

[0292] tt. a macroscopic, production-related titanium profile, and

[0293] uu. a microscopic, production-related layer structure.

[0294] The mass specified for titanium of 3 wt. % up to 10 wt. % relates to the quantity of TiO2 (titanium dioxide), not of elemental titanium.

[0295] FIG. 3 shows the cylindrical glass body 300. A dotted line indicates a portion which, within the scope of the step of dividing 1200, is cut out of the glass body. The rod-like glass body portion 400 thus created is shown in FIG. 4. In particular, the glass body 300 can be divided into a plurality of rod-like glass body portions 400 which have a longitudinal axis 440. In particular, the glass body portions 400 can have a circular sector-like cross section.

[0296] By means of a first homogenization treatment 1600 of a first glass component and a second homogenization treatment 2000 of a second glass component, the microscopic, production-related layer structure is reduced so greatly that the glass body portion 400 is substantially free of layer structures. However, the two homogenization treatments 1600, 2000 do not allow the substrate precursor 900 to be free of long-wave titanium profiles, which substantially influence the quality and usability of the substrate precursor 900 in EUV lithography.

[0297] FIG. 4 shows the glass body portion 400 on which a titanium profile 410 is measured spatially. For this purpose, the content of titanium dioxide is measured at a plurality of measuring points (P1, P2, P3, P4, P5, P6) along the longitudinal axis 420. These measuring points are at a distance of less than 5 cm, in particular less than 2 cm, from one another. This pointwise measurement of the content of titanium dioxide reflects a clear image of the ratios in the glass body portion 400. Any fluctuations in the titanium profile occur on length scales of 0.15 m to 0.75 m.

[0298] In addition, further macroscopic, production-related variations of chemical and/or physical properties of the glass body 300 can occur within the scope of the production 1100 of the soot body 200, due to mechanical influences. At least one of these variations denoted as a property profile 510 can likewise be determined in the step of measuring 1300. The following chemical and/or physical properties, which have macroscopic, production-related property profiles 510, can be measured individually or in any combination: OH content, CTE, fluorine content, bubble content, ODC content, Ti3+ content, and content of metallic impurities.

[0299] The property profile 510 can be measured in parallel with and analogously to the titanium profile 410. For this purpose, the physical property is measured at a plurality of measuring points (P1, P2, P3, P4, P5, P6) along the longitudinal axis 420. Here too, the measuring points are at a distance of less than 5 cm, in particular less than 2 cm, from one another.

[0300] FIG. 5 schematically shows the result of a measurement 1300 of a titanium profile 410 and of a property profile 510 in the glass body portion 400. The quantity in wt. % of titanium dioxide or in ppm of the property is plotted as a function of the position along the longitudinal axis 440 of the glass body portion 400. In order to simplify the description, only measurement results for six measuring points (P1, P2, P3, P4, P5, P6) are shown in FIGS. 4 and 5.

[0301] The steps and/or aspects of the spatial measuring 1300 of the titanium profile 410 described below also apply to a spatial measurement of at least one property profile 510.

[0302] As can be seen from the graph, the content of titanium dioxide is within the predefined interval of 3 wt. % to 10 wt. %. However, for production-related reasons, this content of titanium dioxide fluctuates between 5.4 wt. % to 6.1 wt. % along the longitudinal axis 420 of the glass body portion 400.

[0303] The quantity of a property, here by way of example the OH content in ppm, measured at the six measuring points (P1, P2, P3, P4) is also shown, as the property profile 510. For production-related reasons, this content of OH fluctuates, along the longitudinal axis 420 of the glass body portion 400, between 150 ppm to 175 ppm.

[0304] FIG. 6 shows a connection 1500 of a plurality of, in this case two, rod-like glass body portions 400, 400 for forming an elongate first glass component 600.

[0305] For this purpose, a planar contact surface 401 of the first glass body portion 400 and a planar contact surface 401 of the second glass body portion 400 can be joined together by wringing and welded to one another. This is a cold connection method in which at most the immediate region of the contact surface experiences notable heating.

[0306] Alternatively, the connecting 1500 may comprise a connection step in which both glass

[0307] body portions 400, 400 are softened and joined together in a furnace. This is a hot connection method in which the individual glass body portions 400, 400 are joined together by welding. As described, the titanium dioxide profiles and/or property profiles are measured at a plurality of measuring points. For the glass body portion 400, the titanium profile 410 is measured, by way of example, at the measuring points P1, P2, P3, P4, P5, P6. For the glass body portion 400, the titanium profile 410 is measured, by way of example, at the measuring points P7, P8, P9, P10, P11, P12.

[0308] Within the scope of the method, at least three, in particular at least five, in particular at least eight, glass body portions can thus be connected to one another to form a first glass component 600, which is also illustrated in FIG. 9.

[0309] As illustrated in FIG. 5, the titanium profile 410 fluctuates along the longitudinal axis of the glass body portion 400. In addition, however, the titanium profile also fluctuates between different glass body portions 400, 400. In the prior art, these macroscopic, production-related fluctuations in the individual titanium profiles between different glass body portions 400, 400 were not taken into account further. Rather, only a few, in particular only two, glass body portions 400, 400 were hitherto required for substrate precursors 900 having a low mass, so that the fluctuations occurring between the long-wave titanium profiles 410 in the glass body portions 400, 400 could be ignored. This is no longer possible in the production of substrate precursors having a mass of more than 50 kg, in particular more than 100 kg, in particular if at least four glass body portions have to be connected to one another.

[0310] FIGS. 7a, 7b and FIG. 8 illustrate the steps used within the scope of the step of measuring 1300, which steps serve to overcome the aforementioned disadvantages.

[0311] It is to be set out how, by permutation of the arrangement of the glass body portions 400, 400, 400, 400 relative to one another, with the aid of the model, a titanium apportionment 430 is in each case calculated and compared with the desired titanium distribution 420.

[0312] The steps and/or aspects, described below, of minimizing a difference between titanium apportionment and titanium distribution also apply to the minimization of a second difference between at least one property apportionment and at least one property distribution.

[0313] The starting point is predetermining 1400 a desired titanium distribution 420 in the

[0314] substrate precursor. In one variant, the titanium distribution 420 represents the two-dimensional distribution of the quantity of the TiO2 in the substrate precursor, in particular along a center line, in particular at the outer surface to be mirrored later, through the substrate precursor. In this embodiment, the model can calculate a two-dimensional titanium distribution in the substrate precursor from the two-dimensionally determined titanium profiles and their arrangement relative to one another.

[0315] FIG. 7a shows a substrate precursor 900. Optimally, the latter should have a titanium distribution 420 as shown in the top graph in FIG. 7b. By way of example, a parabolic titanium distribution 420 having a maximum in a center of the substrate precursor is sought within an interval of 4.75 wt. % to 5.5 wt. % TiO2.

[0316] The desired two-dimensional titanium distribution 420 can be found in the substrate precursor 900 along a center line 920 on the outer surface 910 to be mirrored later. The type and design of the titanium distribution 420 can in particular be dependent on the type of use and the conditions of use of the later EUV mirror. A titanium distribution having a parabolic (or Gaussian) profile having a maximum in the center of the substrate precursor is particularly preferred. In particular, the titanium distribution, and thus the CTE, can be adapted to the distribution of the incident EUV radiation.

[0317] In order to illustrate the procedure, it is assumed in FIG. 7b that the substrate precursor 900 is formed from only four glass body portions 400, 400, 400, 400. In a manner analogous to FIG. 6, they are arranged relative to one another such that a rod-like glass body 300 is formed. In this case, the four glass body portions 400, 400, 400, 400 were joined together in the following arrangement to form the first glass component 600:

[0318] end side of the glass body portion 400 is connected to the front face of the glass body portion 400 (point E2),

[0319] end side of the glass body portion 400 is connected to the front face of the glass body portion 400 (point E3),

[0320] end side of the glass body portion 400 is connected to the front face of the glass body portion 400 (point E4).

[0321] The center graph in FIG. 7b shows the titanium profiles 410, 410, 410, 410 of the four glass body portions 400, 400, 400, 400, which were created from at least one glass body 300.

[0322] The set of measured values for the quantities of TiO2 in wt. % in each of the four glass body portions 400, 400, 400, 400 is plotted.

[0323] In order to overcome the aforementioned disadvantages, a model is used which can calculate a titanium apportionment 430 in the substrate precursor 900. In this case the model uses, as input parameters:

[0324] the arrangement of the plurality of glass body portions 400, 400, 400, 400 relative to one another in the first glass component 600,

[0325] the spatial titanium profiles 410, 410, 410, 410 in each of the glass body portions 400, 400, 400, 400, and

[0326] the effects of the step of pushing together 1700 and the step of turning 1800 on the spatial titanium profiles 410, 410, 410, 410 in the glass body portions 400, 400, 400, 400.

[0327] Based on this arrangement, the model calculates the titanium apportionment 430 in the substrate precursor 900. This titanium apportionment 430 is shown in the bottom graph in FIG. 7b.

[0328] As illustrated in FIG. 7b, the illustrated profile of the calculated titanium apportionment 430 does not correspond simply to a linear sequence of the illustrated profiles of the titanium profiles 410, 410, 410, 410 in the assumed arrangement. Rather, the method steps of the method disclosed herein result in the spatial position and orientation of a titanium profile 410, 410, 410, 410, after passing through the method, no longer corresponding to the spatial position that the glass body portion 400, 400, 400, 400 corresponding to the titanium profile had in the first glass body 300. Thus, the spatial orientation of the titanium profile 410, 410, 410, 410 changes such that a model is required to calculate the position and quantity of the TiO2 in the titanium apportionment 430 of the substrate precursor 900.

[0329] The calculated titanium apportionment 430 shown in FIG. 7b has a zigzag profile and thus deviates greatly from the desired parabolic titanium distribution 420.

[0330] In order to achieve an optimal arrangement, the possible arrangements of the glass body portions are permuted. In the model, the effects of all possible arrangements of the glass body portions on the titanium apportionment 430 are calculated. FIG. 8 is intended to illustrate this. The starting point is an arrangement, deviating from FIG. 7, of the four glass body portions 400, 400, 400, 400, which are joined together in the following arrangement to form the first glass component 600:

[0331] end side of the glass body portion 400 is connected to the front face of the glass body portion 400 (point E2),

[0332] end side of the glass body portion 400 is connected to the front face of the glass body portion 400 (point E3),

[0333] end side of the glass body portion 400 is connected to the front face of the glass body portion 400 (point E4).

[0334] The model calculates a titanium apportionment 430 in the substrate precursor 900 from the titanium profiles 410, 410, 410, 410. This titanium apportionment 430 is more similar, both in quantity and in profile, to the desired titanium distribution 420 than the titanium apportionment 430 shown in FIG. 7b.

[0335] The model calculates in particular, from any possible arrangement of the glass body portions 400, 400, 400, 400, the corresponding titanium apportionment 430, 430 and compares it to the desired titanium distribution 420. For this purpose, all possible arrangements of the glass body portions 400, 400, 400, 400 are permuted. Based on this information, the model in each case forms a difference between titanium apportionment and titanium distribution 420. The optimal arrangement is the arrangement in which the magnitude of the difference, in particular the maximum magnitude of the difference, between two spatially identical points on the substrate precursor is minimal.

[0336] Subsequently, the glass body portions 400, 400, 400, 400 are positioned and connected according to the optimal arrangement.

[0337] Analogously, at least one property distribution, in addition to the titanium distribution, can represent a second target value which is optimally fulfilled and/or sought in the substrate precursor 900. The model used in this variant is functionally dependent on

[0338] vv. an arrangement of the plurality of glass body portions 400, 400, 400, 400, relative to one another, in the first glass component 600,

[0339] ww. the spatial titanium profile 410, 410, 410, 410 and a spatial property profile 510 in each of the glass body portions 400, 400, 400, 400, and

[0340] xx. the effects of the step of pushing together and the step of turning on the spatial titanium profile 410, 410, 410, 410 and on the spatial property profile 510 in the glass body portions 400, 400, 400, 400.

[0341] Consequently, both the aspects relating to the element titanium dioxide and the aspects relating to at least one further property (e.g., ODC, Ti3+, etc.) are taken into account in the calculation of the optimal arrangement of the glass body portions.

[0342] Based on the solution space of possible arrangements of the glass body portions relative to

[0343] one another, a best possible arrangement of the glass body portions 400, 400, 400, 400 is determined. In this case, the aim is for the sum difference to be minimal, the sum difference comprising

[0344] i. the difference between titanium apportionment and titanium distribution, and

[0345] ii. the second difference between the at least one property apportionment and the at least one property distribution.

[0346] FIG. 9 shows a first homogenization treatment 1600 of the first glass component 600, which is created from the glass body portions 400, 400, 400, 400. Both the glass body and the first glass component 600 created from the glass body portions 400, 400, 400, 400 comprise microscopic, production-related layer structures. In order to reduce this and/or make it possible to produce a substrate precursor 900 substantially free of layer structures, two homogenization treatments are performed sequentially.

[0347] In the first homogenization treatment 1600, the first glass component 600 is clamped into a glass lathe 605 equipped with one or more burners 220 and is homogenized by means of a reshaping process, as described in EP 673 888 A1 for the purpose of complete removal of layer structures.

[0348] The glass lathe 605 has two chucks 610, 610, which can be caused to rotate 650, 650 independently of one another. The first glass component 600 is clamped between the two chucks 610, 610. Two holding elements 620, 620 can ensure a better fit between the chucks 610, 610 and the first glass component 600. By means of the burner 220, the first glass component 600 is heated at points and softened in the process so that a shear zone 630 results. This shear zone 630 allows an external force, such as a torsional force, tensile or compressive force, to be introduced onto the rod-shaped first glass component 600. Within the shear zone 630, regions which have different stresses or experience different movements thus result, which is associated with a shear effect or expansion and compression effect. In order to generate this force, the two chucks 610, 610 can rotate 650, 650 in opposite directions in each case.

[0349] In the first homogenization treatment 1600, microscopic, production-related layer

[0350] structures in a plane of the shear zone of the first glass component 600 are effectively reduced. However, the reduction of microscopic, production-related layer structures perpendicular to the plane of the shear zone of the first glass component 600 is significantly less.

[0351] In order to eliminate the remaining residues of the layer structures in a second

[0352] homogenization treatment 2000, the first glass component 600 must be reshaped. FIG. 10 illustrates pushing together 1700 the first glass component 600 to create a spherical glass system 700. For this purpose, the first glass component 600 is heated by means of the burner 220 and compressed. The pushing together 1700 can take place in that the two chucks 610, 610 are moved toward one another, which is illustrated by the movement arrow 612. The glass system 700 is subsequently turned 1800 by more than 70 degrees. For this purpose, the glass system 700 is removed from the chucks 610, 610 and rotated, which the movement arrow 615 is intended to illustrate. This rotation ensures that, in the second homogenization treatment 2000, the portion of the layer structure that was only slightly or not at all compensated in the first homogenization treatment 1600 can be effectively reduced. After the turning 1800 of the glass system 700 by more than 70 degrees, said system is again clamped into the chucks 610, 610. This is followed by a stretching 1900 of the glass system 700. This mechanical reshaping of the spherical glass system 700 into an elongate second glass component 800 takes place by heating the glass system 700 using the burner 220, and moving the chucks 610, 610 away from one another, which the movement arrow 613 illustrates.

[0353] FIG. 11 illustrates a second homogenization treatment 2000 of the second glass component 800. The second homogenization treatment 2000 takes place substantially analogously to the first homogenization treatment 1600. The decisive difference is that, by means of the turning 1800, the layer structure that was previously substantially perpendicular to the longitudinal axis of the glass lathe 605 is now located in the direction of the longitudinal axis of the glass lathe 605. The second glass component 800 is clamped between the two chucks 610, 610 of the glass lathe 605. By means of the burner 220, the second glass component 800 is heated at points and softened in the process so that a second shear zone 640 results. This second shear zone 640 allows an external force, such as a torsional force, tensile or compressive force, to be introduced onto the rod-shaped second glass component 800. In the second shear zone 640, regions which have different stresses or experience different movements thereby result, which is associated with a shear effect or expansion and compression effect. In order to generate this force, the two chucks 610, 610 can rotate 650, 650 in opposite directions in each case.

[0354] In this second homogenization treatment 2000, microscopic, production-related layer structures are effectively reduced in the direction perpendicular to the longitudinal axis of the first glass component 600 and/or in the direction of a longitudinal axis of the second glass component 800. After passing through both the first homogenization treatment 1600 and the second homogenization treatment 2000, a substrate precursor 900 results which is substantially free of layer structures.

[0355] FIG. 12 shows a course of the method for producing a substrate precursor 900 having a mass of more than 100 kg, comprising a TiO2-SiO2 mixed glass. It comprises the steps of:

[0356] yy. introducing 1000 a silicon dioxide raw material and a titanium dioxide raw material into a flame,

[0357] zz. producing 1100 a glass body having a titanium dioxide content of 3 wt. % up to 10 wt. %, the glass body having: [0358] i. a macroscopic, production-related titanium profile, and [0359] ii. having a microscopic, production-related layer structure, [0360] aaa. dividing 1200 the glass body into a plurality of rod-like glass body portions, [0361] bbb. spatially measuring 1300 the titanium profile in each of the glass body portions, [0362] ccc. connecting 1500 the glass body portions to form an elongate first glass component, [0363] ddd. first homogenization treatment 1600 of the first glass component, [0364] eee. pushing together 1700 the first glass component to create a spherical glass system, [0365] fff. turning 1800 the glass system by more than 70 degrees, [0366] ggg. stretching 1900 the glass system to form an elongate second glass component, [0367] hhh. second homogenization treatment 2000 of the second glass component to create a substrate precursor 900, the substrate precursor 900 being substantially free of layer structures.

[0368] The method is characterized in that the step of measuring 1300 comprises the steps of: [0369] iii. predetermining 1400 a desired spatial titanium distribution in the substrate precursor 900, [0370] jjj. providing 1420 a model of a titanium apportionment in the substrate precursor 900, the model being dependent on

[0371] i. an arrangement of the plurality of glass body portions in the first glass component relative to one another,

[0372] ii. the spatial titanium profile in each of the glass body portions, and

[0373] iii. the effects of the step pf pushing together and the step of turning on the spatial titanium profiles in the glass body portions, [0374] kkk calculating 1450 an optimal arrangement of the glass body portions relative to one another by means of the model so that a difference between titanium apportionment and titanium distribution is minimal, [0375] lll. positioning 1470 the glass body portions so that, in the step of connecting, the glass body portions are connected according to the calculated optimal arrangement.

Reference Signs

[0376] 100 Apparatus [0377] 200 Soot body [0378] 210 Carrier tube [0379] 220 Burner or flame hydrolysis burner [0380] 225 Flame [0381] 250 Vitrification furnace [0382] 251 Movement arrow [0383] 300 Glass body [0384] 400, 400, 400 Glass body portion [0385] 401, 401 Contact surface [0386] 410, 400, 400, 400 Titanium profile [0387] 420 Titanium distribution [0388] 430 Titanium apportionment [0389] 440 Longitudinal axis [0390] 510 Property profile [0391] 600 First glass component [0392] 605 Glass lathe [0393] 610, 610 Chuck [0394] 612 Movement arrow [0395] 613 Movement arrow [0396] 615 Movement arrow [0397] 620, 620 Two holding elements [0398] 630 Shear zone [0399] 640 Second shear zone [0400] 650, 650 Rotation [0401] 700 Spherical glass system [0402] 800 Second glass component [0403] 900 Substrate precursor [0404] 910 Outer surface [0405] 920 Centerline [0406] 1000 Introducing [0407] 1100 Producing [0408] 1200 Dividing [0409] 1300 Spatially measuring [0410] 1400 Predetermining [0411] 1420 Providing a model [0412] 1450 Calculating an optimal arrangement [0413] 1470 Positioning the glass body portions [0414] 1500 Connecting the glass body portions [0415] 1600 First homogenization treatment [0416] 1700 Pushing together [0417] 1800 Turning the glass system [0418] 1900 Stretching [0419] 2000 Second homogenization treatment