TWI583639B - Silica-titania glass, process for production thereof and silica-titania glass sorting method - Google Patents

Silica-titania glass, process for production thereof and silica-titania glass sorting method Download PDF

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TWI583639B
TWI583639B TW102146894A TW102146894A TWI583639B TW I583639 B TWI583639 B TW I583639B TW 102146894 A TW102146894 A TW 102146894A TW 102146894 A TW102146894 A TW 102146894A TW I583639 B TWI583639 B TW I583639B
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cerium oxide
titanium glass
glass
titanium
tio
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TW201434767A (en
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上田哲司
江崎正信
每田繁
大塚久利
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信越石英股份有限公司
信越化學工業股份有限公司
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    • CCHEMISTRY; METALLURGY
    • C03GLASS; MINERAL OR SLAG WOOL
    • C03BMANUFACTURE, SHAPING, OR SUPPLEMENTARY PROCESSES
    • C03B20/00Processes specially adapted for the production of quartz or fused silica articles, not otherwise provided for
    • CCHEMISTRY; METALLURGY
    • C03GLASS; MINERAL OR SLAG WOOL
    • C03CCHEMICAL COMPOSITION OF GLASSES, GLAZES OR VITREOUS ENAMELS; SURFACE TREATMENT OF GLASS; SURFACE TREATMENT OF FIBRES OR FILAMENTS MADE FROM GLASS, MINERALS OR SLAGS; JOINING GLASS TO GLASS OR OTHER MATERIALS
    • C03C3/00Glass compositions
    • C03C3/04Glass compositions containing silica
    • C03C3/06Glass compositions containing silica with more than 90% silica by weight, e.g. quartz
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/38Concrete; Lime; Mortar; Gypsum; Bricks; Ceramics; Glass
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02PCLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P40/00Technologies relating to the processing of minerals
    • Y02P40/50Glass production, e.g. reusing waste heat during processing or shaping
    • Y02P40/57Improving the yield, e-g- reduction of reject rates

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  • Chemical & Material Sciences (AREA)
  • Glass Compositions (AREA)
  • Engineering & Computer Science (AREA)
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  • Organic Chemistry (AREA)
  • Re-Forming, After-Treatment, Cutting And Transporting Of Glass Products (AREA)
  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)
  • Exposure Of Semiconductors, Excluding Electron Or Ion Beam Exposure (AREA)
  • Preparing Plates And Mask In Photomechanical Process (AREA)
  • Glass Melting And Manufacturing (AREA)
  • Life Sciences & Earth Sciences (AREA)
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  • General Chemical & Material Sciences (AREA)
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Description

氧化矽-鈦玻璃,氧化矽-鈦玻璃之製造方法,以及氧化矽-鈦玻璃之分類方法 Cerium oxide-titanium glass, yttrium oxide-titanium glass manufacturing method, and yttrium oxide-titanium glass classification method

本發明係關於超低膨脹材料的氧化矽-鈦玻璃,該氧化矽-鈦玻璃之製造方法,以及氧化矽-鈦玻璃之分類方法。 The present invention relates to cerium oxide-titanium glass for ultra-low expansion materials, a method for producing the cerium oxide-titanium glass, and a method for classifying cerium oxide-titanium glass.

隨著半導體電路之更微細化,正開始導入EUV微影技術。EUV微影技術係以波長13.5nm之X射線作為光源。進而,亦已檢討使用波長6.5nm之X射線作為次世代之EUV微影技術。由於並無能使該等X射線充分透過之光學材料,因此於EUV微影中採用反射光學系。該反射光學系係由經施以多層膜反射塗層之超低膨脹材料所構成。然而,多層膜反射塗層之反射率低,例如於波長13.5nm之X射線反射中所用之Mo/Si反射膜,反射率70%為其界限,其餘30%之光的大部分被吸收轉成為熱。若因該熱造成之線膨脹使光學系變形,則成像性能惡化而 無法獲得期望之電路圖型。因此,作為光學系之基板係使用因溫度變化所致之線膨脹非常小的超低膨脹材料。作為該超低膨脹材料之代表性材料為含TiO2之氧化矽玻璃,亦即氧化矽-鈦玻璃。 With the further miniaturization of semiconductor circuits, EUV lithography technology is beginning to be introduced. The EUV lithography technique uses X-rays having a wavelength of 13.5 nm as a light source. Further, X-rays having a wavelength of 6.5 nm have been reviewed as the next generation EUV lithography technology. Since there is no optical material that can sufficiently transmit such X-rays, a reflective optical system is employed in EUV lithography. The reflective optical system consists of an ultra-low expansion material to which a multilayer film reflective coating is applied. However, the reflectivity of the multilayer film reflective coating is low, for example, the Mo/Si reflective film used for X-ray reflection at a wavelength of 13.5 nm, the reflectance is 70%, and most of the remaining 30% of the light is absorbed and converted. heat. If the optical system is deformed by the linear expansion caused by the heat, the imaging performance is deteriorated and the desired circuit pattern cannot be obtained. Therefore, as the substrate of the optical system, an ultra-low expansion material having a very small linear expansion due to temperature change is used. As a representative material of the ultra-low expansion materials containing TiO 2 glass of silicon oxide, i.e. silicon oxide - titanium glass.

使用氧化矽-鈦玻璃作為EUV微影裝置之鏡面基板、遮罩基板材料如專利文獻1、專利文獻2所示般係習知技術。且,已提案出在廣泛溫度範圍內熱膨脹係數幾乎為零之含TiO2之氧化矽玻璃(專利文獻3),或TiO2之濃度梯度小且研磨性優異之摻雜氧化鈦之石英玻璃(專利文獻4)等作為適於EUV微影之光學系用基板之材料。 The use of yttrium oxide-titanium glass as a mirror substrate and a mask substrate material of an EUV lithography apparatus is a conventional technique as disclosed in Patent Document 1 and Patent Document 2. Furthermore, TiO 2 -containing yttria glass having a thermal expansion coefficient of almost zero over a wide temperature range has been proposed (Patent Document 3), or titanium oxide-doped quartz glass having a small concentration gradient of TiO 2 and excellent polishing property (patent Document 4) or the like is a material for a substrate for an optical system suitable for EUV lithography.

然而,該等材料均為僅著眼於原材料之初期性能者,並未考慮長期之耐久性。多層膜基板之X射線的反射率為70%左右,其餘30%的光大部分於多層膜中被吸收,但一部分到達至氧化矽-鈦玻璃基板。EUV微影之光源輸出目前在中間集光點雖為50W左右,但為了提高半導體電路之生產性,預測將來將成為其10倍左右,到達至氧化矽-鈦玻璃基板之X射線強度預估亦會大到10倍左右。氧化矽-鈦玻璃長期承受高強度X射線之照射時,會引起氧化矽-鈦玻璃之緻密化(壓實)。該緻密化造成基板形狀之變形,而使光學系之成像性能惡化。 However, these materials are only focused on the initial performance of the raw materials and do not consider long-term durability. The X-ray reflectance of the multilayer film substrate is about 70%, and the remaining 30% of the light is mostly absorbed in the multilayer film, but a part of it reaches the yttrium oxide-titanium glass substrate. The output of the EUV lithography light source is currently about 50W in the middle light collection point. However, in order to improve the productivity of the semiconductor circuit, it is predicted that it will become about 10 times in the future, and the X-ray intensity prediction of reaching the yttrium oxide-titanium glass substrate is also estimated. It will be as big as 10 times. When cerium oxide-titanium glass is subjected to high-intensity X-ray irradiation for a long period of time, densification of cerium oxide-titanium glass (compaction) is caused. This densification causes deformation of the shape of the substrate, which deteriorates the imaging performance of the optical system.

鑑於該氧化矽-鈦玻璃之緻密化,專利文獻5中已提案藉由對堆積有反射膜之面照射<250nm波長之光,預先使表面層緻密化之氧化矽-鈦玻璃。然而,氧化矽-鈦玻璃會有因緻密化而改變線膨脹係數之情況。因 此,於緻密化部與其以外之部位產生線膨脹係數差異,會因溫度變化而引起變形,使成像性能惡化。因此,專利文獻5中提案之氧化矽-鈦玻璃並非作為EUV微影之光學系基板之適當材料。 In view of the densification of the cerium oxide-titanium glass, Patent Document 5 proposes cerium oxide-titanium glass in which the surface layer is densified in advance by irradiating the surface on which the reflecting film is deposited with light having a wavelength of <250 nm. However, cerium oxide-titanium glass may change the coefficient of linear expansion due to densification. because As a result, a difference in coefficient of linear expansion occurs between the densified portion and the portion other than the densified portion, which causes deformation due to temperature change, and deteriorates imaging performance. Therefore, the cerium oxide-titanium glass proposed in Patent Document 5 is not a suitable material for the optical substrate of the EUV lithography.

此外,專利文獻5中雖記載有關氧化矽-鈦玻璃之緻密化,但具體之照射條件或緻密化程度、因氧化矽-鈦玻璃之製造方法或物性對緻密化造成之影響均未觸及。由專利文獻5完全無法得知關於因光照射而抑制緻密化之氧化矽-鈦玻璃之資訊。 Further, in Patent Document 5, the densification of cerium oxide-titanium glass is described, but the specific irradiation conditions, the degree of densification, and the influence of the production method or physical properties of cerium oxide-titanium glass on densification are not touched. From Patent Document 5, information on cerium oxide-titanium glass which suppresses densification by light irradiation is completely unknown.

另一方面,玻璃材料之緻密化程度之判別方法有如專利文獻6所例示般,以干涉計等測定非照射區域與照射區域之折射率差並進行評價之方法。然而,由於氧化矽-鈦玻璃除了基本成分SiO2以外,也含相當量之第二成分TiO2,其難以均勻分散,故折射率之均勻性相較於未摻雜之合成石英玻璃約大2位數。如此大的折射率分佈中,難以掌握因X射線照射所致之折射率變化,專利文獻6中例示之方法難以掌握氧化矽-鈦玻璃之緻密化程度。 On the other hand, as a method of discriminating the degree of densification of the glass material, as described in Patent Document 6, a method of measuring the difference in refractive index between the non-irradiated area and the irradiation area by an interferometer or the like is performed. However, since the yttrium oxide-titanium glass contains a considerable amount of the second component TiO 2 in addition to the basic component SiO 2 , it is difficult to uniformly disperse, so the uniformity of the refractive index is about 2 larger than that of the undoped synthetic quartz glass. Number of digits. In such a large refractive index distribution, it is difficult to grasp the change in refractive index due to X-ray irradiation, and the method exemplified in Patent Document 6 is difficult to grasp the degree of densification of yttrium oxide-titanium glass.

〔先前技術文獻〕 [Previous Technical Literature] 〔專利文獻〕 [Patent Document]

〔專利文獻1〕日本特表2003-505876 [Patent Document 1] Japanese Special Table 2003-505876

〔專利文獻2〕日本特表2003-505891 [Patent Document 2] Japanese Special Table 2003-505891

〔專利文獻3〕日本特開2005-22954 [Patent Document 3] Japan Special Open 2005-22954

〔專利文獻4〕日本特開2007-182367 [Patent Document 4] Japanese Special Opening 2007-182367

〔專利文獻5〕日本特開2012-33934 [Patent Document 5] Japanese Special Opening 2012-33934

〔專利文獻6〕日本特開2005-29452 [Patent Document 6] Japan Special Opening 2005-29452

本發明之目的係提供一種長期耐久性,尤其是因X射線照射所致之緻密化受抑制之氧化矽-鈦玻璃,及其製造方法。 SUMMARY OF THE INVENTION An object of the present invention is to provide a cerium oxide-titanium glass which has long-term durability, in particular, densification which is suppressed by X-ray irradiation, and a method for producing the same.

本發明人等為解決上述課題,針對因X射線照射所致之氧化矽-鈦玻璃之緻密化行為進行積極檢討,發現可正確掌握緻密化強度,可判別緻密化小的氧化矽-鈦玻璃之方法。且,發現X射線照射所致之緻密化會隨氧化矽-鈦玻璃之製造方法、及最終物性而大有不同,因而完成本發明。 In order to solve the above problems, the inventors of the present invention have conducted a positive review on the densification behavior of cerium oxide-titanium glass by X-ray irradiation, and found that the densification strength can be accurately grasped, and the densification of small cerium oxide-titanium glass can be discriminated. method. Further, it has been found that the densification by X-ray irradiation greatly differs depending on the method for producing yttrium oxide-titanium glass and the final physical properties, and thus the present invention has been completed.

亦即,本發明之氧化矽-鈦玻璃之製造方法係包含下列步驟之氧化矽-鈦玻璃之製造方法:a)由Si原料與Ti原料合成含5~9wt%TiO2之氧化矽-鈦玻璃之步驟、b)在高於2150℃之溫度加熱前述步驟a)所得之氧化矽-鈦玻璃之步驟、及c)在700~1300℃下使前述步驟b)所得之氧化矽-鈦玻璃退火之步驟, 其特徵為前述c)步驟後之氧化矽-鈦玻璃以下述條件發生之X射線部分地照射厚度2mm之試驗樣品時之X射線照射區域與X射線非照射區域之間產生之拉伸應力F係侷限於下述式(1)之範圍者,X射線照射條件:Rh靶材X射線管球,管電壓50kV,管電流70mA,照射時間1.5小時,F<0.06×C(TiO2)...(1) That is, the method for producing cerium oxide-titanium glass of the present invention comprises the following steps: a method for producing cerium oxide-titanium glass: a) synthesizing cerium oxide-titanium glass containing 5 to 9 wt% of TiO 2 from a Si raw material and a Ti raw material. a step of b) heating the cerium oxide-titanium glass obtained in the above step a) at a temperature higher than 2150 ° C, and c) annealing the cerium oxide-titanium glass obtained in the above step b) at 700 to 1300 ° C And a tensile stress generated between the X-ray irradiation region and the X-ray non-irradiation region when the X-ray of the cerium oxide-titanium glass after the step c) is partially irradiated with the test sample having a thickness of 2 mm. F is limited to the range of the following formula (1), X-ray irradiation conditions: Rh target X-ray tube ball, tube voltage 50kV, tube current 70mA, irradiation time 1.5 hours, F <0.06 × C (TiO 2 ). ..(1)

(前述式(1)中,F係以下述式(2)算出之拉伸應力(MPa),C(TiO2)為TiO2濃度(wt%)) (In the above formula (1), F is a tensile stress (MPa) calculated by the following formula (2), and C(TiO 2 ) is a TiO 2 concentration (wt%))

F(MPa)=d(nm/cm)/42〔(nm/cm)/(MPa)〕...(2)(前述式(2)中,d為雙折射率)。 F (MPa) = d (nm / cm) / 42 [(nm / cm) / (MPa)] (2) (in the above formula (2), d is a birefringence).

本發明之氧化矽-鈦玻璃之製造方法中,前述步驟b)中之加熱溫度較好為高於2200℃之溫度。 In the method for producing cerium oxide-titanium glass of the present invention, the heating temperature in the above step b) is preferably a temperature higher than 2200 °C.

本發明之氧化矽-鈦玻璃係含5~9wt% TiO2之零膨脹溫度為0~50℃之範圍內之氧化矽-鈦玻璃,其特徵為以下述條件發生之X射線部分地照射厚度2mm之試驗樣品時之X射線照射區域與X射線非照射區域之間產生之拉伸應力F侷限於下述式(1)之範圍,X射線照射條件:Rh靶材X射線管球,管電壓50kV,管電流70mA,照射時間1.5小時;F<0.06×C(TiO2)...(1) The cerium oxide-titanium glass of the present invention contains cerium oxide-titanium glass having a zero expansion temperature of 5 to 90% by weight of TiO 2 in a range of 0 to 50 ° C, and is characterized in that X-rays which are generated under the following conditions partially irradiate a thickness of 2 mm. The tensile stress F generated between the X-ray irradiation region and the X-ray non-irradiation region in the test sample is limited to the range of the following formula (1), and the X-ray irradiation condition: Rh target X-ray tube ball, tube voltage 50 kV , tube current 70mA, irradiation time 1.5 hours; F <0.06 × C (TiO 2 )...(1)

(前述式(1)中,F係以下述式(2)算出之拉伸應力(MPa),C(TiO2)為TiO2濃度(wt%)) (In the above formula (1), F is a tensile stress (MPa) calculated by the following formula (2), and C(TiO 2 ) is a TiO 2 concentration (wt%))

F(MPa)=d(nm/cm)/42〔(nm/cm)/(MPa)〕...(2)(前述式(2)中,d為雙折射率)。 F (MPa) = d (nm / cm) / 42 [(nm / cm) / (MPa)] (2) (in the above formula (2), d is a birefringence).

本發明之氧化矽-鈦玻璃較好經過於高於2150℃之溫度加熱之步驟,更好經過於高於2200℃之溫度加熱之步驟。 The cerium oxide-titanium glass of the present invention preferably passes through a step of heating at a temperature higher than 2150 ° C, and more preferably a step of heating at a temperature higher than 2200 ° C.

本發明之氧化矽-鈦玻璃中,前述F更好滿足下述式(3)。 In the cerium oxide-titanium glass of the present invention, the above F preferably satisfies the following formula (3).

F<0.03×C(TiO2)...(3) F<0.03×C(TiO 2 )...(3)

(前述式(3)中,F及C(TiO2)係與前述式(1)相同)。 (In the above formula (3), F and C(TiO 2 ) are the same as the above formula (1)).

本發明之氧化矽-鈦玻璃可較好地使用作為EUV微影曝光裝置之鏡面基板。 The cerium oxide-titanium glass of the present invention can be preferably used as a mirror substrate of an EUV lithography exposure apparatus.

本發明之氧化矽-鈦玻璃之分類方法為含5~9wt%TiO2之零膨脹溫度在0~50℃之範圍內之氧化矽-鈦玻璃之分類方法,其特徵係將以下述條件發生之X射線部分地照射厚度2mm之試驗樣品時之X射線照射區域與X射線非照射區域之間產生之拉伸應力F侷限於下述式(1)之範圍之氧化矽-鈦玻璃分類為良品,X射線照射條件:Rh靶材X射線管球,管電壓50kV,管電流70mA,照射時間1.5小時,F<0.06×C(TiO2)...(1) The method for classifying cerium oxide-titanium glass of the present invention is a method for classifying cerium oxide-titanium glass containing 5 to 9 wt% of TiO 2 with a zero expansion temperature in the range of 0 to 50 ° C, and the characteristics thereof are generated under the following conditions. The tensile stress F generated between the X-ray irradiation region and the X-ray non-irradiation region when the X-ray is partially irradiated with the test sample having a thickness of 2 mm is limited to the range of the following formula (1), and the cerium oxide-titanium glass is classified as a good product. X-ray irradiation conditions: Rh target X-ray tube ball, tube voltage 50kV, tube current 70mA, irradiation time 1.5 hours, F<0.06×C(TiO 2 )...(1)

(前述式(1)中,F係以下述式(2)算出之拉伸應力(MPa),C(TiO2)為TiO2濃度(wt%)) (In the above formula (1), F is a tensile stress (MPa) calculated by the following formula (2), and C(TiO 2 ) is a TiO 2 concentration (wt%))

F(MPa)=d(nm/cm)/42〔(nm/cm)/(MPa)〕...(2)(前述式(2)中,d為雙折射率)。 F (MPa) = d (nm / cm) / 42 [(nm / cm) / (MPa)] (2) (in the above formula (2), d is a birefringence).

依據本發明,可獲得長期耐久性,尤其是因X射線照射所致之緻密化受抑制之氧化矽-鈦玻璃。 According to the present invention, long-term durability, in particular, cerium oxide-titanium glass whose densification due to X-ray irradiation is suppressed can be obtained.

10‧‧‧氧化矽-鈦玻璃 10‧‧‧Oxide-Titanium Glass

12‧‧‧X射線照射區域 12‧‧‧X-ray area

13‧‧‧緻密化區域 13‧‧‧ Densified area

14‧‧‧X射線非照射區域 14‧‧‧X-ray non-irradiated area

15‧‧‧非緻密化區域 15‧‧‧Non-densified areas

16‧‧‧遮罩 16‧‧‧ mask

22‧‧‧不銹鋼製容器 22‧‧‧Stainless steel containers

24‧‧‧吸氣用閥 24‧‧‧Inhalation valve

26‧‧‧排氣用閥 26‧‧‧Exhaust valve

28‧‧‧真空泵 28‧‧‧vacuum pump

P‧‧‧測定間距 P‧‧‧measuring spacing

圖1係本發明之分類方法中之X射線照射之剖面概略說明圖。 Fig. 1 is a schematic explanatory view showing a cross section of X-ray irradiation in the classification method of the present invention.

圖2係顯示本發明之製造方法及分類方法中所用之評價方法之設定一例的概略剖面說明圖。 Fig. 2 is a schematic cross-sectional explanatory view showing an example of setting of an evaluation method used in the production method and the classification method of the present invention.

以下基於附圖說明本發明之實施形態,但圖示例為例示性表示者,故只要不脫離本發明之技術思想,則亦可進行各種改變。 The embodiments of the present invention will be described below with reference to the drawings, but the illustrated examples are illustrative, and various modifications may be made without departing from the technical spirit of the invention.

本發明發現可感度良好地判定X射線所致之緻密化之方法,且,藉由發現X射線所致之氧化矽-鈦玻璃之緻密化將隨製造步驟或最終製品之物性而大有不同而完成者。 The present invention has found a method for determining the densification by X-rays with good sensitivity, and the densification of yttrium oxide-titanium glass by X-rays is found to vary greatly depending on the manufacturing process or the physical properties of the final product. Completed.

圖1係本發明之X射線照射之剖面概略說明圖。 Fig. 1 is a schematic explanatory view showing a cross section of an X-ray irradiation of the present invention.

本發明之氧化矽-鈦玻璃之分類方法之特徵係讀取以X射線為起因所發生之體積變化作為X射線照射區域12與X射線非照射區域14間發生之應力。藉由進行遮蔽等之手法,僅使X射線照射於作為被檢體之氧化矽-鈦玻璃10之一區域時,於照射區域12中引起緻密化。另一方面,非照射區域14未引起緻密化。因此,經緻密化之照射區域12與未引起緻密化之非照射區域14之間發生拉伸應力(圖1)。又,圖1中之符號13為緻密化區域,符號15為非緻密化區域,符號16為遮蔽所用之遮罩。 The classification method of the cerium oxide-titanium glass of the present invention is characterized by reading a volume change occurring due to X-rays as a stress occurring between the X-ray irradiation region 12 and the X-ray non-irradiation region 14. By performing the masking or the like, only X-rays are irradiated onto one region of the cerium oxide-titanium glass 10 as the object, and densification is caused in the irradiation region 12. On the other hand, the non-irradiated area 14 does not cause densification. Therefore, tensile stress occurs between the densified irradiation region 12 and the non-irradiation region 14 which does not cause densification (Fig. 1). Further, reference numeral 13 in Fig. 1 denotes a densified region, reference numeral 15 denotes a non-densified region, and reference numeral 16 denotes a mask for masking.

本發明係以該應力作為緻密化程度之尺度者。應力較好係以雙折射率進行量測,且自該值與氧化矽-鈦玻璃之光彈性常數算出應力。與折射率分佈不同,氧化矽-鈦玻璃之雙折射率由於與未摻雜之光學用氧化矽玻璃同程度地低,故可精度良好地掌握應力之變化。應力係使用氧化矽-鈦玻璃之光彈性常數42〔(nm/cm)/(MPa)〕,以下述式(2)自雙折射率算出。 The present invention uses this stress as a measure of the degree of densification. The stress is preferably measured by birefringence, and the stress is calculated from the photoelastic constant of the yttrium oxide-titanium glass. Unlike the refractive index distribution, the birefringence of yttrium oxide-titanium glass is as low as that of the undoped yttria glass for optical use, so that the change in stress can be accurately grasped. The stress is calculated from the birefringence by the following formula (2) using the photoelastic constant 42 [(nm/cm) / (MPa) of yttrium oxide-titanium glass.

F(MPa)=d(nm/cm)/42〔(nm/cm)/(MPa)〕...(2) F(MPa)=d(nm/cm)/42[(nm/cm)/(MPa)](2)

前述式(2)中,F為拉伸應力,d為雙折射率。 In the above formula (2), F is a tensile stress and d is a birefringence.

本發明之氧化矽-鈦玻璃之分類方法係將以下述條件發生之X射線部分地照射時,X射線照射區域與X射線非照射區域之間產生之拉伸應力F侷限於下述式(1)之範圍之氧化矽-鈦玻璃判定為良品者。 In the classification method of the cerium oxide-titanium glass of the present invention, when the X-rays generated under the following conditions are partially irradiated, the tensile stress F generated between the X-ray irradiation region and the X-ray non-irradiation region is limited to the following formula (1). The range of cerium oxide-titanium glass is judged to be a good one.

X射線照射條件:Rh靶材X射線管球,管電壓50kV,管電流70mA,照射時間1.5小時。 X-ray irradiation conditions: Rh target X-ray tube ball, tube voltage 50 kV, tube current 70 mA, irradiation time 1.5 hours.

F<0.06×C(TiO2)...(1) F<0.06×C(TiO 2 )...(1)

前述式(1)中,F係以前述式(2)算出之拉伸應力(MPa),C(TiO2)為TiO2濃度(wt%)。 In the above formula (1), F is a tensile stress (MPa) calculated by the above formula (2), and C(TiO 2 ) is a TiO 2 concentration (wt%).

應力F超過上述範圍者,因X射線照射所致之緻密化過強,不適用作為使用X射線之光學系基板用氧化矽-鈦玻璃。使判定基準的應力F之範圍成為下述式(3)時,可分類緻密化更少之氧化矽-鈦玻璃故更佳。 When the stress F exceeds the above range, the densification due to X-ray irradiation is too strong, and it is not suitable as yttrium oxide-titanium glass for an optical substrate using X-rays. When the range of the stress F of the criterion is set to the following formula (3), it is more preferable to classify the cerium oxide-titanium glass having less densification.

F<0.03×C(TiO2)...(3) F<0.03×C(TiO 2 )...(3)

圖2係顯示本發明之分類方法所用之評價方法之設定一例之概略說明圖。被檢體的氧化矽-鈦玻璃10係直徑30mm厚度2mm且經兩面鏡面研磨者。於其上設置直徑30mm、厚度1mm且中央具有直徑10mm孔之不銹鋼製之板作為遮罩16,對其照射自X射線管20發出之X射線。自X射線管20至被檢體10之距離設為20mm,自X射線管20至被檢體10之間設為1kPa以下之真空氛圍。且,X射線管20之靶材為Rh,輸入至X射線管之管電壓設為50kV,管電流設為70mA。又,圖2中,符號22為不銹鋼製容器,24為吸氣用閥,26為排氣用閥、28為真空泵。 Fig. 2 is a schematic explanatory view showing an example of setting of an evaluation method used in the classification method of the present invention. The cerium oxide-titanium glass 10 of the subject is 30 mm in diameter and 2 mm in thickness and is mirror-polished on both sides. A stainless steel plate having a diameter of 30 mm, a thickness of 1 mm, and a hole having a diameter of 10 mm at the center was provided as a mask 16 to irradiate X-rays emitted from the X-ray tube 20. The distance from the X-ray tube 20 to the subject 10 is set to 20 mm, and a vacuum atmosphere of 1 kPa or less is required from the X-ray tube 20 to the subject 10. Further, the target of the X-ray tube 20 was Rh, the tube voltage input to the X-ray tube was set to 50 kV, and the tube current was set to 70 mA. In addition, in Fig. 2, reference numeral 22 is a stainless steel container, 24 is an intake valve, 26 is an exhaust valve, and 28 is a vacuum pump.

本發明之氧化矽-鈦玻璃之分類方法所用之X射線係以Rh作為靶材,對X射線管球以電壓50kV流通電流70mA時發生之X射線。X射線管之波長係隨電壓而改變,強度係隨電流及靶材而改變。因此,將X射線之發生條件設為一定時,必須使靶材、電壓、電流固定。又, 自X射線管20到被照射之氧化矽-鈦玻璃10之距離為20mm。 The X-ray system used in the classification method of the cerium oxide-titanium glass of the present invention uses Rh as a target and X-rays generated when the X-ray tube ball has a current of 70 mA at a voltage of 50 kV. The wavelength of the X-ray tube varies with voltage, and the intensity varies with current and target. Therefore, when the X-ray generation condition is constant, it is necessary to fix the target, voltage, and current. also, The distance from the X-ray tube 20 to the irradiated yttrium oxide-titanium glass 10 is 20 mm.

本發明之氧化矽-鈦玻璃之分類方法所用之靶材的試驗樣品(厚度2mm)係TiO2濃度為5~9wt%之氧化矽-鈦玻璃。緻密化所致之應力於TiO2濃度為5~9wt%中係與TiO2濃度成比例。另一方面,以本發明之照射條件對不含TiO2之合成石英玻璃照射X射線亦不會引起緻密化,因本發明之照射條件所致之緻密化係氧化矽-鈦玻璃所特有之現象。 The test sample (thickness: 2 mm) of the target used in the classification method of the cerium oxide-titanium glass of the present invention is cerium oxide-titanium glass having a TiO 2 concentration of 5 to 9 wt%. Densification due to the stress concentration of TiO 2 of the system and the TiO 2 concentration is proportional 5 ~ 9wt%. On the other hand, the irradiation of the synthetic quartz glass containing no TiO 2 by the irradiation conditions of the present invention does not cause densification, and the densification of the cerium oxide-titanium glass due to the irradiation conditions of the present invention is peculiar. .

緻密化所致之應力與X射線之照射時間雖成比例,但本發明之評價條件係設為1.5小時。若照射1.5小時,則可充分見到因緻密化發生之應力。 Although the stress due to densification is proportional to the irradiation time of X-rays, the evaluation conditions of the present invention are set to 1.5 hours. If it is irradiated for 1.5 hours, the stress due to densification can be sufficiently seen.

照射X射線1.5小時後,取出被檢體10,進行X射線照射區域12與非照射區域14間之雙折射率測定。由所量測之雙折射率之最大值,以式(2)算出應力F。將雙折射率之測定間距P設為1mm以下時,可更正確地求出雙折射率之最大值。且,藉由預先測定X射線照射前之氧化矽-鈦玻璃之雙折射率,且測定照射X射線後相同部位之雙折射率且取其差,可更正確地測定因照射X射線發生之應力。又,雙折射率不僅表示其值,亦具有快軸之方向,其係表示應力之方向。據此,照射X射線後之快軸方向與照射前之快軸方向相同時,只要自照射後之雙折射率值減掉照射前之雙折射率值即可,照射後之快軸方向與照射前之快軸方向成直角時,只要將照射前之雙折射率 值加上照射後之雙折射率值即可。又,本發明中,雙折射率係使用HINDS公司製之雙折射率測定裝置EXICOR350AT進行測定。 After irradiating the X-rays for 1.5 hours, the subject 10 was taken out, and the birefringence measurement between the X-ray irradiation region 12 and the non-irradiation region 14 was performed. From the maximum value of the measured birefringence, the stress F is calculated by the formula (2). When the measurement pitch P of the birefringence is set to 1 mm or less, the maximum value of the birefringence can be obtained more accurately. Further, by measuring the birefringence of the yttrium oxide-titanium glass before the X-ray irradiation and measuring the birefringence of the same portion after the X-ray irradiation and taking the difference, the stress caused by the X-ray irradiation can be more accurately measured. . Further, the birefringence not only indicates the value but also the direction of the fast axis, which indicates the direction of the stress. Accordingly, when the fast axis direction after the X-ray irradiation is the same as the fast axis direction before the irradiation, the birefringence value after the irradiation is reduced by the birefringence value before the irradiation, and the fast axis direction and the irradiation after the irradiation are performed. When the front fast axis direction is at right angles, as long as the birefringence before irradiation The value is added to the value of the birefringence after the irradiation. Further, in the present invention, the birefringence is measured using a birefringence measuring device EXICOR350AT manufactured by HINDS.

本發明之氧化矽-鈦玻璃係含5~9wt%TiO2之零膨脹溫度在0~50℃範圍內之氧化矽-鈦玻璃,且係藉前述本發明之分類方法分類為良品者。 The cerium oxide-titanium glass of the present invention is a cerium oxide-titanium glass containing 5 to 9 wt% of TiO 2 and having a zero expansion temperature in the range of 0 to 50 ° C, and is classified as a good by the classification method of the present invention.

本發明之氧化矽-鈦玻璃係使用作為超低膨脹玻璃。因此TiO2濃度未達5wt%,或者高於9wt%時,在0~50℃之溫度區域中線膨脹係數無法成為0,無法作為超低膨脹玻璃使用。線膨脹係數在氧化矽-鈦玻璃所使用之溫度下之線膨脹係數趨近於0者較佳,尤其是TiO2濃度為6~8wt%時,可容易地使室溫附近之線膨脹係數成為0故較佳。TiO2濃度可藉EPMA(Electron Prove Micro Analysis,電子探針微分析)法測定。 The cerium oxide-titanium glass of the present invention is used as an ultra-low expansion glass. Therefore, when the concentration of TiO 2 is less than 5% by weight, or higher than 9% by weight, the coefficient of linear expansion cannot be zero in the temperature range of 0 to 50 ° C, and it cannot be used as an ultra-low expansion glass. The coefficient of linear expansion is preferably at a temperature at which the yttrium oxide-titanium glass is used, and the coefficient of linear expansion is preferably close to zero. Especially when the concentration of TiO 2 is 6 to 8 wt%, the coefficient of linear expansion near room temperature can be easily made. 0 is better. The TiO 2 concentration can be measured by EPMA (Electron Prove Micro Analysis).

且,零膨脹溫度脫離前述範圍時,室溫附近之線膨脹係數變大,無法作為超低膨脹材料使用。所謂零膨脹溫度係表示線膨脹係數成為0之溫度。零膨脹溫度更好在微影裝置所常用之10~40℃之範圍內。零膨脹溫度可利用ULVAC理工(股)製之LIX-2測定。 Further, when the zero expansion temperature is out of the above range, the coefficient of linear expansion near room temperature becomes large, and it cannot be used as an ultra-low expansion material. The zero expansion temperature means a temperature at which the linear expansion coefficient becomes zero. The zero expansion temperature is better in the range of 10 to 40 ° C commonly used in lithography devices. The zero expansion temperature can be measured using LIX-2 manufactured by ULVAC Laboratories.

本發明之氧化矽-鈦玻璃較好經過於高於2150℃之溫度加熱之步驟。本發明人等使用本發明之氧化矽-鈦玻璃之分類方法,針對各種氧化矽-鈦玻璃之緻密化進行調查。結果,發現經過於高於2150℃之溫度加熱之步驟的氧化矽-鈦玻璃之緻密化極小。 The cerium oxide-titanium glass of the present invention preferably passes through a step of heating at a temperature higher than 2150 °C. The present inventors investigated the densification of various cerium oxide-titanium glasses by using the classification method of cerium oxide-titanium glass of the present invention. As a result, it was found that the densification of the cerium oxide-titanium glass which was subjected to the step of heating at a temperature higher than 2150 ° C was extremely small.

藉由加熱至高於2150℃之溫度而抑制緻密化認為是因為氧化矽-鈦玻璃中存在之TiO2微結晶可藉由加熱而完全熔解玻璃化之故。氧化矽-鈦玻璃中存在微結晶時,容易因X射線照射引起鍵之再排列,促進了緻密化。加熱溫度高於2200℃時,可使微結晶更完全熔解玻璃化故而較佳。加熱溫度之上限並無特別限制,但加熱至高於2240℃之溫度時,玻璃之昇華便顯著而使生產性大幅惡化,故就工業上之觀點而言,以2240℃以下較佳。溫度量測使用放射溫度計即可。加熱時間必須加熱30秒以上,加熱1分鐘以上時,熔解更完全故較佳。加熱時間之上限並無特別限制,但鑒於因玻璃昇華造成之損失時較好為20分鐘以下。且,加熱除了使氧化矽-鈦玻璃全體處於特定溫度以外,亦可使用將氧化矽-鈦玻璃之一部分加熱至特定溫度,隨後,藉由邊移動氧化矽-鈦玻璃或燃燒器等加熱源邊進行加熱,一面移動加熱熔融區域一面加熱之帶域熔融法。 The suppression of densification by heating to a temperature higher than 2150 ° C is considered to be because the TiO 2 microcrystals present in the yttrium oxide-titanium glass can be completely melted by heating. When microcrystals are present in the cerium oxide-titanium glass, the rearrangement of the bonds is easily caused by the X-ray irradiation, and the densification is promoted. When the heating temperature is higher than 2200 ° C, the microcrystals can be more completely melted and glassy, which is preferable. The upper limit of the heating temperature is not particularly limited, but when heated to a temperature higher than 2240 ° C, the sublimation of the glass is remarkably deteriorated, and the productivity is greatly deteriorated. Therefore, from the industrial viewpoint, it is preferably 2240 ° C or lower. The temperature measurement can be performed using a radiation thermometer. The heating time must be heated for 30 seconds or more, and when heated for 1 minute or more, the melting is more complete and therefore preferable. The upper limit of the heating time is not particularly limited, but it is preferably 20 minutes or less in view of the loss due to glass sublimation. Further, in addition to heating the entire yttria-titanium glass to a specific temperature, it is also possible to heat a portion of the yttrium-titanium glass to a specific temperature, and then, by moving the yttrium-titanium glass or a burner or the like while heating the source side. A zone melting method in which heating is performed while heating the molten region while heating.

加熱氧化矽-鈦玻璃之手段並無特別限制,可使用火焰加熱、電加熱、微波加熱等。火焰加熱時可使用氧氫火焰、丙烷火焰之任一者。且,為了抑制因玻璃之流動造成之變形,較好以旋轉盤把持被處理物的氧化矽-鈦玻璃、或者接合有氧化矽-鈦玻璃之虛擬棒(dummy rod),邊旋轉被處理物邊加熱。藉由此方法可不使氧化矽-鈦玻璃與容器等接觸而加熱至高於2150℃之溫度,故亦可避免玻璃與容器等反應而變質。旋轉速度為5rpm以 上時,可維持圓對稱形狀。且,邊加熱邊進行如日本特開2007-186347號公報中例示之均質化處理時,可藉由機械攪拌促進TiO2微結晶之熔融玻璃化,為可使微結晶熔融完全者。再者,由於可藉機械攪拌使TiO2濃度分佈平坦化,故可成為緻密化受抑制,且高均質之氧化矽-鈦玻璃。 The means for heating the cerium oxide-titanium glass is not particularly limited, and flame heating, electric heating, microwave heating, or the like can be used. Any one of an oxyhydrogen flame and a propane flame can be used for heating the flame. Further, in order to suppress deformation due to the flow of the glass, it is preferable to rotate the object to be treated while holding the yttrium oxide-titanium glass of the object to be processed or the dummy rod to which the yttrium oxide-titanium glass is bonded. heating. According to this method, the cerium oxide-titanium glass can be heated to a temperature higher than 2150 ° C without coming into contact with a container or the like, so that the glass can be prevented from being deteriorated by reaction with a container or the like. When the rotation speed is 5 rpm or more, the circular symmetrical shape can be maintained. Further, when the homogenization treatment as exemplified in JP-A-2007-186347 is performed while heating, the glass transition of the TiO 2 microcrystals can be promoted by mechanical stirring to melt the microcrystals. Further, since the concentration distribution of TiO 2 can be flattened by mechanical stirring, it is possible to obtain a high-mass yttria-titanium glass which is suppressed in densification.

本發明之氧化矽-鈦玻璃之氫分子濃度較好未達1×1017個/cm3。氧化矽-鈦玻璃中之氫分子會促進因X射線照射所致之鍵再排列,含較多氫分子之氧化矽-鈦玻璃容易緻密化。氫分子濃度愈低愈好,更好為未達5×1016個/cm3,又更好為未達1×1016個/cm3。氫分子濃度係利用雷射拉曼分光法,依據Zurnal Priladnoi Spectroskopii Vol.46 No.6 pp987~991,June 1987所記載之方法測定。以該測定方法進行之氫分子濃度之檢測下限為2×1015個/cm3The cerium oxide-titanium glass of the present invention preferably has a hydrogen molecule concentration of less than 1 × 10 17 /cm 3 . The hydrogen molecules in the cerium oxide-titanium glass promote the rearrangement of bonds due to X-ray irradiation, and the cerium oxide-titanium glass containing more hydrogen molecules is easily densified. The lower the concentration of the hydrogen molecules, the better, preferably less than 5 × 10 16 /cm 3 , more preferably less than 1 × 10 16 /cm 3 . The hydrogen molecule concentration was measured by a laser Raman spectrometry according to the method described in Zurnal Priladnoi Spectroskopii Vol. 46 No. 6 pp 987-991, June 1987. The detection lower limit of the hydrogen molecule concentration by this measurement method is 2 × 10 15 /cm 3 .

本發明之氧化矽-鈦玻璃之OH基濃度較好為800wtppm以下。氧化矽-鈦玻璃中之OH基濃度超過800wtppm時,加熱至高於2150℃之溫度時之玻璃流動性變大而有形狀難以維持之情況。二氧化矽-鈦玻璃之黏性係OH基濃度愈低愈好,OH基濃度為600wtppm以下時在更高溫度處理時之形狀維持較容易,OH基濃度更好為200wtppm以下。 The cerium oxide-titanium glass of the present invention preferably has an OH group concentration of 800 wtppm or less. When the OH group concentration in the cerium oxide-titanium glass exceeds 800 wtppm, when the temperature is raised to a temperature higher than 2150 ° C, the fluidity of the glass becomes large and the shape is difficult to maintain. The viscosity of the bismuth dioxide-titanium glass is preferably as low as possible. When the OH group concentration is 600 wtppm or less, the shape is maintained at a higher temperature, and the OH group concentration is more preferably 200 wtppm or less.

OH基濃度可使用傅立葉轉換紅外線分光裝置(Nicolet公司製AVATOR360),自因2.7μm之O-H伸 縮振動之吸收的吸光度與試料之厚度t(cm),以下述式(4)求得。 The OH group concentration can be a Fourier-converted infrared spectroscopy device (AVATOR360 manufactured by Nicolet Co., Ltd.), which is derived from the O-H of 2.7 μm. The absorbance of the absorption of the reduced vibration and the thickness t (cm) of the sample were obtained by the following formula (4).

OH基濃度=(吸光度)×100/t...(4) OH group concentration = (absorbance) × 100 / t... (4)

本發明之氧化矽-鈦玻璃特別適於用作EUV微影曝光裝置之鏡面基板。EUV微影中,遮罩基板雖係依據每次期望之曝光圖型進行更換,但若能以一次裝置完成則鏡面基板不需更換而可持續使用。因此,曝光裝置之鏡面基板特別要求耐久性。藉由使用本發明之氧化矽-鈦玻璃,即使長時間使用後基板形狀變化亦少,可成為成像能力高的EUV微影曝光裝置。 The cerium oxide-titanium glass of the present invention is particularly suitable for use as a mirror substrate for an EUV lithography exposure apparatus. In EUV lithography, the mask substrate is replaced according to each desired exposure pattern, but if it can be completed in one device, the mirror substrate can be used without replacement. Therefore, the mirror substrate of the exposure apparatus is particularly required to have durability. By using the cerium oxide-titanium glass of the present invention, even if the shape of the substrate changes little after a long period of use, the EUV lithography exposure apparatus having high image forming ability can be obtained.

本發明之氧化矽-鈦玻璃之製造方法係包含以下步驟a)~c)者。 The method for producing cerium oxide-titanium glass of the present invention comprises the following steps a) to c).

步驟a)係自Si原料與Ti原料合成含5~9wt% TiO2之氧化矽-鈦玻璃之步驟。氧化矽-鈦玻璃之合成方法可為直接法、VAD法、OVD法之任一種方法。TiO2濃度由於無法在後續步驟中調整,故TiO2濃度係在此合成階段中進行調整。具體而言,邊適當調整TiCl4、Ti(OC2H5)4、Ti[OCH2(CH3)2]4等Ti源、與SiCl4、SiCH3Cl3、Si(CH3)2Cl2、SiCH3(OCH3)3、Si(OCH3)4、Si(OC2H5)4等Si源之供給量邊進行水解或氧化燃燒等而合成。VAD法、OVD法係先合成氧化矽-鈦多孔質體,藉由燒結其而可獲得氧化矽-鈦玻璃。又,以OVD法、VAD法合成時,由於藉步驟b)中之加熱可透明玻璃化,故步驟a)中亦可不進行透明玻璃化。 Step a) is a step of synthesizing cerium oxide-titanium glass containing 5 to 9 wt% of TiO 2 from a Si raw material and a Ti raw material. The method for synthesizing cerium oxide-titanium glass may be any one of a direct method, a VAD method, and an OVD method. Since the TiO 2 concentration cannot be adjusted in the subsequent step, the TiO 2 concentration is adjusted in this synthesis stage. Specifically, a Ti source such as TiCl 4 , Ti(OC 2 H 5 ) 4 , Ti[OCH 2 (CH 3 ) 2 ] 4 or the like, and SiCl 4 , SiCH 3 Cl 3 , Si(CH 3 ) 2 Cl are appropriately adjusted. 2. The supply amount of Si source such as SiCH 3 (OCH 3 ) 3 , Si(OCH 3 ) 4 or Si(OC 2 H 5 ) 4 is synthesized by hydrolysis or oxidative combustion. The VAD method and the OVD method first synthesize a cerium oxide-titanium porous body, and by sintering it, cerium oxide-titanium glass can be obtained. Further, when it is synthesized by the OVD method or the VAD method, since it can be transparently vitrified by the heating in the step b), the transparent vitrification may not be performed in the step a).

步驟b)係使步驟a)中獲得之氧化矽-鈦玻璃在高於2150℃之溫度加熱之步驟。加熱溫度高於2200℃時,可製造緻密化更被抑制之氧化矽-鈦玻璃故而較佳。加熱之手段並無特別限制,可使用火焰加熱、電阻加熱、感應加熱、微波加熱等。火焰加熱時,可使用氧氫火焰、丙烷火焰之任一種。且,為了抑制因玻璃流動造成之變形,較好以旋轉盤夾持被處理物的氧化矽-鈦玻璃或者接合有氧化矽-鈦玻璃之虛擬棒,邊旋轉被處理物邊加熱。藉由此方法可使氧化矽-鈦玻璃不與容器等接觸而加熱至高於2150℃之溫度,故可避免玻璃與容器等反應所致之變質。旋轉速度為5rpm以上時,可維持圓對稱形狀。旋轉速度之上限並未特定,但超過300rpm時,無法忽略因離心力造成之形狀變化,故期望為300rpm以下。且,邊加熱邊進行如日本特開2007-186347號公報中例示般之均質化處理時,由於與TiO2微結晶之熔融玻璃化同時進行至TiO2濃度分布之平坦化,故可成為緻密化受抑制且高均質之氧化矽-鈦玻璃。且,藉由邊加熱邊移動單一或二者之夾具,亦可使氧化矽-鈦玻璃之直徑變形成期望之直徑。 Step b) is a step of heating the cerium oxide-titanium glass obtained in the step a) at a temperature higher than 2150 °C. When the heating temperature is higher than 2,200 ° C, it is preferable to produce a cerium oxide-titanium glass which is more densely densified. The means for heating is not particularly limited, and flame heating, resistance heating, induction heating, microwave heating, or the like can be used. When the flame is heated, either an oxyhydrogen flame or a propane flame can be used. Further, in order to suppress deformation due to the flow of the glass, it is preferable to heat the ruthenium-titanium glass to which the object to be treated is held by the rotating disk or the dummy bar to which the yttrium oxide-titanium glass is bonded, while rotating the object to be processed. By this method, the cerium oxide-titanium glass can be heated to a temperature higher than 2150 ° C without coming into contact with a container or the like, so that deterioration due to reaction of the glass with the container or the like can be avoided. When the rotation speed is 5 rpm or more, the circular symmetrical shape can be maintained. The upper limit of the rotational speed is not specified, but when it exceeds 300 rpm, the shape change due to the centrifugal force cannot be ignored, and therefore it is desirably 300 rpm or less. Further, when the homogenization treatment as exemplified in JP-A-2007-186347 is performed while heating, the TiO 2 concentration distribution is flattened simultaneously with the molten vitrification of the TiO 2 microcrystals, so that densification can be achieved. A suppressed and highly homogeneous cerium oxide-titanium glass. Moreover, the diameter of the yttrium oxide-titanium glass can be changed to a desired diameter by moving a single or both of the jigs while heating.

步驟c)係在700~1300℃下使步驟b)所得之氧化矽-鈦玻璃退火之步驟。退火溫度未達700℃無法去除應變,且,超過1300℃時容易引起透明度喪失。退火時間較好為1小時以上500小時以下。退火時間未達1小時時,大多會使應變去除變得不充分,應變去除不充分時,由於在本發明之分類方法中,X射線照射前之雙折射率會 變強,故不易掌握X射線照射前後之雙折射率變化故較不佳。 Step c) is a step of annealing the cerium oxide-titanium glass obtained in the step b) at 700 to 1300 °C. When the annealing temperature is less than 700 ° C, the strain cannot be removed, and when it exceeds 1300 ° C, the transparency is easily lost. The annealing time is preferably from 1 hour to 500 hours. When the annealing time is less than 1 hour, the strain removal is often insufficient, and when the strain removal is insufficient, since the birefringence before X-ray irradiation is in the classification method of the present invention, It becomes stronger, so it is difficult to grasp the change in birefringence before and after X-ray irradiation, which is not preferable.

且,藉由退火亦可使氧化矽-鈦玻璃中所含之氫分子向外擴散而減低玻璃中之氫濃度。該情況期望加熱10小時以上。又,退火時間為500小時即足夠。即使進行較500小時久之時間的退火亦無法獲得其以上之效果,成為生產時間與能源之浪費。又,藉由切斷、研削成期望形狀後進行退火亦可縮短去除應變或氫擴散所花費之時間。 Further, the hydrogen molecules contained in the cerium oxide-titanium glass can be diffused outward by annealing to reduce the hydrogen concentration in the glass. In this case, it is desirable to heat for more than 10 hours. Further, it is sufficient that the annealing time is 500 hours. Even if annealing is performed for more than 500 hours, the above effects cannot be obtained, which is a waste of production time and energy. Further, the time required for removing strain or hydrogen diffusion can be shortened by cutting and grinding into a desired shape and then annealing.

另外,在步驟b)與步驟c)之間,亦可進行將氧化矽-鈦玻璃設置於加熱爐內,藉由在1500~1850℃下加熱20分鐘以上且5小時以下,而成型為所需形狀之步驟。至於成型之氛圍宜為真空氛圍、或者以氮氣、氬氣為代表之惰性氣體氛圍等。成型所用之容器可使用石墨製之容器。 Further, between step b) and step c), the cerium oxide-titanium glass may be placed in a heating furnace and heated at 1,500 to 1,850 ° C for 20 minutes or more and 5 hours or less. The steps of the shape. The atmosphere to be molded is preferably a vacuum atmosphere or an inert gas atmosphere represented by nitrogen or argon. A container made of graphite can be used for the container used for molding.

以前述方法所得之氧化矽-鈦玻璃可藉由本發明之分類方法分類成良品。 The cerium oxide-titanium glass obtained by the above method can be classified into a good product by the classification method of the present invention.

〔實施例〕 [Examples]

以下以實施例具體說明本發明,但本發明並不受限於下述實施例。 The invention will be specifically described below by way of examples, but the invention is not limited to the examples described below.

(實施例1) (Example 1)

使經加熱氣化之SiCl4及TiCl4導入氧氫火焰中生成 之SiO2-TiO2微粒子堆積於旋轉之氧化矽-鈦玻璃靶材上,藉由以使堆積面成為一定位置之方式與伸長一致地使靶材朝垂直方向上拉之VAD法,製作直徑250mm長度500mm之氧化矽-鈦玻璃多孔質體〔步驟a)〕。此時之SiCl4與TiCl4之流量比係調整為所合成之氧化矽-鈦玻璃之TiO2濃度成為6.9wt%。 The SiO 2 -TiO 2 fine particles generated by introducing the heated vaporized SiCl 4 and TiCl 4 into the oxyhydrogen flame are deposited on the rotating yttrium oxide-titanium glass target, and the elongated surface is elongated by a certain position. A VB method in which the target was pulled in the vertical direction in a uniform manner to produce a cerium oxide-titanium glass porous body having a diameter of 250 mm and a length of 500 mm was produced [step a)]. At this time, the flow ratio of SiCl 4 to TiCl 4 was adjusted so that the TiO 2 concentration of the synthesized cerium oxide-titanium glass became 6.9 wt%.

使該氧化矽-鈦多孔質體在真空中於1500℃下加熱5小時,獲得直徑150mm長度400mm之氧化矽-鈦玻璃燒結體〔步驟a)〕。 The cerium oxide-titanium porous body was heated in a vacuum at 1500 ° C for 5 hours to obtain a yttria-titanium glass sintered body having a diameter of 150 mm and a length of 400 mm [step a)].

將前述所得之燒結體兩端熔接於各由旋轉盤把持之氧化矽-鈦玻璃製虛擬棒上,邊以10rpm旋轉邊以氫氧火焰加熱。以使經加熱之玻璃溫度成為2220℃之方式調整氧氫流量〔步驟b)〕。加熱後,氧化矽-鈦玻璃成為透明玻璃體。 Both ends of the sintered body obtained above were welded to each of the virtual rods made of yttria-titanium glass held by a rotating disk, and heated by an oxyhydrogen flame while rotating at 10 rpm. The oxygen-hydrogen flow rate is adjusted so that the heated glass temperature becomes 2220 ° C [step b)]. After heating, the cerium oxide-titanium glass becomes a transparent glass body.

自虛擬棒切離該氧化矽-鈦玻璃,在大氣中於1000℃進行150小時之退火處理,獲得經去除應變之氧化矽-鈦玻璃〔步驟c)〕。 The ruthenium oxide-titanium glass was cut out from the virtual rod and annealed at 1000 ° C for 150 hours in the atmosphere to obtain a strain-removed cerium oxide-titanium glass [step c)].

自所得氧化矽-鈦玻璃切出直徑6mm長度20mm之線膨脹測定用試料,測定零膨脹溫度T1。接著,以下述條件對該線膨脹測定用試料進行X射線照射後,測定該試料之零膨脹溫度T2。照射中之壓力為0.1kPa。X射線源為Rh靶材之X射線管,管電壓為50kV,管電流為70mA,X射線管到樣品之距離設為20mm,照射10小時。結果示於表1。 A sample for linear expansion measurement having a diameter of 6 mm and a length of 20 mm was cut out from the obtained cerium oxide-titanium glass, and the zero expansion temperature T 1 was measured. Next, the sample for linear expansion measurement was subjected to X-ray irradiation under the following conditions, and then the zero expansion temperature T 2 of the sample was measured. The pressure during the irradiation was 0.1 kPa. The X-ray source was an X-ray tube of Rh target, the tube voltage was 50 kV, the tube current was 70 mA, the distance from the X-ray tube to the sample was set to 20 mm, and irradiation was performed for 10 hours. The results are shown in Table 1.

且,自所得氧化矽-鈦玻璃製作直徑30mm厚度2mm之經兩面鏡面研磨之樣品,測定該樣品之OH基濃度、氫濃度。結果示於表1。 Further, a two-mirror surface-polished sample having a diameter of 30 mm and a thickness of 2 mm was prepared from the obtained cerium oxide-titanium glass, and the OH group concentration and the hydrogen concentration of the sample were measured. The results are shown in Table 1.

且,測定該樣品之雙折射率後,以如圖2般罩上直徑30mm厚度1mm之中央開有直徑10mm之孔的不銹鋼製遮罩之狀態照射X射線1.5小時。照射中之壓力為0.1kPa。X射線源為Rh靶材之X射線管,管電壓為50kV,管電流為70mA,X射線管到樣品之距離設為20mm。完成照射後再度測定樣品之雙折射率,藉由求出與照射前之雙折射率之差,求出因X射線照射產生之雙折射率之最大值d。將該雙折射率之最大值d代入式(2)中,求出應力F。結果示於表1。應力F滿足式(1)者評價為○,滿足式(3)者評價為◎,未滿足式(1)者評價為×。 Further, after measuring the birefringence of the sample, X-rays were irradiated for 1.5 hours in a state of a stainless steel mask having a diameter of 10 mm and a hole of 10 mm in the center of a thickness of 30 mm as shown in Fig. 2 . The pressure during the irradiation was 0.1 kPa. The X-ray source is an X-ray tube of Rh target, the tube voltage is 50 kV, the tube current is 70 mA, and the distance from the X-ray tube to the sample is set to 20 mm. After the completion of the irradiation, the birefringence of the sample was measured again, and the maximum value d of the birefringence due to the X-ray irradiation was determined by determining the difference from the birefringence before the irradiation. The maximum value d of the birefringence is substituted into the formula (2) to determine the stress F. The results are shown in Table 1. When the stress F satisfies the formula (1), the evaluation is ○, the one that satisfies the formula (3) is evaluated as ◎, and the one that does not satisfy the formula (1) is evaluated as ×.

(實施例2) (Example 2)

除了將氧氫火焰之加熱溫度設為2230℃以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the heating temperature of the oxyhydrogen flame was set to 2230 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例3) (Example 3)

除了將氧氫火焰之加熱溫度設為2210℃以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。 對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the heating temperature of the oxyhydrogen flame was set to 2210 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例4) (Example 4)

除了將氧氫火焰之加熱溫度設為2200℃以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the heating temperature of the oxyhydrogen flame was set to 2,200 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例5) (Example 5)

除了將氧氫火焰之加熱溫度設為2180℃以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the heating temperature of the oxyhydrogen flame was set to 2180 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例6) (Example 6)

除了將氧氫火焰之加熱溫度設為2160℃以外,餘以與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the heating temperature of the oxyhydrogen flame was set to 2,160 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例7) (Example 7)

除了以使氧化矽-鈦玻璃之TiO2濃度成為6.3wt%之方式調整SiCl4與TiCl4之流量以外,餘與實施例1相同之 方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the flow rates of SiCl 4 and TiCl 4 were adjusted so that the TiO 2 concentration of the cerium oxide-titanium glass was 6.3 wt%. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例8) (Example 8)

除了以使氧化矽-鈦玻璃之TiO2濃度成為5.4wt%之方式調整SiCl4與TiCl4之流量以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the flow rates of SiCl 4 and TiCl 4 were adjusted so that the TiO 2 concentration of the cerium oxide-titanium glass was 5.4 wt%. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例9) (Example 9)

除了以使氧化矽-鈦玻璃之TiO2濃度成為7.5wt%之方式調整SiCl4與TiCl4之流量以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the flow rates of SiCl 4 and TiCl 4 were adjusted so that the TiO 2 concentration of the cerium oxide-titanium glass was 7.5 wt%. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例10) (Embodiment 10)

使經加熱氣化之SiCl4及TiCl4導入氧氫火焰中生成之SiO2-TiO2微粒子邊堆積於旋轉之氧化矽-鈦玻璃靶材上並熔融,邊利用使堆積位置成為一定之方式與伸長一致地使靶材朝水平方向後退之直接法,獲得直徑130mm長度700mm之氧化矽-鈦玻璃〔步驟a)〕。此時之SiCl4與TiCl4之流量比係調整為使所合成之氧化矽-鈦玻璃之TiO2濃度成為6.6wt%。又,以放射溫度計測定藉直接法合成中之氧化矽-鈦玻璃之堆積面溫度後,為1910℃。藉由使 該氧化矽鈦玻璃進行與實施例1相同之氧氫火焰加熱〔步驟b)〕、退火處理〔步驟c)〕,獲得經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The heated and vaporized SiCl 4 and TiCl 4 are introduced into the oxidized cerium-titanium glass target by the SiO 2 -TiO 2 fine particles generated by the oxyhydrogen flame, and are melted, and the deposition position is made constant. A direct method in which the target is retracted in the horizontal direction in a uniform manner is obtained, and a cerium oxide-titanium glass having a diameter of 130 mm and a length of 700 mm is obtained [step a)]. At this time, the flow ratio of SiCl 4 to TiCl 4 was adjusted so that the TiO 2 concentration of the synthesized cerium oxide-titanium glass became 6.6 wt%. Further, the temperature of the deposition surface of the cerium oxide-titanium glass in the direct synthesis was measured by a radiation thermometer to be 1910 °C. The yttria-titanium glass was subjected to the same oxyhydrogen flame heating (step b) as in Example 1 and an annealing treatment [step c)] to obtain a strain-removed cerium oxide-titanium glass. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例11) (Example 11)

除了退火處理時間設為5小時以外,餘與實施例10相同之方法,獲得經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass was obtained in the same manner as in Example 10 except that the annealing treatment time was set to 5 hours. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例12) (Embodiment 12)

除了將Si源設為SiCH3Cl3,將氧氫火焰之加熱溫度設為2170℃以外,餘與實施例10相同之方法,獲得直徑120mm長度800mm之經去除應變之氧化矽-鈦玻璃。合成時之SiCH3Cl3與TiCl4之流量比係調整為使所合成之氧化矽-鈦玻璃之TiO2濃度成為7.1wt%。又,合成中之堆積面溫度為1950℃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表1。 The strain-removed cerium oxide-titanium glass having a diameter of 120 mm and a length of 800 mm was obtained in the same manner as in Example 10 except that the Si source was changed to SiCH 3 Cl 3 and the heating temperature of the oxyhydrogen flame was set to 2170 °C. The flow ratio of SiCH 3 Cl 3 to TiCl 4 at the time of synthesis was adjusted so that the TiO 2 concentration of the synthesized cerium oxide-titanium glass became 7.1% by weight. Further, the temperature of the deposition surface in the synthesis was 1950 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 1.

(實施例13) (Example 13)

除了退火處理時間設為5小時以外,餘與實施例12相同之方法,獲得經去除應變之氧化矽-鈦玻璃。 The strain-removed cerium oxide-titanium glass was obtained in the same manner as in Example 12 except that the annealing treatment time was set to 5 hours.

又,表1中,T1為X射線照射前之零膨脹溫度,T2為X射線照射10小時後之零膨脹溫度。 Further, in Table 1, T 1 is the zero expansion temperature before the X-ray irradiation, and T 2 is the zero expansion temperature after the X-ray irradiation for 10 hours.

如表1所示,實施例1~13所得之氧化矽-鈦玻璃之X射線照射前及X射線照射10小時後之零膨脹溫度均包含在0~50℃之範圍,係超低膨脹材料,且具有優異之耐久性。 As shown in Table 1, the zero expansion temperature of the cerium oxide-titanium glass obtained in Examples 1 to 13 before X-ray irradiation and 10 hours after X-ray irradiation is included in the range of 0 to 50 ° C, and is an ultra-low expansion material. And has excellent durability.

此外,如表1所示,實施例1~13之氧化矽-鈦玻璃之起因於X射線照射所致之緻密化所產生之應力均未達上限,係X射線照射所致之緻密化受抑制之氧化矽-鈦玻璃。 Further, as shown in Table 1, the stresses caused by the densification by X-ray irradiation of the yttrium oxide-titanium glasses of Examples 1 to 13 did not reach the upper limit, and the densification by X-ray irradiation was suppressed. Cerium oxide-titanium glass.

(比較例1) (Comparative Example 1)

除了未進行氧氫火焰之加熱以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表2。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the heating by the oxyhydrogen flame was not carried out. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 2.

(比較例2) (Comparative Example 2)

除了將氧氫火焰之加熱溫度設為2130℃以外,餘與實施例1相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表2。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 1 except that the heating temperature of the oxyhydrogen flame was set to 2130 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 2.

(比較例3) (Comparative Example 3)

除了未進行氧氫火焰之加熱以外,餘與實施例10相 同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表2。 Except that the heating of the oxyhydrogen flame was not performed, the remainder was the same as that of Example 10. In the same manner, a strain-removed cerium oxide-titanium glass is produced. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 2.

(比較例4) (Comparative Example 4)

除了將氧氫火焰之加熱溫度設為2130℃以外,餘與實施例10相同之方法,製作經去除應變之氧化矽-鈦玻璃。對所得之氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表2。 The strain-removed cerium oxide-titanium glass was produced in the same manner as in Example 10 except that the heating temperature of the oxyhydrogen flame was set to 2130 °C. The obtained cerium oxide-titanium glass was subjected to the same measurement as in Example 1. The results are shown in Table 2.

(比較例5) (Comparative Example 5)

取得市售氧化矽-鈦玻璃的Corning公司ULE C7972。測定其TiO2濃度後,TiO2濃度為6.5wt%。對該氧化矽-鈦玻璃進行與實施例1相同之測定。結果示於表2。 Corning ULE C7972, a commercially available yttria-titanium glass, was obtained. After measuring the TiO 2 concentration, the TiO 2 concentration was 6.5 wt%. The same measurement as in Example 1 was carried out on the cerium oxide-titanium glass. The results are shown in Table 2.

又,表2中,T1為X射線照射前之零膨脹溫度,T2為X射線照射10小時後之零膨脹溫度。 Further, in Table 2, T 1 is the zero expansion temperature before the X-ray irradiation, and T 2 is the zero expansion temperature after the X-ray irradiation for 10 hours.

如表2所示,比較例1~5之氧化矽-鈦玻璃之起因於緻密化產生之應力均大幅超過上限,係X射線照射所致之緻密化大的氧化矽-鈦玻璃。且,由照射X射線10小時後之零膨脹溫度之結果,判知耐久性有問題,而不適合作為超低膨脹材料。 As shown in Table 2, the yttrium oxide-titanium glass of Comparative Examples 1 to 5 caused the stress generated by the densification to greatly exceed the upper limit, and was a dense yttrium oxide-titanium glass due to X-ray irradiation. Further, as a result of the zero expansion temperature after the X-ray irradiation for 10 hours, it was found that there was a problem in durability, and it was not suitable as an ultra-low expansion material.

10‧‧‧氧化矽-鈦玻璃 10‧‧‧Oxide-Titanium Glass

12‧‧‧X射線照射區域 12‧‧‧X-ray area

13‧‧‧緻密化區域 13‧‧‧ Densified area

14‧‧‧X射線非照射區域 14‧‧‧X-ray non-irradiated area

15‧‧‧非緻密化區域 15‧‧‧Non-densified areas

16‧‧‧遮罩 16‧‧‧ mask

P‧‧‧測定間距 P‧‧‧measuring spacing

Claims (1)

一種氧化矽-鈦玻璃之製造方法,其特徵係包含下列步驟之氧化矽-鈦玻璃之製造方法:a)由Si原料與Ti原料合成含5~9wt%TiO2之氧化矽-鈦玻璃之步驟、b)在高於2150℃之溫度加熱前述步驟a)所得之氧化矽-鈦玻璃之步驟、c)在700~1300℃下使前述步驟b)所得之氧化矽-鈦玻璃退火之步驟、及將前述c)步驟後之氧化矽-鈦玻璃以下述條件發生之X射線部分地照射厚度2mm之試驗樣品時之X射線照射區域與X射線非照射區域之間產生之拉伸應力F係侷限於下述式(1)之範圍者分類為良品之步驟,X射線照射條件:Rh靶材X射線管球,管電壓50kV,管電流70mA,照射時間1.5小時,F<0.06×C(TiO2)...(1)(前述式(1)中,F係以下述式(2)算出之拉伸應力(MPa),C(TiO2)為TiO2濃度(wt%))F(MPa)=d(nm/cm)/42〔(nm/cm)/(MPa)〕...(2)(前述式(2)中,d為雙折射率)。 A method for producing cerium oxide-titanium glass, which comprises the following steps for producing cerium oxide-titanium glass: a) a step of synthesizing cerium oxide-titanium glass containing 5 to 9 wt% of TiO 2 from a Si raw material and a Ti raw material And b) heating the cerium oxide-titanium glass obtained in the above step a) at a temperature higher than 2150 ° C, c) annealing the cerium oxide-titanium glass obtained in the above step b) at 700 to 1300 ° C, and The tensile stress F generated between the X-ray irradiation region and the X-ray non-irradiation region when the X-ray of the cerium oxide-titanium glass after the above-mentioned step c) is partially irradiated with the test sample having a thickness of 2 mm is limited. The range of the following formula (1) is classified into a good product step, X-ray irradiation conditions: Rh target X-ray tube ball, tube voltage 50 kV, tube current 70 mA, irradiation time 1.5 hours, F < 0.06 × C (TiO 2 ) (1) (In the above formula (1), F is a tensile stress (MPa) calculated by the following formula (2), and C(TiO 2 ) is a TiO 2 concentration (wt%)) F (MPa) = d (nm/cm) / 42 [(nm / cm) / (MPa)] (2) (in the above formula (2), d is a birefringence).
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