JP4825972B2 - Method for obtaining the relationship between leakage surface acoustic wave velocity, chemical composition ratio and linear expansion coefficient of material having striae, and TiO2 concentration measuring method and linear expansion coefficient measuring method of TiO2-SiO2 glass using the relationship - Google Patents

Description

The present invention is essential for evaluating TiO ₂ --SiO ₂ ultra-low expansion glass using an ultrasonic material characterization apparatus, leaky surface acoustic wave (LSAW) velocity, chemical composition ratio and linear expansion. The present invention relates to a method for obtaining an accurate relationship between a coefficient (Coefficient of Thermal Expansion: CTE) and a method for obtaining a TiO ₂ concentration and a linear expansion coefficient of TiO ₂ —SiO ₂ glass using the relationship.

  Extreme Ultra-Violet Lithography (EUVL) is promising as a next-generation semiconductor manufacturing technology for mass production of super-integrated circuits. This exposure apparatus becomes a reflective optical system, and as the base material for photomasks and optical mirrors, the ultimate super CT is less than ± 5 ppb / K at the desired temperature (for example, 22 ± 3 ° C with respect to the mask substrate). Low expansion glass is required [Non-patent Document 1]. Currently, several glass manufacturers are developing EUVL grade glass.

  It is important to analyze the CTE characteristics with high accuracy in order to develop the glass, the production process, and quality control between lots. In the conventional evaluation method, CTE is obtained indirectly by a method of directly measuring CTE with a linear dilatometer [Non-Patent Document 2] and measuring chemical composition ratio, longitudinal wave velocity, refractive index [Non-Patent Document 1], and the like. There is a way. However, there are problems such as insufficient measurement accuracy, measurement of average characteristics in the thickness direction of the substrate, and evaluation of the vicinity of the surface, which is important for EUVL. Not applicable to evaluation.

As a new evaluation technology for CTE, a method using an ultrasonic material characteristic analysis apparatus ([Non-patent Document 3], [Non-Patent Document 4]) has been developed. This evaluation technique may be able to overcome the above problems. In particular, a quantitative measurement method (V (z) curve analysis method [Non-Patent Document 3]) using focused ultrasound is effective. This is a material evaluation by measuring the phase velocity (V _LSAW ) of a leaky surface acoustic wave (LSAW) excited on the surface of a sample loaded with water. According to this method, it is possible to measure the characteristic distribution of the glass substrate surface with high accuracy in a non-destructive and non-contact manner. For measurement, a point-focused ultrasonic beam (PFB) and a linearly-focused ultrasonic beam (LFB) can be used. Here, an explanation will be given using an LFB ultrasonic material property analyzer ([Non-Patent Document 3]. ] And [Non-Patent Document 4]).

ここで、fは超音波周波数、V_Wは水中の縦波音速である。V_Wは、V(z)曲線測定時に熱電対により測定される水カプラ温度から［非特許文献５］により得ることができる。
このように、LFB音響レンズと試料の相対距離zを変化させたときのトランスデューサ出力V(z)曲線を測定・解析することによりLSAW速度V_LSAWが求められる。図２Aに、市販のTiO₂-SiO₂ガラス試料（C-7972, Corning社製）に対して、超音波周波数fを225 MHzとして測定したV(z)曲線を示す。V(z)曲線解析法［非特許文献３］に基づいて解析することにより、図２Bに示すようなスペクトラム分布が最終的に得られる。図２Bのスペクトラム分布のピーク波数から干渉周期Dz を求め、式(3)に代入して、LSAW速度を求める。 The LSAW velocity measurement method and measurement system using the LFB ultrasonic material characteristic analyzer are well known in the literature ([Non-Patent Document 3], [Non-Patent Document 4]). The LFB ultrasonic material characterization analyzer analyzes the V (z) curve obtained when the relative distance z between the LFB ultrasonic device and the sample is changed, so that the leakage elastic wave propagating through the water / sample boundary is analyzed. Propagation characteristics can be obtained. FIG. 1 is a cross-sectional view of an ultrasonic device composed of an ultrasonic transducer 1 and an LFB acoustic lens 2 and a glass sample 3 system, and shows the principle of measurement. The focal point in water is the origin Oxy, and the coordinate axes are taken as shown in the figure. The plane ultrasonic wave excited by the ultrasonic transducer 1 is focused in a wedge shape by the LFB acoustic lens 2 and irradiated onto the surface of the glass sample 3 through the water coupler 4. When the sample is brought closer to the ultrasonic device side than the focal plane 5, the component dominantly contributing to the output of the ultrasonic transducer 1 in the reflected wave from the glass sample 3 is approximated by the effect of the aperture surface of the acoustic lens 2. Thus, only the components taking the paths P0 and P1 shown in FIG. The component P0 is a component directly reflected from the sample, and the component P1 is a component that is incident on the glass sample 3 at the LSAW excitation critical angle θ _LSAW and propagates as LSAW on the surface of the glass sample 3. The transducer output V (z) is obtained as an interference waveform of these two components. In the V (z) curve analysis model (Non-patent Document 5), it is approximately expressed as the following equation.
V (z) = V _I (z) (LSAW) + V _L (z) (1)
However,
V _L (z) = V _L '(z) + ΔV _L (z) (2)
Here, V _I (z) (LSAW) is an LSAW interference component, and V _L (z) is a component reflecting the characteristics of the ultrasonic device. ΔV _L (z) is a deviation of V _L (z) from V _L ′ (z) of a sample (for example, Teflon (registered trademark)) in which a leaky elastic wave is not excited. V _I (z) (LSAW) is extracted based on the V (z) curve analysis method [Non-Patent Document 3], its interference period Δz _LSAW is obtained, and is substituted into Δz in the following equation (3) to obtain the LSAW velocity V _{Find LSAW} .

Here, f is the ultrasonic frequency, and V _W is the longitudinal wave velocity in water. V _W can be obtained from [Non-Patent Document 5] from the water coupler temperature measured by a thermocouple when measuring the V (z) curve.
Thus, the LSAW velocity V _LSAW is obtained by measuring and analyzing the transducer output V (z) curve when the relative distance z between the LFB acoustic lens and the sample is changed. FIG. 2A shows a V (z) curve measured for a commercially available TiO ₂ —SiO ₂ glass sample (C-7972, manufactured by Corning) at an ultrasonic frequency f of 225 MHz. By analyzing based on the V (z) curve analysis method [Non-Patent Document 3], a spectrum distribution as shown in FIG. 2B is finally obtained. The interference period Dz is obtained from the peak wave number of the spectrum distribution of FIG. 2B, and is substituted into equation (3) to obtain the LSAW speed.

The area where the LSAW contributing to the V (z) curve propagates on the sample surface (ultrasonic measurement area; WxD) is W, where W is the width in the focusing direction (LSAW propagation distance) and D is the width in the non-focusing direction. 2 | z | tan θ _LSAW (θ _LSAW is the critical angle of _LSAW , θ _LSAW = sin ^-1 V _W / V _LSAW ) and a function of z, and D is the effective beamwidth in the unfocused direction And depends on the operating parameters of the ultrasonic device. The acoustic lens of the 200 MHz band ultrasonic device used here has a radius of curvature of 1 mm, the width of the transducer in the focusing direction is 1.73 mm, and that in the non-focusing direction is 1.50 mm. In this case, D is about 900 μm. Become. From FIG. 2A measured at f = 225 MHz, the maximum | z | that can be used for LSAW analysis for C-7972 is about 275 μm, and W is 280 μm at the maximum. In addition, the characteristics of a region of about one wavelength of LSAW are reflected in the substrate depth direction, and when V _LSAW = 3308 m / s and f = 225 MHz, it is about 15 μm.

When the LFB ultrasonic material characteristic analyzer is applied to a material having periodic striae, since the distribution of acoustic characteristics corresponding to the striae exists in the sample, the measured value generally differs depending on the measurement position. For a TiO ₂ —SiO ₂ glass having periodic striae, from a glass ingot 6 as shown in FIG. 3A, a sample whose substrate surface is parallel to the striae as shown in FIGS. 3B and 3C ( Studies have been conducted on the LSAW velocity measured by cutting a sample (perpendicular to the z-axis) and a sample (parallel to the z-axis) [Non-Patent Document 6]. As a result, in the case of a sample (FIG. 3B) in which the substrate surface is parallel to the striatal surface, the LSAW velocity measurement value varies greatly depending on the cut-out position of the substrate surface. In addition, since the striae is not a perfect plane but is generally a curved surface, the LSAW velocity measurement value varies greatly depending on the measurement position. On the other hand, for the sample whose substrate surface is perpendicular to the striae (FIG. 3C), the magnitude and distribution of the LSAW velocity are apparently different depending on the LSAW propagation direction. This depends on the relationship between the striae period on the sample surface (here, about 160 μm) and the ultrasonic measurement region. When the LSAW propagation direction is perpendicular to the striae plane, W is approximately the same as the striae period, so the LSAW speed changes periodically reflecting the striae, and the exact period can be measured. When the LSAW propagation direction is parallel to the striae plane, D is sufficiently larger than the striae period, so a sufficiently average LSAW velocity value that is not affected by local striae can be captured. The characteristic distribution on the surface can be measured.

Various physical quantities (physical constants) of the glass change as the chemical composition of the glass changes. For example, a change amount of a physical quantity or a chemical quantity when the LSAW speed is changed by a unit amount is defined as a sensitivity of the LSAW speed to the physical quantity or the chemical quantity. If the linear expansion coefficients and LSAW velocities of glasses A and B with different chemical compositions are CTE _A , V _LSAWA and CTE _B , V _LSAWB , respectively, the sensitivity of the LSAW speed to the linear expansion coefficient is (CTE _A -CTE _B ) / ( V _LSAWA -V _LSAWB ), and the resolution is obtained by multiplying the LSAW velocity measurement accuracy by this sensitivity. Similarly, the sensitivity and resolution of the LSAW speed for density, concentration of specific components (eg TiO ₂ ), or other physical quantities can be defined.
The CTE of TiO ₂ —SiO ₂ glass can be adjusted by the TiO ₂ concentration. Also, the LSAW speed changes linearly with changes in TiO ₂ concentration [Non-Patent Document 7]. Therefore, in order to perform an accurate evaluation of CTE using the LFB ultrasonic material characterization apparatus, not only the relationship between LSAW velocity and CTE but also the exact relationship between LSAW velocity and TiO ₂ concentration is obtained. There is a need. So far, from the viewpoint of experimental examination of glass materials for acoustic fibers, the sensitivity of the LSAW rate to changes in TiO ₂ concentration has been determined to be -0.065 wt% / (m / s) [Non-Patent Document 7]. Further, by comparing the chemical composition and LSAW velocity of commercial TiO ₂ -SiO ₂ glass (C-7971, Corning Inc.) and the synthetic quartz glass (C-7980, Corning Inc.), with respect to the change of the TiO ₂ concentration The sensitivity of the LSAW speed was determined to be -0.058 wt% / (m / s) ([Non-patent document 8], [Non-patent document 9]). However, at this time, uncertainties due to striae are included, so it is considered inadequate in terms of CTE evaluation for EUVL grade glass.
KE Hrdina, BG Ackerman, AW Fanning, CE Heckle, DC Jenne and WD Navan, "Measuring and tailoring CTE within ULE glass," Proc.SPIE, Emerging Lithographic Technologies VII, ed.RL Engelstad (SPIE--The International Society for Optical Engineering, Bellingham, WA, 2003) Vol. 5037, pp. 227-235. VG Badami and M. Linder, "Ultra-high accuracy measurement of the coefficient of thermal expansion for ultra-low expansion materials," Proc. SPIE Emerging Lithographic Technologies VI, ed.RL Engelstad (SPIE--The International Society for Optical Engineering, Bellingham, WA, 2002) Vol. 4688, pp. 469-480. J. Kushibiki and N. Chubachi, "Material characterization by line-focus-beam acoustic microscope," IEEE Trans. Sonics Ultrason., Vol. SU-32, pp. 189-212 (1985). J. Kushibiki, Y. Ono, Y. Ohashi, and M. Arakawa, "Development of the line-focus-beam ultrasonic material characterization system," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 49, pp. 99-113 (2002). W. Kroebel and K.-H. Mahrt, "Recent results of absolute sound velocity measurements in pure water and sea water at atmospheric pressure," Acustica, Vol. 35, pp. 154-164 (1976). Kushibiki, Arakawa, Ohashi, Suzuki, Maruyama, "Standard sample for LFB ultrasonic material analysis system for evaluation of ultralow expansion glass with striae and its acoustic properties," IEICE Tech. Report, Vol. US2005-4, pp 19-26 (2005). CK Jen, C. Neron, A. Shang, K. Abe, L. Bonnell, and J. Kushibiki, "Acoustic characterization of silica glassses," J. Am. Ceram. Soc., Vol. 76, pp. 712-716 (1993). J. Kushibiki, M. Arakawa, Y. Ohashi, K. Suzuki, and T. Maruyama, "A promising evaluation method of ultra-low-expansion glasses for the extreme ultra-violet lithography system by the line-focus-beam ultrasonic material characterization system, "Jpn. J. Appl. Phys., Vol. 43, pp. L1455-L1457 (2004). J. Kushibiki, M. Arakawa, Y. Ohashi, K. Suzuki, and T. Maruyama, "A super-precise CTE evaluation method for ultra-low-expansion glasses using the LFB ultrasonic material characterization system," Jpn. J. Appl Phys., Vol. 44, pp. 4374-4380 (2005). KE Hrdina, BZ Hanson, PM Fenn, and R. Sabia, "Characterization and characteristics of a ULE® glass tailored for the EUVL needs," in Proc. SPIE, Emerging Lithographic Technologies VI, Vol. 4688, 2002, pp 454-461. J. Kushibiki and M. Arakawa, "A method for calibrating the line-focus-beam acoustic microscopy system," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 45, pp. 421-430 (1998) . J. Kushibiki, M. Arakawa, and R. Okabe, "High-accuracy standard specimens for the line-focus-beam ultrasonic material characterization system," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 49, pp. 827-835 (2002). JE Shelby, Introduction to glass science and technology (The Royal Society of Chemistry, Cambridge, 1997) pp. 78-90. RB Greegor, FW Lytle, DR Sandstrom, J. Wong, and P. Schultz, "Investigation of TiO2-SiO2 glasses by X-ray absorption spectroscopy," J. Non-Cryst. Solids, Vol. 55, pp. 27-43 (1983).

When evaluating TiO ₂ —SiO ₂ glass with an ultrasonic material property analyzer, it is necessary to obtain an accurate relationship between the LSAW speed and the chemical composition ratio or CTE. However, since striae exist in this glass, the measurement value varies greatly depending on which region is measured, and therefore there is a possibility that an accurate relationship between them cannot be obtained.
Therefore, in the present invention, an accurate relationship between the LSAW speed and the TiO ₂ concentration or CTE is obtained by preparing an appropriate sample, selecting the LSAW propagation direction, and analyzing the exact chemical composition ratio. Give way.

The method for determining the relationship between the LSAW rate and the chemical composition ratio and CTE according to the present invention is as follows:
(a) cutting a sample substrate and a CTE measurement sample plate adjacent to each other at a surface perpendicular to the striae of the glass ingot from each of at least two glass ingots having different chemical composition ratios;
(b) obtaining a measured value of the LSAW velocity that propagates in a direction parallel to the striae plane for a predetermined region of each sample substrate;
(c) measuring a chemical composition ratio of the predetermined region of each sample substrate;
(d) measuring the CTE of each of the above CTE measurement sample plates;
(e) determining the relationship between the measured LSAW rate and the chemical composition ratio and the change amount of the chemical composition ratio and the change amount of the CTE from the CTE to the change amount of the LSAW rate;
Including.

The method for determining the relationship between the LSAW rate and the chemical composition ratio and CTE according to the present invention is as follows:
The step (c) includes a step of measuring the chemical composition ratio of one of the sample substrate and the CTE measurement sample plate by X-ray Fluorescence (XRF) method, and high-frequency induction from a part of the glass ingot. The chemical composition of the chemical composition ratio measured by the ICP-OES method and the step of measuring the chemical composition ratio by Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES) Determining the ratio.

The method for determining the relationship between the LSAW rate and the chemical composition ratio and CTE according to the present invention is as follows:
As one of the at least two glass ingots, quartz glass having 100% SiO ₂ is used.
Further, in the above method, data known as the CTE of the quartz glass may be used.

As described above, according to the present invention, an accurate relationship between the LSAW speed and the chemical composition ratio or CTE can be obtained for the TiO ₂ —SiO ₂ glass, and the LSAW speed was used. High-precision evaluation can be performed.

Also in this invention, as described above, for example, the amount of physical change such as the amount of change in LSAW speed and the amount of change in CTE is linearly related to the amount of change in the chemical composition ratio (for example, TiO ₂ concentration) of TiO ₂ -SiO ₂ glass. To determine the relationship between the chemical composition ratio and the physical quantity. For this purpose, the chemical composition ratio and LSAW velocity of a plurality of sample substrates cut out from a plurality of glass ingots having different chemical composition ratios are measured, and the relationship between the chemical composition ratio and the LSAW velocity is measured by, for example, the least square method. Determine the straight line expression for. Further, by measuring the CTE of the CTE measurement substrate cut out from each glass ingot, the relationship among the chemical composition ratio, the LSAW speed, and the CTE can be determined in the same manner.
In the present invention, an average LSAW with little influence of striae is measured by cutting a sample substrate along a plane perpendicular to the striae surface of the glass ingot and measuring the LSAW velocity propagating parallel to the striae surface. The simplest method is to determine the straight lines representing the relationship between the chemical composition ratio, LSAW speed, and CTE without using the least squares method by performing the above measurements on two sample substrates with different chemical composition ratios. May be. Further, as one of the two sample substrates, for example, glass having a TiO ₂ concentration of 0%, that is, SiO ₂ of 100% (that is, quartz glass) may be used. In that case, a known value may be used as the CTE of SiO ₂ glass. In the following examples, a case where quartz glass is used as one of the sample substrates will be described.

A TiO ₂ —SiO ₂ glass ingot generally has a TiO ₂ concentration distribution depending on the striae 7, that is, the manufacturing process conditions, and its period is about 0.16 mm [Non-patent Document 10]. A TiO ₂ —SiO ₂ glass substrate is obtained by cutting out from a glass ingot 6 having striae as shown in FIG. 3A. As a substrate sample, as shown in FIG. 3C, a sample obtained by cutting parallel to the z-axis and having a substrate surface perpendicular to the striatal surface is prepared.

  When performing measurements on the above substrates using the LFB ultrasonic material property analyzer, it is possible to measure the average characteristics in the measurement area by measuring the LSAW propagation direction parallel to the striae. is there. In order to accurately compare the LSAW speed with the value obtained by chemical analysis when there is non-uniformity of characteristics in the substrate surface, the LSAW speed must be measured in the same area as the chemical analysis area. Don't be.

Next, the chemical composition ratio is measured for the same substrate. As a method for performing chemical analysis, for example, there is an XRF analysis method. This method can analyze an average chemical composition ratio for a certain area of the sample surface (for example, 25 ^mmφ ). However, in order to accurately determine the absolute value of the analytical concentration by this method, a standard sample calibrated by another analytical method must be used. One method is to create a calibration curve using a standard sample with a known concentration, perform analysis using ICP-OES, obtain the relationship with the analysis value by the XRF method, and obtain the analysis value by the XRF method. Just calibrate.
CTE measurement generally requires a specially shaped sample (for example, 6 mm ^φ x 100 mm long), so from the vicinity of the area of the ingot where the substrate for LSAW velocity measurement was cut, A sample for CTE measurement is cut out and measured with a linear dilatometer.

  By comparing the LSAW speed obtained above with the chemical composition ratio and CTE, average characteristics in the same ingot can be obtained, so an accurate calibration curve is required.

Samples were extracted from a plurality of commercially available TiO ₂ —SiO ₂ glass (C-7972, Corning) ingots (1500 mm ^φ × 150 mm ^t ). In this glass, striae having a period of about 0.16 mm are formed in the manufacturing process [Non-Patent Document 10], and the direction is perpendicular to the z-axis direction as shown in FIG. 3A. In order to obtain an accurate relationship between the LSAW speed and the TiO ₂ concentration, a substrate whose sample surface was perpendicular to the striatal surface was cut out as shown in FIG. 3C. 7 sample substrates from 4 different ingots (A, B, C, D) (1 from ingot A (A1), 2 from ingot B (B1, B2), 1 from ingot C (C1), Three pieces (D1, D2, D3) from Ingot D were prepared. All the sample substrates have a size of 50 mm × 50 mm × 4.8 mm ^t and are subjected to double-sided parallel optical polishing.

Measurement was performed at 169 points every 2 mm in a 24 mm × 24 mm two-dimensional area near the center of each sample substrate. This region corresponds to a chemical composition ratio measurement region by XRF analysis described later. LSAW propagates in the y direction (FIG. 3C) on the vertical sample surface. As an example, the measurement results for sample A1 are shown in FIG. The average value of LSAW speed was 3308.29 m / s, and the maximum speed difference in the region was 1.23 m / s. The measurement results for all the samples are shown in FIG. In addition, the measured value was subjected to absolute calibration using a TiO ₂ —SiO ₂ glass standard sample obtained in the literature ([Non-Patent Document 6]) ([Non-Patent Document 11], [Non-Patent Document 12]). The maximum difference in the average value of the LSAW velocities among the seven samples was 4.07 m / s, and the maximum velocity distribution in the same sample plane was 1.87 m / s at maximum.

Next, the chemical composition of seven samples was analyzed using a fluorescent X-ray analyzer. Due to the limitation of the measurement jig, the sample was formed into a disk having a diameter of 50 mm, and the measurement was performed on a 25 mm diameter region near the center of each sample. As a result, the main components were SiO ₂ and TiO ₂ , and a small amount of V ₂ O ₅ (0.019 wt% to 0.024 wt%) and P ₂ O ₅ (0.0012 wt% to 0.0020 wt%) were detected. The change of LSAW rate when P ₂ O ₅ is added to SiO ₂ glass is −14.0 (m / s) / wt% ([Non-patent Document 7]), and LSAW for 0.002 wt% of P ₂ O ₅ The impact on speed is very small at -0.03 m / s. Although V ₂ O ₅ is one order of magnitude higher than P ₂ O ₅ , it is two orders of magnitude smaller than the TiO ₂ concentration, and the influence of these elements is negligible. As a result of repeating 20 measurements on one sample, the reproducibility of the TiO ₂ concentration was within 0.02 wt%. The result is shown as C (XRF) in FIG.

In order to obtain the absolute value of the analysis value by the XRF analysis method, it is necessary to calibrate using a standard sample. Therefore, for each sample, the TiO ₂ concentration was analyzed by ICP-OES using the remaining part of the molded sample. About 100 mg of sample was dissolved with acid (hydrofluoric acid, nitric acid, sulfuric acid) to prepare a sample solution. In the process of preparing the solution, Si was vaporized as SiF, and the solution was diluted to exactly 100 ml with distilled water. By adding yttrium (1 mg) as an internal standard sample, the effect of system sensitivity drift due to plasma intensity fluctuations was corrected. Several standard solutions with known Ti concentrations were prepared, and a calibration curve was prepared to sufficiently cover the TiO ₂ concentration obtained by XRF. The measurement results are also shown in FIG. 5 as C (ICP). Two sample solutions were prepared from the same sample and measured, and the difference between them was a maximum of 0.02 wt%. The TiO ₂ concentration by ICP-OES was 0.23-0.38 wt% higher than that by XRF analysis.

FIG. 6 shows the relationship between the XRF analysis method and ICP-OES TiO ₂ concentration and LSAW velocity. As the TiO ₂ concentration increased, the LSAW velocity V _LSAW decreased. The measurement reproducibility of the LSAW velocity at 225 MHz is ± 0.14 m / s (± 2σ, σ: standard deviation) [Non-Patent Document 6], and the variation in the measured value is mainly due to the low measurement accuracy of the TiO ₂ concentration. It is considered a thing. As a result of performing linear approximation by the least square method, the slope of the data analyzed by the XRF method is -17.04 (m / s) / wt% and σ is 0.010 wt%, and the data analyzed by ICP-OES On the other hand, the slope was -12.15 (m / s) / wt% and σ was 0.043 wt%. The s in ICP-OES was more than 4 times larger than that obtained by XRF analysis. The difference between the two slopes is thought to be due to the large variation in TiO ₂ concentration obtained by ICP-OES. From this result, it is considered that the analysis value by the XRF analysis method has higher relative accuracy than the value by the ICP-OES. However, the absolute value is analyzed using a calibration curve with a known Ti concentration, so the ICP-OES value is more accurate. Therefore, C (XRF) is calibrated using C (ICP). By approximating to a linear equation assuming passing through the origin, the relationship C (ICP) = 1.047 × C (XRF) was obtained. Therefore, the TiO ₂ concentration C _CAL (XRF) calibrated as shown in FIG. 5 can be obtained by multiplying the TiO ₂ concentration obtained by the XRF analysis method by 1.047.

Regarding the relationship between the calibrated TiO ₂ concentration and the LSAW velocity, the slope was −16.27 (m / s) / wt%, and σ was 0.010 wt%. The LSAW speed of a standard sample of synthetic quartz glass (C-7980, manufactured by Corning) with 100% SiO ₂ is 3426.18 m / s [Non-patent Document 12]. The relationship between the LSAW speed and the calibrated TiO ₂ concentration when C-7980 data is added to seven C-7972 samples is shown in FIG. 7A. In addition, FIG. 7B shows an enlarged view of data only when the LSAW speed is around 3310 m / s. The linear approximation gives a more accurate slope of -16.65 (m / s) / wt%, where σ is 0.009 wt%, between V _LSAW [m / s] and C _CAL (XRF) [wt%]. Then, the following relational expression is obtained.

V _LSAW = -16.65 × C _CAL (XRF) + 3426.18 (4)

TiO ₂ concentration C (V _LSAW ) [wt%] is obtained from V _LSAW [m / s] from the following equation (5) obtained by _modifying equation (4).

C (V _LSAW ) =-0.06006 × (V _LSAW -3426.18) (5)

From equation (5), the sensitivity of the LSAW rate to the TiO ₂ concentration was determined to be -0.06006 wt% / (m / s). The maximum difference of 4.07 m / s in the average value of LSAW velocities among the seven samples corresponds to the difference in TiO ₂ concentration of 0.244 wt%. The TiO ₂ concentration of the TiO ₂ —SiO ₂ ultra-low expansion glass standard sample [Non-Patent Document 6] having an LSAW speed of 3308.18 m / s is determined to be 7.09 wt%. Si in the SiO ₂ glass is tetracoordinated [Non-patent Document 13]. On the other hand, in the TiO ₂ —SiO ₂ glass, in the range of 0.05-9 wt% of TiO ₂ , Ti that is four-coordinated is dominant like Si in SiO ₂ [Non-patent Document 14]. For this reason, it is considered that the relationship between the LSAW speed and the TiO ₂ concentration is proportional to at least about 9 wt%, including around 7 wt%, which is important for EUVL.

Here, in order to estimate the effect of the method for obtaining an accurate relationship between the LSAW rate and the chemical composition ratio according to the present invention, the uncertainty of the slope of equation (5) is estimated. The cause of the uncertainty of the slope of equation (5) is the influence of the LSAW speed and the chemical composition ratio. Here, the influence of fluctuations in the sample surface of the LSAW speed is considered. From Fig. 5, the maximum difference in LSAW velocity within the same sample surface is 0.70 to 1.87 m / s, and the average value for seven samples is 1.13 m / s (± 0.57 m / s for ± 3σ). is there. By using seven samples, the uncertainty of the LSAW velocity value is reduced, and ± 0.14 m / s at ± 2σ. From FIG. 5, the average value of the TiO ₂ concentration of the seven samples is 7.04 wt%, and the LSAW speed is 3308.95 m / s from equation (4). The slope of formula (5) is 7.04 / (3308.95 ± 0.14 -3426.18) =-(0.06006 ± 0.00008) [wt% / (m / s)], and ± 0.00008 wt% / (m / s) at ± 2σ It will include uncertainty. From [Non-Patent Document 9], the variation of the LSAW speed in the substrate surface when using a standard sample with the striae surface parallel to the substrate surface as shown in FIG. 3B is 2.39 m / s. If the fluctuation is the maximum LSAW speed change due to striae, the LSAW speed fluctuation is ± 1.19 m / s for ± 3σ. At this time, the uncertainty of the LSAW speed is ± 0.80 m / s with respect to ± 2σ, and the uncertainty of the slope of equation (5) is ± 0.0004 wt% / (m / s) with ± 2σ. Therefore, it can be seen that when determining the relationship between the LSAW velocity and the chemical composition ratio, it is possible to accurately determine the relationship by selecting an appropriate substrate surface and the LSAW velocity propagation direction. If a TiO ₂ -SiO ₂ glass with a sufficiently small variation in characteristics in the sample and its surface (ie, without striae) can be produced and used for the sample, the LSAW velocity of the sample surface above can be reduced. The influence of the fluctuation is eliminated, and the error of the LSAW speed is considered to be only ± 0.14 m / s (± 2σ) [Non-Patent Document 6] which is the reproducibility of the measurement. At this time, the uncertainty of the slope of equation (5) is estimated to be ± 0.00008 wt% / (m / s) (± 2σ).

Next, the relationship between LSAW speed and CTE is obtained. The CTE of synthetic quartz glass is assumed to be 520 ppb / K which is a catalog value, and that of C-7972 is assumed that the average value of 7 samples is 0 ppb / K. At this time, the following relational expression is obtained between CTE (V _LSAW ) [ppb / K] and V _LSAW [m / s] by linear approximation.

CTE (V _LSAW ) = 4.436 × (V _LSAW -3308.95) (6)

From the equation (6), the sensitivity of the LSAW speed to CTE was determined to be 4.436 (ppb / K) / (m / s). The relationship between V _LSAW and CTE in Equation (6) is also shown by performing scale conversion in FIG. 7 (CTE is shown on the right axis). In order to obtain a more accurate relationship between CTE and LSAW speed, CTE absolute measurement may be performed on a CTE measurement sample plate.

The reproducibility of the LSAW rate at f = 225 MHz is ± 0.14 (m / s) (± 2σ) [Non-Patent Document 6]. By applying this value to the TiO ₂ concentration and CTE sensitivity of the LSAW rate, the LSAW rate The resolution for TiO ₂ concentration and CTE is determined to be ± 0.0084 wt% and ± 0.62 ppb / K (± 2σ), respectively. From this, the TiO ₂ concentration and CTE can be obtained with higher accuracy than the conventional method by substituting the LSAW velocity measurement value into the equations (5) and (6).

Based on the embodiment described above, a basic process for obtaining an accurate relationship between the LSAW speed and the chemical composition ratio or CTE for evaluating the TiO ₂ —SiO ₂ glass according to the present invention. The procedure will be described below with reference to the flowchart shown in FIG.
Step S1: From a TiO ₂ —SiO ₂ glass ingot, a sample substrate whose substrate surface is perpendicular to the striatal surface and a CTE measurement sample plate adjacent thereto are cut out.
Step S2: The LSAW velocity is measured with respect to the sample substrate prepared in step S1, with the same region as the region where the chemical composition ratio is measured in step S3, with the LSAW propagation direction parallel to the striae.
Step S3: The chemical composition ratio is measured in the same region as in Step S2 for the sample substrate prepared in Step S1. Moreover, CTE is measured with respect to the sample substrate for CTE measurement.
Step S4: The relationship between them is obtained from the LSAW speed obtained in Step S2 and the chemical composition ratio and CTE obtained in Step S3.
When the TiO ₂ —SiO ₂ glass is uniformly manufactured and there is no striae in the ingot, the sample is arbitrarily cut out in step S1, and the LSAW propagating in an arbitrary direction may be measured in step S2.

The accurate relationship between the LSAW rate obtained by using the present invention and the TiO ₂ concentration and CTE enables the TiO ₂ concentration and CTE to be determined from the LSAW rate measurement value with higher accuracy than the conventional method. It is useful to use LFB ultrasonic material characterization equipment as ultra-high precision CTE measuring equipment to develop EUVL grade glass, glass manufacturing process and product quality control.

The figure explaining the formation principle of a V (z) curve. It is a figure showing the V (z) curve and its analysis result for the C-7972 sample, A is the V (z) curve measured at f = 225 MHz, B is the wave number spectrum obtained by the V (z) curve analysis method. FIG. It is a figure explaining the preparation method of a TiO ₂ -SiO ₂ glass sample, A is a figure showing an overview of the ingot, B is a figure showing a sample surface cut out from the ingot is parallel to the striatal plane, C is The figure which shows the sample with the sample surface cut out from the ingot perpendicular | vertical with respect to the striae surface. For C-7972 sample (A1), f = 225 MHz, the LSAW propagation direction is the y direction, and a 24 mm x 24 mm region is measured every 2 mm in the y and z directions. FIG. It shows the LSAW velocity and TiO ₂ concentration on C-7972 sample. Is a diagram showing the relationship between the TiO ₂ concentration and LSAW velocity for C-7972 sample, A is a diagram showing the relationship between the TiO ₂ concentration and LSAW speed obtained by XRF analysis, B is ICP emission spectrometry It is a figure which shows the relationship between the TiO2 density | concentration calculated | required by ( ₃₎ and the LSAW speed | rate. FIG. 7 shows the relationship between LSAW velocity and TiO ₂ concentration and CTE for the C-7972 sample, A shows data at LSAW velocity from 3300 m / s to 3440 m / s, and B shows 3305 m It is a figure which shows the data of only the LSAW speed of / s-3315 m / s. FIG. 3 is a block diagram of a method for obtaining an accurate method between LSAW velocity and chemical composition ratio for a striae material.

Explanation of symbols

1: ultrasonic transducer, 2: LFB acoustic lens, 3: glass sample, 4: water coupler, 5: focal plane, 6: glass ingot, 7: striae, 8: glass substrate

Claims (6)

Leakage surface acoustic wave velocity, hereinafter referred to as LSAW velocity, and the chemical composition ratio and coefficient of linear expansion, hereinafter referred to as CTE, is a method for determining the relationship between,
(a) cutting a sample substrate and a CTE measurement sample plate adjacent to each other at a surface perpendicular to the striae of the glass ingot from each of at least two glass ingots having different chemical composition ratios;
(b) obtaining a measured value of the LSAW velocity that propagates in a direction parallel to the striae plane for a predetermined region of each sample substrate;
(c) measuring a chemical composition ratio of the predetermined region of each sample substrate;
(d) measuring the CTE of each of the above CTE measurement sample plates;
(e) determining the relationship between the measured LSAW rate and the chemical composition ratio and the change amount of the chemical composition ratio and the change amount of the CTE from the CTE to the change amount of the LSAW rate;
A method for determining a relationship between an LSAW rate, a chemical composition ratio, and a CTE characterized by comprising: 2. The method according to claim 1, wherein said step (c) comprises measuring a chemical composition ratio of one of said sample substrate and said CTE measurement sample plate by fluorescent X-ray analysis, hereinafter referred to as XRF method, and said glass A step of measuring the chemical composition ratio from a part of an ingot using a high frequency inductively coupled plasma-emission analysis method, hereinafter referred to as ICP-OES method, and absolute calibration of the measurement result by the XRF method with the measurement result by the ICP-OES method A method for determining the relationship between the LSAW speed, the chemical composition ratio, and the CTE . 2. The method according to claim 1, wherein quartz glass with 100% SiO ₂ is used as one of the at least two glass ingots, the relationship between the LSAW rate and the chemical composition ratio and CTE. How to ask.   4. The method according to claim 3, wherein the known data is used as CTE of the quartz glass, and the relationship between the LSAW speed, the chemical composition ratio, and the CTE is obtained. TiO ₂ -SiO ₂ is a method for measuring the TiO ₂ concentration of ultra-low expansion glass,
(a) measuring the LSAW speed;
(b) Using the LSAW velocity V _LSAW [m / s] obtained in the above step (a), the following equation expressing the relationship between the LSAW velocity obtained by the method of claim 1 and the chemical composition ratio :
C (V _LSAW ) = 0.06006 × (V _LSAW -3426.18)
Obtaining TiO ₂ concentration C (V _LSAW ) [wt%] from
TiO ₂ concentration measuring method characterized by including. TiO ₂ -SiO ₂ is a method for measuring the linear expansion coefficient of ultra-low expansion glass,
(a) measuring the LSAW speed;
(b) Using the LSAW velocity V _LSAW [m / s] obtained in step (a) above, the following equation representing the relationship between the LSAW velocity and CTE determined by the method of claim 1
CTE (V _LSAW ) = 4.436 × (V _LSAW -3308.95)
_{Obtaining the} linear expansion coefficient CTE (V _LSAW ) [wt%] from
And a linear expansion coefficient measuring method.

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