Evaluation method for coefficient of thermal expansion of ultra-low-expansion glass material

#This invention pertains to an evaluation method for a coefficient of thermal expansion of an ultra-low-expansion glass material using the propagation characteristics of leaky acoustic waves, in particular phase velocity, measured by means of an ultrasonic material characterization system.

#At present, the development of generation-after-next Extreme Ultraviolet Lithography (EUVL) is being conducted. As elemental technologies for EUVL systems, the five items of EUV light sources, aspherical optical systems, exposure apparatuses, multilayered photomasks, and photoresist processes can be cited, and the development of those technologies is being conducted in parallel. The most essential and important issue in this development of EUVL systems is to develop ultra-low-expansion glasses as the basic substrate material suitable for optical systems and photomasks. At the same time, measurement and evaluation technologies for accurately ascertaining and analyzing the materials characteristics are vital to the development of those materials.

#In EUVL systems, thermal stability in the sub-nanometer range is required for optical lens materials and photomask substrate materials. Specifically, ultra-low-expansion glasses having coefficients of thermal expansion (CTE) not exceeding ±5 ppb/K at the desired temperature (e.g. 22±3° C. in the photomask substrate) become necessary (Non-Patent Reference 1). Here, if the length of a solid at 0° C. is taken to be L0 and the length at a temperature T° C. is taken to be L, the coefficient of thermal expansion is given as (dL/dT)/L0. At present, two types of TiO2—SiO2 glass and Li2O—Al2O3—SiO2 crystallized glass can be cited as commercially available ultra-low-expansion glasses and are used conventionally as materials for lenses for large astronomical telescopes and semiconductor manufacturing apparatuses (steppers). The former glass realizes an ultra-low expansion coefficient by an adjustment of the ratio of SiO2 and TiO2, and the latter glass realizes it by an adjustment of the crystallization process (annealing temperature and time) in addition to that of the chemical composition ratio (Non-Patent Reference 1 and Non-Patent Reference 2). Even with the best grade among these glasses, the specification for the coefficient of thermal expansion stands at ±20 ppb/K (distribution in a glass ingot; ±10 ppb/K), which is insufficient for the specification for ultra-low-expansion glass for EUVL systems of within ±5 ppb/K at the desired temperature. Recently, manufacturing companies in Japan and other countries have started to carry out trial manufacture of EUVL-grade ultra-low-expansion glasses. For the development of those materials, a measurement accuracy of ±0.2 ppb/K (±σ, σ being the standard deviation) or less with respect to the coefficient of thermal expansion is required (Non-Patent Reference 1).

#FIG. 1 is a schematic diagram for explaining the principle of generation of a V(z) curve;

#FIG. 2 is a flowchart for the V(z) curve analysis method;

#FIG. 3A is a diagram showing an example of a V(z) curve;

#First, an explanation will be given of a method of preparing a standard specimen for absolute calibration of an LFB ultrasonic material characterization system for the case of performing a normal evaluation with respect to an isotropic material exhibiting a velocity dispersion characteristic (normal glass material with no striae). For a substrate used as a standard specimen, the frequency dependency of the acoustic velocities and the attenuation coefficients, of the bulk waves (longitudinal wave and shear wave), as well as the density, are measured by the method mentioned hereinafter.

#As a measurement method for the bulk-wave acoustic properties (acoustic velocity and attenuation coefficient), a complex-mode measurement method using a radio-frequency (RF) tone burst pulse 6 will be taken as an example and explained. The experimental configuration for the measurement of the bulk-wave acoustic velocities is shown in FIG. 6. An ultrasonic device with a buffer rod 7 (e.g. of synthetic silica glass), equipped on one end face with an ultrasonic transducer 1, is used. In the case of longitudinal velocity measurements, by using pure water as a coupler 8, adjusting the propagation length of the coupler so that a reflected signal V2 from the front face of glass specimen 3 and a reflected signal V3 from its back face do not overlap with a spurious signal in the time domain, and measuring the amplitude of V3/V2, |V3/V2|, and phase φ at each frequency (shown in FIG. 7), the specimen longitudinal velocity V1 and the longitudinal attenuation coefficient α1 are respectively obtained from Eqs. (4) and (5).

#V l ⁢ ⁢ • = - 2 ⁢ ω ⁢ ⁢ h ϕ - π - Δ ⁢ ⁢ θ ( 4 ) α l ⁢ ⁢ • = 1 2 ⁢ h ⁢ ln ⁢ { | V 2 V 3 | · | T 23 · T 32 R 23 | } - 1 2 ⁢ h ⁢ ln | ATT 2 ATT 3 | ( 5 ) where, ω is the angular frequency, h is the thickness of the specimen, π is the phase rotation in the case of reflection at the back face of the specimen, Δθ is the difference in phase advance due to diffraction of the signals V2 and V3, and |ATT3/ATT2| is the diffraction loss ratio. T23 and T32 are the respective transmission coefficients from the coupler to the specimen and from the specimen to the coupler, and R23 is the reflection coefficient of the specimen seen from the coupler. The influence of diffraction (Δθ and ATT3/ATT2) is corrected with a numerical calculation using the exact integral expression of Williams (Non-Patent Reference 10). Since silicate glass normally exhibits velocity dispersion in the VHF range, the influence of the velocity dispersion is taken into account in performing the diffraction correction (Non-Patent Reference 11). Moreover, in order to accurately obtain the frequency characteristics of the acoustic properties, the effective diameter of the ultrasonic transducer used in the measurement as a circular piston sound source is obtained, and the influence of the diffraction is corrected (Non-Patent Reference 12). The specimen thickness is measured e.g. by a contact-type digital length gauging system with an optical linear encoder built in (Patent Reference 1).