Temperature behavior of sound velocity of fluorine-doped vitreous silica thin films studied by picosecond ultrasonics

Abstract

Vitreous silica (v-SiO 2 ) shows anomalous temperature dependence of velocity, including positive temperature coefficient of velocity (TCV) and velocity minimum around 70 K. The former characteristic allows its application in acoustic-resonator devices as a temperature compensating material. In this paper, we study the temperature dependence of velocity of fluorine-doped v-SiO 2 (v-SiO 2-x F x ) thin films using picosecond ultrasonic spectroscopy. To correct the temperature increase caused by irradiation with light pulses, we calculated the steady temperature increase in the measuring volume with a finite volume method, considering the temperature dependence of thermal conductivity, and find that temperature in the measurement region remains high even when the back surface is cryogenically cooled. Using the corrected temperature, we determine TCV of v-SiO 2-x F x thin films for 0 < x < 0:264, which increases as x increases and is smaller than reported bulk values by a factor of 0:5 À 0:7. The velocity minimum is absent for the film with x ¼ 0, but it is clearly observed at 70 K for the film with the highest fluorine concentration of x ¼ 0.264. These temperature behaviors are attributed to the change in the Si-O-Si bond angle caused by the fluorine doping. V

Temperature dependence of hypersound attenuation in silica films via picosecond acoustics

“…Reduced T -coefficients for v(T ) have also been reported recently in CVD SiO 2 -layers from picosecond acoustics. 62 Finally one notes that an enhanced TAR-defects density is found in the sputtered layer while, in contrast, the slope of the static v ∞ (T )-changes is almost reduced by half. This provides further evidence that both anomalies likely have different origins.…”

Elastic constant C11 of 12C diamond between 10 and 613 K

“…On the other hand, we obtain the isothermal sound velocity when 4Df =v 2 ) 1. 47 We calculated the temperature dependence of 4Df =v 2 using the reported temperature dependence of j 48 and C P , 40,49 whereas we considered f and v to be constant because their change ratios will not exceed 0.2% between 10 and 613 K. 4Df =v 2 monotonically decreases as temperature increases above 30 K, and it is larger than unity below 480 K. Even at 613 K, 4Df =v 2 ¼ 0:6, indicating that we measured isothermal sound velocity at low temperatures (at 300 K, 4Df =v 2 ¼ 4:3). Therefore, we evaluate the difference between the adiabatic elastic constant C A 11 and the isothermal elastic constant C I 11 .…”

Zero temperature coefficient of sound velocity in vitreous silicon oxynitride thin films

“…3. A pure v-SiO 2 film shows positive TCV, 26 but TCV of the v-SiO x N y film decreases as the nitrogen ratio N r increases. We determined TCV using data between 200 and 300 K, which are shown in Table I and Fig.…”

“…1(a), together with reference values. 17,[25][26][27] As the nitrogen ratio increases, the mass density increases because of reduction of the bond angles between polyhedrons (angles of O-Si-O, O-Si-N, and N-Si-N), leading to the decrease in the averaged atomic distance. This causes the significant increase in the elastic modulus.…”

“…Values of pure v-SiO 2 were obtained from our previous work. 26 measured the phonon frequency of the TO-x 4 mode. With the temperature increase, phonon frequencies of the x 3 and x 4 modes increase and decrease, respectively, as shown in Fig.…”