Power-law scaling of proton conductivity in amorphous silicate thin films

Amorphous hafnium silicate, a-Hf_0.1Si_0.9O _x, thin film with thickness of 32, 41, 55, 80, 110, 120, 180 and 320 nm was prepared by multiple spin-cast process and the proton conductivity across the films was measured at intermediate temperatures (100-400 °C) in dry atmosphere. The morphologically- and compositionally-uniform films were prepared on a substrate as confirmed by SEM, RBS and XPS measurements. a-Hf _0.1Si_0.9O_x thin film clearly revealed the H/D isotope effect on ionic conductivity, indicating that protonic conduction is dominant in the measured temperature range. The films did not reveal thickness-dependent proton conductivity in dry air and the σ at given temperatures is almost constant at any thickness. No increment of σ in a-Hf_0.1Si_0.9O_x thin films by reduction of thickness might be related to the absence of the highly-conductive acid network with mesoscopically-sized length because of the relatively low concentration of Brønsted acid sites inside films.