Electrical and dielectric properties of the ${\mathrm{Bi}}_4$${\mathrm{Sr}}_3$${\mathrm{Ca}}_3$${\mathrm{Cu}}_4$${\mathrm{O}}_{\mathit{x}}$ (4:3:3:4) glassy semiconductor

The first measurements, in the temperature range of 80–420 K, are reported for the dc and ac conductivities and dielectric constant of the ${\mathrm{Bi}}_4$ ${\mathrm{Sr}}_3$ ${\mathrm{Ca}}_3$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_{\mathit{x}}$ (4:3:3:4) oxide glass which, when properly annealed, becomes a superconductor with $T_c$∼80 K. The experimental electrical-conductivity data have been analyzed with reference to various theoretical models based on a polaron-hopping conduction mechanism. Hopping of the polaron seems to be adiabatic in nature. At low temperature the dc conductivity data for this glass qualitatively obey Mott’s $T^{\mathrm{-}1/4}$ law. The analysis shows that the correlated-barrier-hopping model is the most appropriate one for explaining the ac conductivity of the (4:3:3:4) glass. This model quantitatively predicts the temperature dependence of both the ac conductivity and its frequency exponent. The other models such as the quantum-mechanical tunneling model appear to be consistent with the behavior of low-temperature ac conductivity, but fail to interpret the observed temperature dependence of the frequency exponent. Similarly, the overlapping-large-polaron tunneling model qualitatively explains the temperature dependence of ac conductivity at low temperature, but fails in the high-temperature regime. This (4:3:3:4) glassy semiconductor is also found to show Debye-type dielectric dispersion characterized by a relaxation frequency.