Transport characterization of calcium-doped ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films

We report systematic studies of the normal-state conductivity and thermopower of epitaxial ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ca}}_{\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films with 0≤x≤0.3 as a function of oxygen content. The superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ is found to be parabolic in conductivity σ for each sample, with a universal scaling behavior for all films with x≤0.2. The room-temperature thermopower, ${\mathit{S}}_{295\mathrm{K}}$, follows the universal correlation between ${\mathit{T}}_{\mathit{c}}$ and ${\mathit{S}}_{295\mathrm{K}}$ reported by S. D. Obertelli et al. [Phys. Rev. B 46, 14 928 (1992)] for all films studied, despite the reduction in maximum ${\mathit{T}}_{\mathit{c}}$ with increasing calcium content. The thermopower is found to be superior to the conductivity as a measure of the hole concentration because of its reduced sensitivity to extrinsic contributions such as grain boundaries. By assuming that all the charge from oxygen deficiencies and Ca substitution is transferred to the Cu-O planes, and by using Obertelli’s empirically-derived expression for hole concentration, we show that ${\mathit{S}}_{295\mathrm{K}}$ can be used to determine the oxygen content of the films. The equilibrium oxygen content is found to be reduced to compensate for the additional carriers introduced by Ca substitution in these films, just as has been previously observed in bulk ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ca}}_{\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$.