D.C. sputtering process: its characterization and its problems when applied to tin-dioxide thin-films: Anant G. Sabnis. Electrocomp. Sci. Technol.7, 19 (1980)

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The depression of the order parameter at grain boundaries in high critical temperature superconducting oxides is determined using two formulations. First, we use the Bardeen-Cooper-Schrieffer formulation and assume formation of Cooper pairs by an attractive interaction potential. The spatial variation of the density of energy states at the Fermi level near the boundary, estimated as a function of hydrostatic stress field, is used to determine the depression of the order parameter. Second, the proximity-effect formulation is used in the form of a boundary condition on the order parameter at the interface. The boundary conditions are solved taking into account the spatial variation of the density of energy states. The depression of the order parameter from the two formulations is used in conjunction with atomic modeling to determine the critical current density associated with the grain boundaries. The model correctly predicts dependence of the critical current density across grain boundaries on the misorientation angle and temperature, in good agreement with experimental observations.