A phenomenological model for the thickness dependence of the critical current density in high temperature superconducting epitaxial films

A phenomenological model is suggested to describe the thickness dependence of the critical current density in YBCO films by two processes, which occur in each elementary layer of the growing film. The first process is the formation of the high temperature superconductivity (HTS) phase. The second is an evolution of the dislocation nanostructure. Its dilution appears to be responsible for the decrease of critical current density with film thickening. The characteristic time of this process determined by slow volume diffusion is evaluated to be 50-100 s. The characteristic time of ex situ HTS phase formation has the same order, while the time of in situ formation is found to be about 10 s because of much faster surface diffusion. A slower critical current density (Jc) decrease with thickening of multilayers and films with nanoparticles can be interpreted as retardation of dislocation crawling due to their pinning on extra interfaces and nanoparticles. The dependences of the critical current density on the deposition rate are predicted using the model.