Time evolution of nonequilibrium quasiparticle and phonon distributions in superconducting films

Superconducting tunneling junctions are promising candidates for low energy X-ray detectors. To fully exploit the possibilities of the high energy resolution it is necessary to understand the microscopic processes and to get a clear insight into the importance of the different loss mechanisms. The linearized coupled kinetic equations for the nonequilibrium quasiparticle f(ω, t) and phonon n(Ω, t) distributions were solved by Chang and Scalapino for the stationary case. The time evolution of the full set of equations was investigated later by Zehnder. In this work we report results of calculations for the time dependence of f(ω, t) and n(Ω, t) which were obtained in a more general approach. In particular, the volume expansion of the initial distribution created by the absorption process was considered by making the distribution functions space dependent and adding a diffusion term to the equations. Results for Nb are discussed in detail.