Analysis of the nonequilibrium photoresponse of superconducting films to pulsed radiation by use of a two-temperature model

Photoresponse of a superconducting film in the resistive state to pulsed radiation has been studied in the framework of a model assuming that two different effective temperatures can be assigned to the quasiparticle and phonon nonequilibrium distributions. The coupled electron-phonon-substrate system is described by a system of time-dependent energy-balance differential equations for effective temperatures. An analytical solution of the system is given and calculated voltage transients are compared with experimental photoresponse signals taking into account the radiation pulse shape and the time resolution of the readout electronics. It is supposed that a resistive state (vortices, fluxons, network of intergrain junctions, hot spots, phase slip centers) provides an ultrafast connection between electron temperature changes and changes of the film resistance and thus plays a minor role in the temporal evolution of the response. In accordance with experimental observations a two-component response was revealed from simulations. The slower component corresponds to a bolometric mechanism while the fast component is connected with the relaxation of the electron temperature. Calculated photoresponse transients are presented for different ratios of the electron and phonon specific heat, radiation pulse durations and fluences, and frequency band passes of registration electronics. From the amplitude of the bolometric component we determine the radiation energy absorbed in a film. This enables us to reveal an intrinsic electron-phonon scattering time even if it is much shorter than the time resolution of readout electronics. We analyze experimental voltage transients for NbN, ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, and ${\mathrm{TlBa}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_9$ superconducting films and find the electron-phonon interaction times at the transition temperatures of 17, 2.5, and 1.8 ps, respectively. The values are in reasonable agreement with data of other experiments.