  We developed an electro thermal model of NbN superconducting nanowire
avalanche photodetectors (SNAPs) on sapphire substrates. SNAPs are single
photon detectors consisting of the parallel connection of N superconducting
nanowires. We extrapolated the physical constants of the model from
experimental data and we simulated the time evolution of the device resistance,
temperature and current by solving two coupled electrical and thermal
differential equations describing the nanowires. The predictions of the model
were in good quantitative agreement with the experimental results.
