Superconducting properties of three series of amorphous WxSi1-x films with different thickness and stoichiometry were investigated by dc transport measurements in a magnetic field up to 9 T. These amorphous WxSi1-x films were deposited by magnetron co-sputtering of the elemental source targets onto silicon substrates at room temperature and patterned in form of bridges by optical lithography and reactive ion etching. Analysis of the data on magnetoconductivity allowed us to extract the critical temperature, superconducting coherence length, magnetic penetration depth, and diffusion coefficient of electrons in the normal state as a function of film thickness for each stoichiometry. Two basic time constants were derived from transport and time-resolving measurements. A dynamic process of the formation of a hot-spot was analyzed in the framework of a diffusion-based vortex-entry model. We used the two stage diffusion approach and defined a hotspot size by assuming that the quasi-particles and normal-state electrons have the equal diffusion constant. Our findings are consistent with the most recent results on a hot-spot relaxation time in the WxSi1-x superconducting nanowire single-photon detector. In the 5 nm thick W0.85Si0.15 film the hot-spot has a diameter of 105 nm at the peak of the number of non-equilibrium quasi-particles.
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