Characteristics of superconducting tungsten silicide ${\mathrm{W}}_x\mathrm{S}{\mathrm{i}}_{1-x}$ for single photon detection

Superconducting properties of three series of amorphous ${\mathrm{W}}_x\mathrm{S}{\mathrm{i}}_{1-x}$ films with different thickness and stoichiometry were investigated by dc transport measurements in a magnetic field up to 9 T. These amorphous ${\mathrm{W}}_x\mathrm{S}{\mathrm{i}}_{1-x}$ films were deposited by magnetron cosputtering of the elemental source targets onto silicon substrates at room temperature and patterned in the form of bridges by optical lithography and reactive ion etching. Analysis of the data on magnetoconductivity allowed us to extract the critical temperatures, superconducting coherence lengths, magnetic penetration depths, and diffusion constants of electrons in the normal state as functions 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 hotspot was analyzed in the framework of a diffusion-based vortex-entry model. We used a two-stage diffusion approach and defined a hotspot size by assuming that the quasiparticles and normal-state electrons have the same diffusion constant. With this definition and these measured material parameters, the hotspot in the 5-nm-thick ${\mathrm{W}}_{0.85}\mathrm{S}{\mathrm{i}}_{0.15}$ film had a diameter of 107 nm at the peak of the number of nonequilibrium quasiparticles.

Figure 1

SEM images of the specimens. (a) The microstrip used for transport measurement. The calculations in this paper are based on the measured strip geometries. (b) The bowtie structure used for the ${\tau }_R$ measurement. The inset shows the enlarged sensitive area and the WSi microbridge located between the two gold pads.

Figure 2

(a) Square resistance for the 100-nm-thick and 100-$\mu \mathrm{m}$-wide ${\mathrm{W}}_{0.8}\mathrm{S}{\mathrm{i}}_{0.2}$ strip as a function of temperature. The superconducting transition is fitted with Eq. (1). (b) Temperature dependence of the square resistance from the 5-nm-thick and 100-$\mu \mathrm{m}$-wide ${\mathrm{W}}_{0.8}\mathrm{S}{\mathrm{i}}_{0.2}$ strip. The superconducting transition is fitted with Eq. (2). (c) The mean-field critical temperatures as functions of the film thickness.

Figure 3

The critical magnetic field at different temperatures for a series of 100-$\mu \mathrm{m}$-wide ${\mathrm{W}}_{0.8}\mathrm{S}{\mathrm{i}}_{0.2}$ strips. Through linear fitting of these temperature dependences we extracted the zero-temperature critical magnetic field $B_{c2}\left(0\right)$.

Figure 4

The GL coherence length at zero temperature $\xi \left(0\right)$ as a function of film thickness.

Figure 5

Thickness dependence of the diffusion constant of the electrons in the normal-conducting state.

Figure 6

The magnetic penetration depth $\lambda \left(0\right)$ as a function of film thickness.

Figure 7

(a) The excess magnetoconductivity $\delta \sigma \left(H,T\right)/(2{\pi }^2\hslash /e^2)$ vs applied magnetic field at temperatures $T=20\mathrm{K}$ (black), 15 K (green), 14 K (blue), 13 K (cyan), 12 K (magenta), 11 K (yellow), 10 K (dark yellow), 9 K (navy), 8 K (purple), 7 K (wine), 6 K (olive), 5 K (dark cyan), 4.8 K (royal), 4.5 K (orange). The black arrow indicates the decreasing temperature. The red curves are fits using the Eqs. (7), (8), and (9). Inset: magnification of the detailed MC data in the high-temperature and high-magnetic-field range. (b) The characteristic magnetic field extracted from the fitting procedure as a function of temperature.

Figure 8

The inelastic scattering time calculated from the characteristic field $H_i$ for 5-nm-thick films. Inset: The inelastic scattering rate $1/{\tau }_{qp}$ temperature for ${\mathrm{W}}_{0.75}\mathrm{S}{\mathrm{i}}_{0.25}$ (black), ${\mathrm{W}}_{0.8}\mathrm{S}{\mathrm{i}}_{0.2}$ (red), and ${\mathrm{W}}_{0.85}\mathrm{S}{\mathrm{i}}_{0.15}$ (blue) stoichiometries. The solid curve shows the best fit according to $1/{\tau }_{qp}=1/{\tau }_{e-e}+1/{\tau }_{e-ph}+1/{\tau }_{e-fl}$.

Figure 9

(a) The I-V curve of the ${\mathrm{W}}_{0.85}\mathrm{S}{\mathrm{i}}_{0.15}$ microbridge measured at $T=3.2\mathrm{K}$. The critical current for the device is around $119\mu \mathrm{A}$ and the series resistance of the bias circuit is $14 \mathrm{\Omega }$. The filled dot shows the regime where the voltage response was measured. (b) The voltage response vs time. The rising and the falling edges of $V_{out}\left(t\right)$ were fitted separately to exponential functions with time constants ${\tau }_{\mathrm{rising}}$ and ${\tau }_{\mathrm{falling}}$, respectively.