Scalable nanofabrication of high-quality $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ nanowires for single-photon detectors

The realization of superconducting single-photon detectors operating above the liquid-helium temperature is currently the focus of intense research efforts. Here, we present the fabrication of ultraclean encapsulated nanowires from commercially available thin films of $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ by high-energy oxygen-ion irradiation. The structured nanowires, ranging from 0.1 to $5\text{μ}\mathrm{m}$ in width, exhibit sharp resistive transitions to the superconducting state above 85 K. The $I$-$V$ characteristics reveal that the evolution from the superconducting to the normal state shows a large voltage jump in the volt range. This demonstrates that the entire nanowire transits—a prerequisite for the development of a hot spot upon absorption of a single photon. Our results pave the way for the fabrication of $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$-based scalable superconducting single-photon-detection devices.

Figure 1

The simulation of the DPA generated by a ponctual source of $\mathrm{He}$${}^{+}$ and $\mathrm{O}$${}^{+}$ ions with an energy of 30 keV into a stack of $\mathrm{Ce}$$\mathrm{O}$${}_2$ (8 nm)/$\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ (30 nm)/$\mathrm{Ce}$$\mathrm{O}$${}_2$ (40 nm)/$\mathrm{Al}$${}_2$$\mathrm{O}$${}_3$ (${10}^5$ ions simulation). (a) The scheme of the irradiated sample, with the axes ($x$, $y$, and $z$), the different layers, and their thicknesses. Note that the scales are not respected. (b) The DPA averaged along the depth $x$ in the $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ layer at $y=0$ as a function of the lateral dimension $z$. (c) The DPA at $y=0$ and $z=0$ as a function of the depth $x$. The dose is adjusted such that the maximum DPA values in (a) are equal for the $\mathrm{He}$${}^{+}$ ions and the $\mathrm{O}$${}^{+}$ ions. The black dashed lines separate the different material layers.

Figure 2

The simulation of 30-keV $\mathrm{O}$${}^{+}$ irradiation in a sample of a 30-nm-thick $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ thin film, protected by a 100-nm-wide and 500-nm-thick ma-N2405 resist for an ion dose of $D=5\times {10}^{14}\mathrm{ions}{\mathrm{cm}}^{-2}$. The DPA are converted to $T_c$ using Eq. (1) for better understanding. (a) The scheme of the irradiated sample, where the axes ($x$, $y$, and $z$), the different layers, and their thicknesses are indicated. Note that the scales are not respected. (b) A heat-map plot of $T_c$ in the $x$-$z$ plane of the $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ layer. The white contour corresponds to $T_c=0K$. (c) The lateral variation of $T_c$ at different depths $x$. (d) Variation of the wire width for different depths and temperatures, taken from (b). (e) The evolution of the width of the wire as a function of the temperature. The color scales in (d) and (e) are the same as the color bar in (b).

Figure 3

(a)–(d) The fabrication work flow described in the text.

Figure 4

SEM pictures of different devices on 30-nm-thick $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ protected by a 8-nm-thick $\mathrm{Ce}$$\mathrm{O}$${}_2$ capping layer. The visible part is the resist layer, which protects against ionic irradiation. (a) The meander geometry of a long nanowire with dimensions $450\text{μ}\mathrm{m}\times 500$ nm. (b) A tilted view on one part of the meander shown in (a). (c) A nanowire with dimensions $150\mathrm{nm}\times 20\text{μ}\mathrm{m}$. (d) An enlargement of one part of the long wire shown in (c). (e) A short nanowire with dimensions $200\mathrm{nm}\times 500$ nm. (f) An enlargement of one part of the short wire shown in (e).

Figure 5

The temperature evolution of the resistivity of superconducting nanowires patterned on 30-nm-thick $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ film, in (a) linear and (b) logarithmic scales, respectively. (c) The evolution of the critical temperature at zero resistance ${\mathrm{T}}_{c0}$ with respect to the width for nanowires patterned on 30-nm-thick samples of different types.

Figure 6

(a) The evolution of the critical current $j_c$ at 10 K as a function of the nanowire width. (b)–(d) Depending on the $j_c$ value, the nanowires belong to two categories: if $j_c>j_{h0}$, the $I$-$V$ curve is hysteretic as represented in (b) while for $j_c<j_{h0}$, the $I$-$V$ curve has a flux flow behavior as shown in (d). The orange circle and purple diamond represent the critical current densities for short and long wires, respectively, made here, and the red and green triangles are, respectively, the critical current densities for protected and unprotected wires made using other techniques [51, 55, 78]. (c) The hysteretic $I$-$V$ curve in log-log scale, with an enlargement around 0 V. The switching current $j_s$ (red arrow), the returning current $j_r$ (green arrow), and the critical current $j_c$ (blue arrow) are indicated. (e) A typical evolution of the critical current $j_c$ as a function of the temperature for two short nanowires of width 200 nm and 126 nm.

Figure 7

(a) The schematics of a biased current wire in the framework of the SBT thermal model. A normal hot region of length $2y_0$ along the $y$ axis (in red) transfers thermal energy laterally to the superconducting wire via heat conduction $\kappa$ and through the substrate due to the heat transfer $\alpha$. Depending on the values of $\alpha$ and $\kappa$, the hot region either expands or self-heals. (b) $I$-$V$ curves measured at different temperatures for C8, a 30-nm-thick 500-nm-long 200-nm-wide $\mathrm{YBa}$${}_2$$\mathrm{Cu}$${}_3$$\mathrm{O}$${}_{7-\delta }$ nanowire. (c) The SBT self-heating model in linear scale with a C8 $I$-$V$ curve at 66 K. The solid lines are simulations of the $I_h{V}_h$ parametric curves given by Eqs. (4) and (5). We set different values of $\alpha$, displayed in the legend in units of ${10}^7\mathrm{W}{\mathrm{K}}^{-1}{\mathrm{m}}^{-2}$, with $\kappa =1.6\mathrm{W}{\mathrm{K}}^{-1}{\mathrm{m}}^{-1}$. The pink area defines the zone in which the device is thermally unstable for $\alpha =2.6\times {10}^7\mathrm{W}{\mathrm{K}}^{-1}{\mathrm{m}}^{-2}$. The corresponding minimum healing current $j_{h0}$ is highlighted by the black circle. The dashed line is the asymptotic line of the ohmic state in the SBT simulation. (d) The temperature evolution of the returning current density for C8. The lines correspond to the simulations of the healing-current density $j_{h0}$ for different values of the surface heat transfer $\alpha$ (in units of ${10}^7\mathrm{W}{\mathrm{K}}^{-1}{\mathrm{m}}^{-2}$) and for a temperature-dependent $\alpha (T)$ using the phonon mismatch model (“Mismatch” in the key).