Sub-50-mK Electronic Cooling with Large-Area Superconducting Tunnel Junctions

In electronic cooling with superconducting tunnel junctions, the cooling power is counterbalanced by the interaction with phonons and by the heat flow from the overheated leads. We study aluminum-based coolers that are equipped with a suspended normal metal and an efficient quasiparticle drain. At intermediate temperatures, the phonon bath of the suspended normal metal is cooled. By adjusting the junction transparency, we control the injection current and, thus, the temperature of the superconducting lead at the optimum cooling point. The best device shows remarkable cooling from 150 mK down to about 30 mK, a factor of 5 in temperature at a power of 40 pW. We discuss heat transport in our device and the reasons for cooling saturation at the low-temperature end.

Figure 1

(a) Schematic cross-sectional view of the $S\text{−}I\text{−}N\text{−}I\text{−}S$ cooler, where Cu is for the normal-metal island and quasiparticle traps, Al for the superconducting leads, and AlMn for the quasiparticle drains. The blue arrow indicates the charge current, and the red arrows show the heat current. (b) Normal-metal electronic temperature $T_N$ reached at the optimum bias vs bath temperature $T_{\text{bath}}$ for samples made on the same wafer but differing in their geometries. Compared to the standard sample $A1$ ($70\times 4\mu {\mathrm{m}}^2$ for one junction), $A2$ has twice the junction area, $A3$ has half the junction area, and $A4$ has 20% of its normal-metal volume. The left inset shows an image of the standard sample $A1$, and the right inset shows an image of $A5$ with an interdigitated junction shape. The $N\text{−}I\text{−}S$ junctions are bordered with dashed lines.

Figure 2

Temperature of the normal-metal island $T_N$ at the optimum bias as a function of bath temperature $T_{\text{bath}}$. Samples $A1$, $B$, $C1$, and $D$ differ only in their tunnel resistances $R_T$ (Table 1). $C2$ is an improved version of $C1$; see the text. The gray dotted line is the 1-1 line at the boundary between cooling and heating. The error bar for each data set from the measurement is represented. The inset shows thermometer calibrations, i.e., voltages of the probing junctions at a current of 1.5 nA for samples $C1$ and $D$ at cryostat temperatures below 200 mK. Dots are experiment data and dashed lines fit to the BCS theory.

Figure 3

(a) Apparent efficiency calculated with the assumption of metal phonons thermalized at the bath temperature for samples $A1$, $C1$, and $D$ compared to the theory prediction Eq. (2) (black dashed line). The inset shows the calculated ${\dot{Q}}_{NIS}$ when assuming $T_S=T_{\text{bath}}$ and ${\dot{Q}}_{e\text{−}\mathrm{ph}}$ when assuming $T_{\mathrm{ph}}=T_{\text{bath}}$ for sample $C1$. (b) Extracted phonon temperature of the normal island $\mathrm{\Delta }{T}_{\mathrm{ph}}=T_{\mathrm{ph}}-T_{\text{bath}}$ assuming the theoretical efficiency and no overheating of the leads.

Figure 4

(a) Sketch of the thermal transport when the superconductor couples to the quasiparticle drain. The red arrows represent the heat current where quasiparticles relax. We label their most notable dependences; see the text. (b) Optimum cooling power normalized by that of an ideal uniform junction as a function of the gap nonuniformity at different temperatures.