Tunnel-Junction Thermometry Down to Millikelvin Temperatures

We present a simple on-chip electronic thermometer with the potential to operate down to 1 mK. It is based on transport through a single normal-metal–superconductor tunnel junction with rapidly widening leads. The current through the junction is determined by the temperature of the normal electrode that is efficiently thermalized to the phonon bath, and it is virtually insensitive to the temperature of the superconductor, even when the latter is relatively far from equilibrium. We demonstrate here the operation of the device down to 7 mK and present a systematic thermal analysis.

Figure 1

In panel (a), we show the relative deviation of the present thermometer reading using method $B$ with a numerically calculated $I\text{−}V$, Eq. (1). Sets of curves present the values of $t$ for three $\gamma$ parameters: ${10}^{-7}$, $2.2\times {10}^{-5}$ (the actual value in the experiment), and ${10}^{-4}$ shown as the red, blue, and green curves from left to right. For each $\gamma$ parameter, temperatures 1, 3, and 7 mK are shown as dash-dotted, dashed, and solid lines, respectively. All curves are calculated using the parameters of the measured device with $\mathrm{\Delta }=200\mu \mathrm{eV}$ and $R_T=7.7\mathrm{k}\mathrm{\Omega }$. The main panel (b) shows the measured $I\text{−}V$ characteristic (blue dots) together with full fit (solid red line) enlarged in the superconducting gap region. (Inset) Measured and calculated $I\text{−}V$ curve on a wider voltage scale at approximately 10 mK.

Figure 2

A scanning-electron micrograph of the $N\text{−}I\text{−}S$ device together with a schematic of the experimental setup. In the main panel, the $S$ and $N$ leads of the junction are visible, and underneath the pads, the ground plane of a square shape is indicated by a dashed line. Enlarged inset shows the actual tunnel junction where the $S$ and $N$ leads are shown in blue and brown, respectively.

Figure 3

Panel (a) shows measured $I\text{−}V$ characteristics (blue dots), when $T_{\text{bath}}$ is lowered from left to right together with fits as solid black and dashed red lines (see text). (Inset) Close-up of two $I\text{−}V$ characteristics for temperatures of 10 and 7 mK. The electronic temperatures extracted from both the full fit (red squares) of the $I\text{−}V$ characteristics and their slopes (black triangles) are shown in (b).

Figure 4

Scheme of a dilution unit together with a NR. Radiation shields (not shown) are attached to the still and cold plate (approximately 50 mK). The resistor-capacitor (RC) filters are $1.6\mathrm{k}\mathrm{\Omega }/2.2\mathrm{nF}$ and $2.4\mathrm{k}\mathrm{\Omega }/470\mathrm{pF}$. The 21 NR plates are $0.25\times 3.2\times 9.0{\mathrm{cm}}^3$ each, amounting to 64-g Cu per plate. The NRs cool as low as 0.2 mK. In the present experiment, the lowest $T_{\text{bath}}$ used is 3 mK. Compared to Ref. [11], the improved setup depicted here features a Ag epoxy socket, a Ag epoxy chip carrier, and a second filtering stage with radiation-tight feedthroughs into an additional sample radiation shield. The abbreviations BW, $B_c$ and GND presented in the schematic stand for bandwidth, critical magnetic field and electrical ground, respectively.

Figure 5

The theoretical deviations $t$ and $t_g$ of the thermometer reading using method $B$ based on $I(V)$ and $g(V)$, respectively. These deviations are shown for temperatures 1, 3, and 7 mK as dash-dotted, dashed, and solid lines, respectively. Parameters used are $\gamma =2.2\times {10}^{-5}$, $\mathrm{\Delta }=200\mu \mathrm{eV}$, and $R_T=7.7\mathrm{k}\mathrm{\Omega }$ as in the actual experiment.

Figure 6

The thermal diagram of the $N\text{−}I\text{−}S$ thermometer. Present schematic does not reflect the real thicknesses of the materials. In this thermal model, we assume the normal-metal shadow that acts as the trap to be at $T_{\text{bath}}$.