Primary Tunnel Junction Thermometry

We describe the concept and experimental demonstration of primary thermometry based on a four-probe measurement of a single tunnel junction embedded within four arrays of junctions. We show that in this configuration random sample specific and environment-related errors can be avoided. This method relates temperature directly to Boltzmann constant, which will form the basis of the definition of temperature and realization of official temperature scales in the future.

Figure 1

The single-junction thermometer (SJT). (a) A typical conductance curve of a thermometer. (b) Schematics of the SJT. The white bounded areas are conductors, and the gray interconnects are tunnel junctions.

Figure 2

The influence of environment on SJT thermometry. (a) $R$ dependence of the half width of the conductance dips for $N^{\prime }=1$, 2, 3, 7, 15 ($N=2$, 3, 4, 8, 16 in linear arrays) from top to bottom. (b) The normalized depth of the conductance drop, with the same parameters as in (a). At low values of $R$, $N$ grows from bottom to up. (c),(d) The corresponding quantities on the logarithmic resistance scale for a single bare junction ($N^{\prime }=0$, $N=1$). In these plots $E_C/k_{B}T=0.1$.

Figure 3

Samples and comparison of the data on SJT and a bare single junction. (a) Electron micrographs of the reference structure with one junction connected to four leads (top), and the SJT structure with $N^{\prime }=20$ junctions in the leads (center). Zoom of the central junction and of a section of a junction array are shown at the bottom. (b) Measurement of the conductance of the bare single junction and the SJT in sample $B$ at $T\simeq 0.3\mathrm{K}$. The deeper and narrower drop in conductance corresponds to the SJT. The calculated conductance curves for the two samples based on the model described are shown by the solid lines assuming $R=80\Omega$.

Figure 4

Measurements on a SJT (sample $A$). Conductance dips at four temperatures are shown together with fits according to the model presented, including the self-heating correction [13]. The inset shows a comparison of the temperature deduced from SJT (vertical axis) against that obtained by an ordinary CBT measurement across one of the embedding arrays (horizontal axis). The solid line has unit slope, the error bars indicate the confidence interval of the fits, and the dashed lines the $\pm 3\%$ uncertainty of the reference temperature scale.