On thermometer operation of ultrasmall tunnel junctions

Abstract

The temperature dependence of the I-Vcharacteristics of many single-electron tunneling devices enables thermometer operation of these systems. Two normal conducting kinds of them are investigated, a) a single junction in a high-impedance environment and b) a double junction. The characteristics of both devices show a cross-over from Coulomb blockade at low temperatures to ohmic behavior at high temperatures. The related differential conductivity dip allows the determination of the temperature of the junctions. Both configurations a) and b) are expected to work at least within the range 0.5 5 BE, 10, where E, is the Coulomb energy of the system under investigation. An analytical solution for both low-and high-temperature cases of a) and b) as well as numerical results and their fit are presented, including the effect of co-tunneling in case of a double junction.

Thermometry at the nanoscale

“…The advanced design gathers superconductor-insulator-normal metal tunnel junctions embedded in a rf resonant circuit with nanometric dimensions (typically hundreds of nanometres). 51,52,245 While conductance at zero bias voltage is suppressed, the conductance at non-zero broadens as temperature increases, resulting in a peak with a fwhm being proportional to the number of junctions and to k B T. Moreover the high temperature limit is determined by the electric characteristics of the junction, which allows the tailoring of the thermometer using an appropriate configuration. The sensitivity of Coulomb blockade thermometers decreases when temperature increases, resulting in hypothetical infinite maximum relative sensitivity at the limit of T / 0 K. For temperatures of the order of tens of Kelvin a monotonical decrease of S m towards 1 is expected.…”

The influence of incoherent co-tunnelling on single-electron-tunnelling thermometry

“…where σ (n, V , T ) is the temperature-dependent occupation probability of n charges. At voltages e V k B T this probability becomes independent of the bias voltage V [17]:…”

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“…Nevertheless, when all relevant factors are taken into account, the device has a minimal resolution G of ∂G t (T )/∂T . A reasonable estimate [4] gives T + /T − 10. That is, the presently available SET thermometer works in a temperature range about one order of magnitude around E C /k B .…”

“…In ultrasmall tunnel junctions the Coulomb interaction produces the single-electron tunnelling (SET) phenomenon. The temperature characteristics of SET in tunnel junctions allows the fabrication of a new type of thermometer [2][3][4]. The simplest SET thermometer is a symmetric double tunnel junction (SDTJ) [3,4] (shown schematically in the inset of figure 1), where each junction is characterized by a junction capacitance C and a junction resistance R. It has been shown [2][3][4] that the normalized conductance 2RG(T ) of a SDTJ at zero bias voltage is a universal function of the normalized temperature k B T /E C , where E C = e 2 /2C is the Coulomb charging energy with the effective capacitance C = 2C.…”

“…The temperature characteristics of SET in tunnel junctions allows the fabrication of a new type of thermometer [2][3][4]. The simplest SET thermometer is a symmetric double tunnel junction (SDTJ) [3,4] (shown schematically in the inset of figure 1), where each junction is characterized by a junction capacitance C and a junction resistance R. It has been shown [2][3][4] that the normalized conductance 2RG(T ) of a SDTJ at zero bias voltage is a universal function of the normalized temperature k B T /E C , where E C = e 2 /2C is the Coulomb charging energy with the effective capacitance C = 2C. This universal function is plotted in figure 1, and can be approximated [4] by…”