Thermal properties in mesoscopics: physics and ... - ResearchGate

on the cross-over between two noise mechanisms, both
of which represent white noise, whereby the frequency
window is ideally not a concern, since the same readout
system is used in all the bias regimes. Moreover, the
gains of the amplifiers are not that critical either because
of the same argument. One can also use relatively high
bandwidth which increases the absolute noise signal to be
measured, and thereby makes the measurement faster.
The SNT technique has a few further attractive features.
It is likely that its operation can be easily extended
up to higher temperatures despite the deviations
observed in the first experiments. The sensor consists
of just one, relatively large size tunnel junction, which
means that it is easy to fabricate with high precision.
Also it is likely, although not yet demonstrated, that the
SNT is not sensitive to magnetic field, since its operation
is based on tunnelling characteristics in a NIN tunnel
junction as in CBT.
Finally, noise measurements can in principle be used
to measure the distribution function in non-equilibrium
as well, as proposed by Pistolesi et al. (2004).
D. Thermometry based on the temperature dependent
conductance of planar tunnel junctions
The effect of temperature on the current across a tunnel
barrier with finite height is a suitable basis for thermometry
in a wide temperature range (Gloos et al.,
2000). Simmons (1963a) showed that the tunnelling conductance
at zero bias across a thin insulating barrier depends
on temperature as
G(T ) = G0[1 + (T/T0) 2 ], (61)
where G0 is the temperature independent part of conductance
and the scaling temperature T0 depends on the
barrier height φ0. For a rectangular barrier of width s one
has T 2 0 = 32 φ0
π 2 k 2 B ms2 , where m is the effective mass of the
electrons within the insulating barrier. Experiments over
a temperature range from 50 K up to 400 K on Al-AlOx-
Al tunnel junctions have demonstrated that Eq. (61) is
obeyed remarkably well (Gloos et al., 2000; Suoknuuti
et al., 2001). Moreover, in these measurements the scaling
temperature was found to be T0 720 K in all samples,
without a clear dependence on the specific (zero
temperature) conductance of the barrier, which varied
over three orders of magnitude from 3 µS/µm 2 up to 3000
µS/µm 2 . This property makes the method attractive in
wide range thermometry, and T0 can indeed be considered
as a material specific, but geometry and thickness
independent parameter up to a certain accuracy.
E. Anderson-insulator thin film thermometry
As regards to temperature read-out of microcalorimetric
devices, resistive thin film thermometers
near the metal-insulator transition (MIT) are relatively
23
FIG. 16 The suspended thermal sensor employed in (Bourgeois
et al., 2005). The Nbx ′N1−x ′ thermometer can be seen
in the lower part of the rectangular silicon membrane. The
450 000 Al superconducting rings are located in the middle
part of the membrane; examples of them are shown in (b) and
(c). Figure from (Bourgeois et al., 2005).
popular. Electrical resistivity properties on both sides
of the MIT are rather well understood (Belitz and Kirkpatrick,
1994), and in general resistance of such thin films
shows strong temperature dependence, suitable for thermometry
and in particular for calorimetry. On the insulator
side resistivity ρ is determined by hopping, and
it has typically ρ ∝ e (T0/T ) n
temperature dependence,
with T0 and n constants. On the metallic side, weaker
dependence can be found. In practice, both NbxSi1−x
(Denlinger et al., 1994; Marnieros et al., 1999, 2000) and
Nbx ′N1−x ′ (Bourgeois et al., 2005; Fominaya et al., 1997)
thin film based thermometers have been successfully employed.
The suitable conduction regime can be tailored
by adjusting x (x ′ ) in electron beam co-evaporation (Denlinger
et al., 1994) or in dc magnetron sputtering of Nb
in a nitrogen atmosphere (Fominaya et al., 1997).
Bolometric and calorimetric radiation detectors are
discussed in detail in Sec. IV. Here we briefly mention
the application of a Nbx ′N1−x ′ thermometer in a measurement
of the heat capacity of 450 000 superconducting
thin film loops on a silicon membrane (Bourgeois et al.,
2005), see Fig. 16. The heat capacity of the loops is proportional
to their total mass, which was about 80 ng in
this case. Vortices entering simultaneously into the 450
000 loops under application of magnetic field could be
observed. A similar measurement (Lindell et al., 2000),
employing a NIS thermometer could resolve the specific
heat jump at Tc of 14 thin film titanium disks with total
mass of 1 ng on a silicon nitride membrane.