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

(a)
(c)
V th (μV)
0
100
200
-0.4 -0.2 0.0 0.2 0.4
Vrefr (mV)
1400
410
320
280
230
50
T e,N (mK)
(b)
(d)
0.1
T min /T c
0.01
1E-4 1E-3 0.01
FIG. 28 (Color in online edition) (a) SEM micrograph of an
Al/Al2O3/Cu SINIS microrefrigerator exploiting large-area
junctions (∼ 10 µm 2 ) with quasiparticle traps. (b) SEM
image of a part of comb-like SINIS structure with 10 + 10
junctions for cooling and a SINIS thermometer. (c) Electron
temperature Te,N in the N region of an Al/Al2O3Cu SINIS
refrigerator versus Vrefr measured at different bath temperatures.
The lowest curve (red dash-dotted line) shows the
anomalous heating effect observable at the lowest temperatures
and attributed to the presence of quasiparticle states
within the superconducting gap. (d) Theoretical ultimate
minimum electron temperature of a SINIS cooler Tmin/Tc at
V 2 ∆/e versus Γ/∆ in quasiequilibrium. (a) is adapted
from (Pekola et al., 2000a); (b) from (Luukanen et al., 2000);
(c) and (d) from (Pekola et al., 2004a).
issue is not so straightforward, as already discussed in
Subs. II.F.2, due to the intrinsic difficulty in fabricating
high-quality low-Rc barriers, although optimized barriers
are currently under investigation (see Sec. VI.F.1).
Latter option was experimentally addressed by Fisher
et al. (1999) in Al/Al2O3/Ag refrigerators, where large
cooling powers of a few tens of pW were obtained with
junctions of 20 × 20 µm 2 surface area. The reduction in
electron temperature was, however, much inferior to that
achievable with sub-micron sized junction. The problem
intrinsic to junctions with large overlap (especially
at the lowest temperatures) stems from the larger density
of quasiparticles present in the superconductor, due
to the fact that quasiparticles require a larger time to
exit the junction region and escape from the superconductor.
Therefore, this excess of quasiparticles alters in
general the refrigerator performance by returning energy
to the normal electrode, mainly due to back-tunneling
from the superconductor as well as due to recombination
processes, where phonons can enter and heat up the
N region (Jochum et al., 1998; Kaplan et al., 1976; Ullom
and Fisher, 2000). In addition, inelastic scattering
with phonons and dynamic impurities can also lead to
an excess of quasiparticles. These contributions can easily
overcompensate the junction cooling power, so that
Γ/Δ
36
it is crucial to remove this excess of quasiparticles from
the superconductor. Toward this end a number of techniques
exist among which we mention the exploitation
of defect-free and thick S electrodes (that allow quasiparticles
to escape ballistically from the junction area as
well as to decrease their density near the barrier) and the
exploitation of quasiparticle ”traps” (Parmenter, 1961),
i.e., normal metal films connected to the superconductor
in the junction region through a tunnel barrier or in direct
metallic contact (Irwin et al., 1995b; Pekola et al.,
2000a) (see Fig. 28(a)). Such traps act as sinks of quasiparticles
absorbing almost all the excess quasiparticle
energy present in the superconductor, and have proved
to efficiently help heat removal from the superconductor
leading to a significant improvement of SINIS device
cooling performance (Luukanen et al., 2000; Pekola et al.,
2000a, 2004a). All these are commonly exploited tricks
for the thermalization of the superconducting electrodes,
and in these conditions, it is a reasonable approximation
to set Te,S = Tph. Furthermore, the experiments
(Pekola et al., 2000a) demonstrated that the trap performance
is in general superior when it is in direct metallic
contact at short distance from the cooling junction (typically
below 1 µm, although the optimal distance mainly
depends on the superconductor coherence length), nevertheless
in small-area junctions even a contact through an
insulating barrier seems sufficient for the purpose. The
effectiveness of trapping in SINIS structures was theoretically
addressed in detail by Voutilainen et al. (2005)
and Golubev and Vasenko (2002). Another possibility
to achieve high cooling by maximizing the ratio of the
junction area to the size of the region to be cooled is
to use several small-area junctions (with size in the submicron
range) connected in parallel to the N electrode
(to limit the drawbacks typical of large junctions) (Arutyunov
et al., 2000; Leoni et al., 1999; Luukanen et al.,
2000; Manninen et al., 1999), as shown in Fig. 28(b).
The issue of tunnel junction asymmetry in SINIS refrigerators
was addressed by Pekola et al. (2000b). This
effect is fortunately weak: these authors theoretically
showed that the maximum cooling power is reduced by
7% in the case the junction resistances differ by a factor
of two, as compared to a symmetric structure with
the same total junction area. Furthermore, the reduction
is only about 25% even when the resistance ratio
is four. This effect stems from the ”self aligning” character
of the double junction structure: the voltage drop
across each junction is simultaneously close to ∆/e, thus
corresponding to the maximum cooling power, when the
voltage across the whole SINIS system is close to 2∆/e.
This fact is due to the high non-linearity of the currentvoltage
characteristics of the two junctions which carry
the same current. The experiments have confirmed such
a weak dependence of the cooling power on the structure
asymmetry (Pekola et al., 2000b).
In the low-temperature regime the situation is rather
different. While power load from electron-phonon interaction
becomes less and less dominant by decreasing the