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

FIG. 35 (a) Scheme of a quantum-dot refrigerator. (b)
Energy-level diagram of the structure. The reservoir R is
cooled as its quasiparticle distribution function is sharpened
by resonant tunneling through quantum dots DL and DR to
the electrodes VL and VR. From (Edwards et al., 1995).
temperature reduction can be achieved by using a multilayered
heterostructure (Mahan and Woods, 1998; Shakouri
and Bowers, 1997; Zhou et al., 1999). According
to theory (Mahan and Woods, 1998; Shakouri and Bowers,
1997), heterostructure-based thermionic refrigerators
perform somewhat better as compared to thermoelectric
coolers. The predicted temperature reduction of a singlestage
device at room temperature can be as high as 40
K, and this value can be significantly increased in a multilayer
configuration. So far, however, the experimental
implementations of single barrier (Shakouri et al., 1999)
and superlattice (Fan et al., 2001; Zhang et al., 2003)
refrigerators have reported temperature reductions of a
few degrees at room temperature.
Further improvement of thermionic refrigeration can,
in principle, be achieved by combining laser cooling
and thermionic cooling (Mal’shukov and Chao,
2001; Shakouri and Bowers, 1997). In such an optothermionic
device, hot electrons and holes extracted
through thermionic emission lose their energy by emitting
photons rather than by heating the lattice. The
theoretical investigation of a GaAs/AlGaAs-based optothermionic
refrigerator predicted specific cooling power
densities of the order of several W/cm 2 at 300 K
(Mal’shukov and Chao, 2001).
The presence of singularities in the energy spectrum
of low-dimensional systems can be used in solid state refrigeration.
For instance, the discrete energy spectrum
in quantum dots can be exploited for refrigeration at
cryogenic temperatures (Edwards et al., 1995, 1993). In
such a quantum-dot refrigerator (QDR) (see Fig. 35(a))
a reservoir (R) is coupled to two electrodes via quantum
dots (DL and DR) whose energy levels can be tuned
through capacitively-coupled electrodes. The QD energy
levels can be adjusted so that resonant tunneling to the
electrode VL is used to deplete the states in R above µ0
and, similarly, holes below µ0 in R tunnel to VR (see
Fig. 35(b)). As a consequence, the net result will be to
sharpen the quasiparticle distribution function in R, thus
leading to electron refrigeration. In spite of a rather mod-
45
erate achievable cooling power, the QDR was predicted
to be effective for cooling electrons of a micrometer-sized
two-dimensional electron gas reservoir at mK temperatures,
and even of a macroscopic reservoir at lower temperatures
(Edwards et al., 1995, 1993).
VI. DEVICE FABRICATION
A. Structure typologies and material considerations
This section is devoted to the description of the main
techniques and experimental procedures used for the fabrication
of typical superconducting electronic refrigerators
and detectors. Owing to the great advances reached
in the last decades in micro- and nanofabrication technology
(Bhushan, 2004; Timp, 1999), the amount of information
related to fabrication methods is too large to
be covered here and beyond the scope of the present review.
Therefore, we only briefly highlight all those issues
that we believe are strictly relevant for this research field.
In particular we first of all focus on the two typologies
of existing superconducting structures, namely all-metal
and hybrid devices, and on the main differences between
them, both in terms of materials and fabrication techniques.
The former concern structures where the active
parts of the device, i.e., both the superconducting elements
and the normal regions are made of metals; in
hybrid structures, the non superconducting active part
of the device is made of doped semiconducting layers.
As far as all-metal-based structures are concerned,
they are realized with low-critical-temperature thin-film
superconductors (normally Al, Nb, Ti and Mo), while the
normal regions usually consist of Cu, Ag or Au. Their
fabrication protocol includes patterning of a suitable
radiation-sensitive masking layer through electron-beam
or optical lithography in combination with a shadowmask
(angle) evaporation technique (Dolan, 1977). The
final device is thus realized in a single step in the deposition
chamber, where additional tunnel barriers between
different regions of the structure are in-situ created
by suitable oxidation of the metallic layers. Although
all this leads to an efficient way for fabricating metallic
structures, however the electronic properties typical of
metals are only weakly dependent on their growth conditions
and on the specific employed technique. As a
consequence, it is hard to tailor the metallic properties
in order to finally match some specific requirements.
On the other hand, the situation is rather different
with semiconductors that offer some advantages in comparison
to metals. The large magnitude difference of
Fermi wave-vector between metals and semiconductors
allows in general to observe quantum effects in structures
much bigger than with metals. In addition, the
availability of several techniques for growing high-purity
crystals (e.g., molecular beam epitaxy) yields the capacity
to tailor the semiconductor electronic properties and,
at the same time, enables the fabrication of structures