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

Fermi-level pinning at the NSm interface (Bardeen, 1947;
Heine, 1965; Mönch, 1990).
The current across a Schottky junction depends on
a number of different mechanisms. In the limit where
thermionic emission dominates the electric transport, the
rectifying action of a biased NSm junction is described
as I(V ) = Is[exp(eV/kBT ) − 1], where the detailed expression
for the saturation current Is depends on the
assumptions made on carrier transport (Brennan, 1999;
Sze, 1981, 1985). In such a case the junction specific
resistance is Rc ∝ T −1 exp(eφSBn/kBT ), thus meaning
that it can be lowered mainly by decreasing φSBn (typical
Rc values at doping levels ND ≤ 10 17 cm −3 for
metal/n-Si contacts are of the order of 10 11 ...10 13 Ωµm 2
almost independent of ND). By contrast, tunneling
across the SB can be the dominating transport mechanism
if the semiconductor is heavily doped. In such a case
I(V ) ∝ exp[−α(φSBn − V )/ √ ND], with α = 2 −1√ m ∗ ɛ
where m ∗ is the semiconductor effective mass and ɛ the
dielectric permittivity, i.e., the junction is not rectifying
and the current is proportional to V for small voltages.
The contact is thus said to be ohmic and yields
Rc ∝ exp(αφSBn/ √ ND). This shows that Rc can be
reduced up to a large extent by lowering the SB height
and doping as heavily as possible (again, for metal/n-
Si contacts and ND ≥ 10 19 cm −3 , Rc can be in the
range 10 2 ...10 8 Ωµm 2 ). All this shows the advantage of
using NSm contacts owing to the possibility of tuning
the contact specific resistance over several orders of magnitude
(from metallic-like to tunnel-like characteristics)
through a careful choice of metal-semiconductor combinations
and proper doping levels. This trick is commonly
exploited to control the NSm interface resistance in current
semiconductor technology, although heavy doping of
the semiconductor just in proximity to the metal is often
preferred (Giazotto et al., 2001a,b; Kastalsky et al.,
1991; Shannon, 1976; Taboryski et al., 1996).
VII. FUTURE PROSPECTS
Low temperature solid-state cooling is still at its infancy,
although operation of a number of individual
principles and techniques have been demonstrated to
work successfully. Yet combinations of cascaded microrefrigerators
over wider temperature ranges employing
several stages, or combinations of different refrigeration
principles, e.g., fluidic coolers together with electronic
coolers, do not exist. In principle, compact low-power
refrigerators could be fabricated using micro-machined
helium-based fluidic refrigerators, for instance based on
Joule-Thomson process (Little, 1984), and these devices
could then be directly precooling NIS-refrigerators with
niobium (Tc = 9 K) as a superconductor. A lot of engineering
effort is, however, needed to make this approach
work in practise as a targeted micro-refrigerator.
The solid-state micro-circuits have already proven to
yield new operation principles and previously unknown
50
concepts have been discovered in cryogenic devices, as
demonstrated throughout this review. We believe that
what was demonstrated here is just a presentation of a
beginning of a new era in low temperature physics and
instrumentation. As possible new classes of devices we
could mention those utilizing thermodynamic Carnot cycles
with electrons. Brownian heat engines with electrons
are predicted to achieve efficiencies close to ideal
(Humphrey et al., 2002). It may be possible in the future
to make use of other types of gated cycles where
energy selective extraction of electrons is producing the
refrigeration effect. As a conceivable example, a combination
of Coulomb effects and superconducting energy
gap could form the basis of operation of a refrigerator
where cooling power would be proportional to the operating
frequency of the gate cycle. Such a device would
thus be principally different from the static electronic refrigerators
presented in this review, where a DC bias is
in charge of the redistribution of hot electrons.
At low temperatures, additional relaxation channels
besides the electron-phonon scattering, such as coupling
between electrons and photons, become important. More
knowledge is needed on these mechanisms.
In Subs. V.C.7, we describe how the non-equilibrium
shape of the distribution function sometimes leads to improved
characteristics of the device. It would be interesting
to see if such effects could be employed to improve
also the properties of the radiation detectors or other
practical devices.
The presently obvious application fields of electronic
micro-refrigerators include astronomical detectors both
in space as well as those based on the earth, materials
characterization instrumentation, e.g., those devices employing
ultra high resolution x-ray micro-analysis, and
security instrumentation, e.g., concealed weapon search
on the airports. It is, however, evident that once realized
in a user-friendly and economic way, refrigeration
becomes very important in high-tech based industry in
a much broader perspective. Low temperature electronics
and superconducting devices are often characterized
by their undeniably unique possibilities, but they are often
superior to the room temperature ones also in speed
and power consumption. Therefore, mesoscopic on-spot
refrigerators to attain the low temperatures forming the
basis of these instruments are urgently needed.
Acknowledgments
We thank H. Courtois, R. Fazio, F. Hekking, M. Paalanen,
F. Taddei and P. Virtanen for their insightful comments
and for critically reading the manuscript. D.
Anghel, A. Anthore, F. Beltram, M. Feigelman, E. Grossman,
K. Irwin, M. Meschke, A. J. Miller, S. Nam, D.
Schmidt, and J. Ullom are gratefully acknowledged for
enlightening discussions. This work was supported by
the Academy of Finland.