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e 2 R /Δ T 2 (0)(×10 -2 Q&Q& ) 6 k T/Δ(0) = 0.4 B 3 0 6 -3 3 = 1 0.94 ¡ = 1 0.98 0.96 0.96 0.98 (a) Q& (nW/μm A 2 )(×10 2 ) -6 0 0.0 -9 0.0 0.94 0.4 kBT/Δ(0) 0.5 0.8 1.0 1.5 eV/Δ(0) 8 7 6 5 4 3 k T/ Δ (0)=0.4 2 B 1 0 ¢ = 1 0.98 0.96 0.94 25 20 15 10 5 0.0 0.4 0.8 0 k T/Δ(0) B 0.3 0.2 0.15 0.94 0.96 0.98 1.00 FIG. 31 (Color in online edition) (a) Calculated heat current ˙ Q of a SF junction vs bias voltage V at T = Te,F = Te,S = 0.4 ∆(0)/kB for several spin polarizations P. The inset shows the same quantity calculated at the optimal bias voltage against temperature for some values of P. (b) Calculated maximum cooling power surface density ˙ QA versus P for various temperatures. The inset shows the coefficient of performance η calculated at the optimal bias voltage versus temperature for some P values. Adapted from (Giazotto et al., 2002, 2005). a possible higher-temperature first stage in cascade cooling (for instance, over or around 1 K), where it could dominate over the large thermal coupling to the lattice characteristic for such temperatures. The results given above point out the necessity of strongly spin-polarized ferromagnets for a proper operation of the SF refrigerator. Among the predicted half-metallic candidates it is possible to indicate CrO2 (Brener et al., 2000; Kämper et al., 1987; Schwartz, 1986), for which values of P in the range 85...100% have been reported (Coey et al., 1998; Dedkov et al., 2002; Ji et al., 2001; Parker et al., 2002), (Co1−xFex)S2 (Mazin, 2000), NiMnSb (de Groot et al., 1983), Sr2FeMoO6 (Kobayashi et al., 1998) and NiMnV2 (Weht and Pickett, 1999). So far no experimental realizations of SF structures for cooling applications have been reported. 5. HTc NIS systems Heat transport in high-critical temperature (HTc) NIS junctions was theoretically addressed by Devyatov et al. (2000). In these systems the cooling power depends on interface transmissivity as well as on orientation of the superconductor crystal axes and temperature. In particular, these authors showed that the maximum positive heat current in these structures can be achieved in junctions with zero superconducting crystallographic angle, at temperature T = 0.45 Tc and bias voltage V ≈ 0.8 ∆(0)/e. The behavior of ˙ Q(V ) turns out to be qualitatively similar to that of NIS junctions based on low-critical temperature superconductors (see Fig. 26(a)), and with comparable values (in relative units). P η (%) (b) 40 From this it follows that the cooling power of electronic refrigerators based on HTc materials is approximately two orders of magnitude larger than in NIS junctions based on low-critical temperature superconductors (at much lower temperatures). A somewhat different cooling effect in HTc superconductors was predicted by Svidzinsky (2002), who showed that an adiabatic increase of the supercurrent in a ring (or cylinder) made from a HTc superconductor may lead to a cooling effect. The maximum cooling occurs if the supercurrent is equal to its critical value. For a clean HTc superconductor, the minimum achievable temperature (Tmin) was found to be around Tmin = T 2 0 /Tc, with T0 the initial temperature of the ring, thus meaning that substantial cooling can be achieved using large Tc values. Experimentally, Fee (1993) realized a Peltier refrigerator junction exploiting a HTc superconductor and operating around liquid nitrogen temperatures. In particular, his device consisted of a BiSb alloy and YBa2Cu3O7−δ superconducting rods connected by a small copper plate which acted as the cold junction of the device. The latter showed a maximum cooling of 5.35 K below the bath temperature T0 = 79 K. The figure of merit of the junction, Z, was estimated to be as large as 2.0 × 10 −3 K −1 . 6. Application of (SI)NIS structures to lattice refrigeration One well established application of SINIS refrigerators concerns lattice cooling (Clark et al., 2005; Luukanen et al., 2000; Manninen et al., 1997). As a matter of fact, while NIS tunneling directly cools the electron gas of the normal electrode, the phonon system can be refrigerated through the electron-phonon coupling (see Eq. (24)). The latter, however, is typically very small at the lowest temperatures, thus limiting the heat transfer from the surroundings to the electrons. This situation normally happens whenever the metal to be cooled is in direct contact with a thick substrate, for instance, oxidized Si (Leivo et al., 1996; Nahum et al., 1994): only the electrons of the N region cool down while the metal lattice presumably remains at the substrate temperature. The metal lattice can be refrigerated considerably if the thermal resistance between the phonons and the substrate is not negligible compared to that between the electrons and the phonons. One effective choice to meet this requirement, that was indeed suggested at the beginning of cooling experiments (Fisher et al., 1995; Nahum et al., 1994) as well as for detector applications (Deiker et al., 2004; Doriese et al., 2004; Irwin et al., 1996; Nahum and Martinis, 1995; Pekola et al., 2004b; Ullom et al., 2004), is to exploit a thermally isolated thin dielectric membrane on which the N region of the cooler is extended. In this way, tunneling through the NIS junction will cool down the electrons of the metal, then the phonons of the metal (via electron-phonon coupling) that subsequently will refrigerate the membrane phonons (Clark et al., 2005; Luukanen et al., 2000; Manninen et al., 1997)
(a) (b) T min / T 0 1.05 1.00 0.95 0.90 thermometer SINIS junctions Electron temperature at cooling junctions Electron temperature on the membrane Lattice temperature on the membrane 200 300 400 500 600 T 0 (mK) SINIS junctions cold fingers (d) (c) SIN junctions cold finger FIG. 32 (Color in online edition) (a) SEM image of a Si3N4 membrane (in the center) with self-suspended bridges. Two normal-metal cold fingers extending onto the membrane are used to cool down the dielectric platform. The Al/Al2O3/Cu SINIS coolers are on the bulk (far down and top) and the thermometer stands in the middle of the membrane. (b) Maximum temperature decrease (Tmin/T0) versus bath temperature T0 measured at different positions in the cooler shown in (a). (c) Maximum lattice temperature decrease on the membrane versus bath temperature measured in two other samples similar to that shown in (a). In this case, the refrigerators exploited many small-area junctions arranged in parallel in a comb-like configuration. (d) SEM micrograph of a NIS refrigerator device with a neutron transmutation doped (NTD) Ge resistance thermometer attached on top of it. (c) is adapted from (Luukanen et al., 2000), (d) from (Clark et al., 2005). according to ˙QSINIS(V ; Te,N , Te,S) + ˙ Qph−sub(Tph, Tsub) = 0, (81) where Te,N Tph, Te,S Tsub, Tph is the lattice temperature in the dielectric membrane, Tsub is the lattice temperature in the substrate, and ˙ Qph−sub is the rate of exchanged energy between the membrane phonons and substrate phonons. Eventually, if additional devices are standing on the same dielectric platform (for instance, detectors, etc.), the latter will cool down first the phonons of the device and then its electrons through the electron-phonon interaction. Dielectric membranes made of silicon nitride (Si3N4) have proved to be attractive for this purpose in light of their superior thermal isolation properties at low temperatures. Low-temperature heat transport characterization as well as thermal relaxation in low-stress Si3N4 membranes and films were quite recently addressed (Holmes et al., 1998; Leivo and Pekola, 1998). The first demonstration reported of lattice cooling (Manninen et al., 1997) exploited such membranes in combination with Al/Al2O3/Cu SINIS refrigerators. In this experiment the authors were able to achieve a 2% temperature decrease in the membrane at bath temperatures T0 ≈ 200 mK. 41 Figure 32(a) shows a SEM image of a typical newgeneration lattice cooler fabricated on a Si3N4 membrane with self-suspended bridges. The membrane consists of a low-stress Si3N4 film deposited by low pressure chemical vapor deposition (LPCVD) on Si, and subsequently etched (with both wet and dry etching) in order to create the suspended bridge structure. In such thin membranes phonon propagation is essentially two-dimensional. The condensation of the phonon gas into lower dimensions in ultrathin membranes was also theoretically discussed (Anghel and Manninen, 1999; Anghel et al., 1998; Kuhn et al., 2004). The self-suspended bridges improve thermal isolation of the dielectric platform from the heat bath (Leivo and Pekola, 1998). The image also shows the Al/Al2O3/Cu refrigerators of the SINIS type that are placed on the bulk substrate (i.e., outside the membrane) to ensure good thermal contact with the bath. The N cold fingers extend onto the silicon nitride membrane, whose temperature is determined through an additional SINIS thermometer placed in the middle of the structure. The lattice refrigeration effect achieved in this SINIS refrigerator is shown in Fig. 32(b). Here the maximum temperature decrease of the membrane (Tmin/T0) against bath temperature T0 is displayed (red circles), and shows that temperature reduction as high as about 12% was reached in the 400...500 mK range. The electron refrigeration effect in the Cu region was also measured at two different positions in the device, i.e., nearby the cooling junctions and on the membrane. Notably, the Tmin/T0 behavior is almost the same for the different sets of data; this basically means that: a) good thermalization was achieved in the cold fingers; b) the electron-phonon coupling was sufficiently large while Kapitza resistance between Cu and Si3N4 was sufficiently small to ensure the lattice temperature on the membrane to be nearly equal to the Cu electron temperature on the membrane itself. The best results of lattice refrigeration by SINIS coolers reported to date are shown in Fig. 32(c) (Luukanen et al., 2000) for two other devices (labeled C and D in the figure) similar to that of Fig. 32(a). These devices exploited three Cu cold fingers and several small-area junctions arranged in parallel in a comb-like configuration for the SINIS cooling stage. The junction specific resistances were Rc = 1.39 kΩµm 2 and Rc = 220 Ωµm 2 for device C and D, respectively. Lattice temperature reduction as high as 50% at 200 mK was achieved in the sample with lower Rc, thus confirming the effectiveness of small-area junctions in yielding larger temperature reductions. The achieved cooling power in these devices was estimated on the pW level. The reduction of the refrigeration effect at the lowest temperatures can be explained in terms of larger decoupling of electrons and phonons, but also the effects discussed in Sec. V.C.1 should play a role. Figure 32 (d) demonstrates the realization of a complete refrigerator device including a thermometer (Clark et al., 2005), where four pairs of NIS junctions are used to cool down a 450 × 450 µm 2 suspended Si3N4 dielectric
Page 1 and 2: Thermal properties in mesoscopics:
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Page 5 and 6: other types of contacts, it is typi
Page 7 and 8: Te (mK) Tph Σ (W (mK) m −3 K −
Page 9 and 10: N(E) = 1 for a normal metal and N(E
Page 11 and 12: E F eV (a) e E Δ Δ N I S E F forb
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Page 15 and 16: that for a ”cross” system witho
Page 17 and 18: T/T 0 3 2 (a) T(r ) = 3.0 T 0 0 0.5
Page 19 and 20: FIG. 10 (Color in online edition):
Page 21 and 22: (a) T CBT (mK) 100 10 10 100 T (mK)
Page 23 and 24: on the cross-over between two noise
Page 25 and 26: that the performance improvement is
Page 27 and 28: Here γ describes the effect of the
Page 29 and 30: over a limited bandwidth. The SCUBA
Page 31 and 32: FIG. 21 An energy spectrum of the 5
Page 33 and 34: FIG. 24 Thermoelectric refrigeratio
Page 35 and 36: (b) R 1 R 2 R P I 0 V refr V th R T
Page 37 and 38: temperature, and typically below 0.
Page 39: (Savin et al., 2003). It displays t
Page 43 and 44: trol line of length LSINIS. The sup
Page 45 and 46: FIG. 35 (a) Scheme of a quantum-dot
Page 47 and 48: oration from a source material per
Page 49 and 50: much higher resolution). Several ma
Page 51 and 52: References Adams, A. C., 1983, in V
Page 53 and 54: Ferry, D. K., and S. M. Goodnick, 1
Page 55 and 56: Y. M. Galperin, 2004, Phys. Rev. B
Page 57 and 58: ogy, edited by S. M. Rossnagel, J.

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