https://engineering.purdue.edu/~tsfisher/ME595M/Lepri%20thermal%20cond%20review%202004.pdf

Thermal conduction in classical low-dimensional lattices

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices.

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Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

The physics of mesoscopic electronic systems has been explored for more than 15 years. Mesoscopic phenomena in transport processes occur when the wavelength or the coherence length of the carriers becomes comparable to, or larger than, the sample dimensions. One striking result in this domain is the quantization of electrical conduction, observed in a quasi-one-dimensional constriction formed between reservoirs of two-dimensional electron gas. The conductance of this system is determined by the number of participating quantum states or 'channels' within the constriction; in the ideal case, each spin-degenerate channel contributes a quantized unit of 2e^2/h to the electrical conductance. It has been speculated that similar behaviour should be observable for thermal transport in mesoscopic phonon systems. But experiments attempted in this regime have so far yielded inconclusive results. Here we report the observation of a quantized limiting value for the thermal conductance, G_(th), in suspended insulating nanostructures at very low temperatures. The behaviour we observe is consistent with predictions for phonon transport in a ballistic, one-dimensional channel: at low temperatures, G_(th) approaches a maximum value of g_0 = π^2k^2BT/3h, the universal quantum of thermal conductance.

Measurement of the quantum of thermal conductance

Controlling thermal transport is commonly achieved by introducing scattering centres. Here, the authors demonstrate that coherent band structure effects can also be used to control phonon transport, via the use of periodically nanostructured phononic crystals.

/pdf/engineering-thermal-conductance-using-a-two-dimensional-3kx4r5kel9.pdf

Engineering thermal conductance using a two-dimensional phononic crystal

Controlling thermal transport has become relevant in recent years. Traditionally, this control has been achieved by tuning the scattering of phonons by including various types of scattering centres in the material (nanoparticles, impurities, etc). Here we take another approach and demonstrate that one can also use coherent band structure effects to control phonon thermal conductance, with the help of periodically nanostructured phononic crystals. We perform the experiments at low temperatures below 1 K, which not only leads to negligible bulk phonon scattering, but also increases the wavelength of the dominant thermal phonons by more than two orders of magnitude compared to room temperature. Thus, phononic crystals with lattice constants ≥1 μm are shown to strongly reduce the thermal conduction. The observed effect is in quantitative agreement with the theoretical calculation presented, which accurately determined the ballistic thermal conductance in a phononic crystal device.

/pdf/engineering-thermal-conductance-using-a-two-dimensional-a7jak7z5xw.pdf

We have measured the thermal conductance, G, of ≈1 μm thick low stress silicon nitride membranes over the temperature range, 0.06 4 K, G is independent of surface condition indicating that the thermal transport is determined by bulk scattering. For T<4 K, scattering from membrane surfaces becomes significant. Membranes which have submicron sized Ag particles glued to the surface or are micromachined into narrow strips have a G that is reduced by a factor as large as 5 compared with that of clean, solid membranes with the same ratio of cross section to length.

W. Holmes

Papers

Measurements of thermal transport in low stress silicon nitride films