Rapid progress in the synthesis and processing of materials with structure on nanometer length scales has created a demand for greater scientific understanding of thermal transport in nanoscale devices, individual nanostructures, and nanostructured materials. This review emphasizes developments in experiment, theory, and computation that have occurred in the past ten years and summarizes the present status of the field. Interfaces between materials become increasingly important on small length scales. The thermal conductance of many solid–solid interfaces have been studied experimentally but the range of observed interface properties is much smaller than predicted by simple theory. Classical molecular dynamics simulations are emerging as a powerful tool for calculations of thermal conductance and phonon scattering, and may provide for a lively interplay of experiment and theory in the near term. Fundamental issues remain concerning the correct definitions of temperature in nonequilibrium nanoscale systems. Modern Si microelectronics are now firmly in the nanoscale regime—experiments have demonstrated that the close proximity of interfaces and the extremely small volume of heat dissipation strongly modifies thermal transport, thereby aggravating problems of thermal management. Microelectronic devices are too large to yield to atomic-level simulation in the foreseeable future and, therefore, calculations of thermal transport must rely on solutions of the Boltzmann transport equation; microscopic phonon scattering rates needed for predictive models are, even for Si, poorly known. Low-dimensional nanostructures, such as carbon nanotubes, are predicted to have novel transport properties; the first quantitative experiments of the thermal conductivity of nanotubes have recently been achieved using microfabricated measurement systems. Nanoscale porosity decreases the permittivity of amorphous dielectrics but porosity also strongly decreases the thermal conductivity. The promise of improved thermoelectric materials and problems of thermal management of optoelectronic devices have stimulated extensive studies of semiconductor superlattices; agreement between experiment and theory is generally poor. Advances in measurement methods, e.g., the 3ω method, time-domain thermoreflectance, sources of coherent phonons, microfabricated test structures, and the scanning thermal microscope, are enabling new capabilities for nanoscale thermal metrology.

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Nanoscale thermal transport

A diverse spectrum of technology drivers such as improved thermal barriers, higher efficiency thermoelectric energy conversion, phase-change memory, heat-assisted magnetic recording, thermal management of nanoscale electronics, and nanoparticles for thermal medical therapies are motivating studies of the applied physics of thermal transport at the nanoscale. This review emphasizes developments in experiment, theory, and computation in the past ten years and summarizes the present status of the field. Interfaces become increasingly important on small length scales. Research during the past decade has extended studies of interfaces between simple metals and inorganic crystals to interfaces with molecular materials and liquids with systematic control of interface chemistry and physics. At separations on the order of ∼1 nm, the science of radiative transport through nanoscale gaps overlaps with thermal conduction by the coupling of electronic and vibrational excitations across weakly bonded or rough interface...

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Nanoscale thermal transport. II. 2003–2012

Since the late 1980s there have been spectacular developments in micromechanical or microelectro-mechanical (MEMS) systems which have enabled the exploration of transduction modes that involve mechanical energy and are based primarily on mechanical phenomena. As a result an innovative family of chemical and biological sensors has emerged. In this article, we discuss sensors with transducers in a form of cantilevers. While MEMS represents a diverse family of designs, devices with simple cantilever configurations are especially attractive as transducers for chemical and biological sensors. The review deals with four important aspects of cantilever transducers: (i) operation principles and models; (ii) microfabrication; (iii) figures of merit; and (iv) applications of cantilever sensors. We also provide a brief analysis of historical predecessors of the modern cantilever sensors.

Cantilever transducers as a platform for chemical and biological sensors

The elastic properties, elastic models and elastic perspectives of metallic glasses

Graphene, a single layer of carbon atoms in a honeycomb lattice, offers a number of fundamentally superior qualities that make it a promising material for a wide range of applications, particularly in electronic devices. Its unique form factor and exceptional physical properties have the potential to enable an entirely new generation of technologies beyond the limits of conventional materials. The extraordinarily high carrier mobility and saturation velocity can enable a fast switching speed for radio-frequency analog circuits. Unadulterated graphene is a semi-metal, incapable of a true off-state, which typically precludes its applications in digital logic electronics without bandgap engineering. The versatility of graphene-based devices goes beyond conventional transistor circuits and includes flexible and transparent electronics, optoelectronics, sensors, electromechanical systems, and energy technologies. Many challenges remain before this relatively new material becomes commercially viable, but laboratory prototypes have already shown the numerous advantages and novel functionality that graphene provides.

Graphene: An Emerging Electronic Material

In order to test whether the low-energy excitations explored extensively in amorphous solids are indeed universal, all measurements published on the low-temperature thermal conductivity and acoustic attenuation in these solids have been reviewed, on a total of over 60 different compositions. The ratio of the phonon wavelength \ensuremath{\lambda} to the phonon mean free path l has been found to lie between ${10}^{\ensuremath{-}3}$ and ${10}^{\ensuremath{-}2}$ in almost all cases, independent of chemical composition and frequency (wavelength) of the elastic waves, which varied by more than nine orders of magnitude in the different experiments. When the data were fitted with the tunneling model, which is based on the assumption of atomic or molecular tunneling states with a certain spectral distribution, the tunneling strength C, which describes their coupling to the lattice, was found to range from ${10}^{\ensuremath{-}4}$ to ${10}^{\ensuremath{-}3}$ in almost all cases. The only exceptions reported so far are certain films of amorphous silicon, germanium, and carbon. In these films, low-temperature acoustic attenuations over two orders of magnitude smaller have been observed compared to all other amorphous solids. Another remarkable observation is that a large number of disordered crystals, and even a thermally equilibrated quasicrystal, have low-energy lattice vibrations that are quantitatively indistinguishable from those of amorphous solids. Their tunneling strengths also range from ${10}^{\ensuremath{-}4}$ to ${10}^{\ensuremath{-}3}.$ These measurements have also been reviewed. It is concluded that the absence of long-range order is neither sufficient nor necessary for the existence of the low-energy excitations.

Low-temperature thermal conductivity and acoustic attenuation in amorphous solids

We have measured the low temperature internal friction (Q{sup -1}) of amorphous silicon (a-Si) films {ital e}-beam evaporation or {sup 28}Si{sup +} implantation leads to the temperature-independent Q{sup -1}{sub 0} plateau common to all amorphous solids For hydrogenated amorphous silicon with 1 at {percent} H produced by hot wire chemical vapor deposition, however, Q{sup -1}{sub 0} is over 200 times smaller than for {ital e}-beam {ital a}-Si This is the first observation of an amorphous solid without any significant low energy excitations It offers the opportunity to study amorphous solids containing controlled densities of tunneling defects, and thus to explore their nature {copyright} {ital 1997} {ital The American Physical Society}

Amorphous Solid without Low Energy Excitations

We report shear modulus (G) and internal friction (Q–1) measurements of large-area monolayer graphene films grown by chemical vapor deposition on copper foil and transferred onto high-Q silicon mechanical oscillators. The shear modulus, extracted from a resonance frequency shift at 0.4 K where the apparatus is most sensitive, averages 280 GPa. This is five times larger than those of the multilayered graphene-based films measured previously. The internal friction is unmeasurable within the sensitivity of our experiment and thus bounded above by Q–1 ≤ 3 × 10–5, which is orders-of-magnitude smaller than that of multilayered graphene-based films. Neither annealing nor interface modification has a measurable effect on G or Q–1. Our results on G are consistent with recent theoretical evaluations and simulations carried out in this work, showing that the shear restoring force transitions from interlayer to intralayer interactions as the film thickness approaches one monolayer.

Shear Modulus of Monolayer Graphene Prepared by Chemical Vapor Deposition

A simple model of thermoelastic dissipation is proposed for general, free standing microelectromechanical (MEMS) and nanoelectromechanical (NEMS) oscillators The theory defines a flexural modal participation factor, the fraction of potential energy stored in flexure, and approximates the internal friction by assuming the energy loss to occur solely via classical thermoelastic dissipation of this component of the motion The theory is compared to the measured internal friction of a high Q mode of a single-crystal silicon double paddle oscillator The loss at high temperature (above 150 K) is found to be in good agreement with the theoretical prediction The importance of this dissipation mechanism as a function of scale is briefly discussed We find that the relative importance of this mechanism scales with the size of the structure, and that for nanoscale structures it is less important than intrinsic phonon–phonon scattering

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Thermoelastic loss in microscale oscillators

The ubiquitous low-energy excitations, known as two-level tunneling systems (TLSs), are one of the universal phenomena of amorphous solids. Low temperature elastic measurements show that e-beam amorphous silicon (a-Si) contains a variable density of TLSs which diminishes as the growth temperature reaches 400 °C. Structural analyses show that these a-Si films become denser and more structurally ordered. We conclude that the enhanced surface energetics at a high growth temperature improved the amorphous structural network of e-beam a-Si and removed TLSs. This work obviates the role hydrogen was previously thought to play in removing TLSs in the hydrogenated form of a-Si and suggests it is possible to prepare "perfect" amorphous solids with "crystal-like" properties for applications.

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Xiao Liu

Papers

Low-temperature thermal conductivity and acoustic attenuation in amorphous solids

Amorphous Solid without Low Energy Excitations

Shear Modulus of Monolayer Graphene Prepared by Chemical Vapor Deposition

Thermoelastic loss in microscale oscillators

Hydrogen-free amorphous silicon with no tunneling states.