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The electron beam (e-beam) in the scanning electron microscopy (SEM) provides an appealing mobile heating source for thermal metrology with spatial resolution of ∼1 nm, but the lack of systematic quantification of the e-beam heating power limits such application development. Here, we systemically study e-beam heating in LPCVD silicon nitride (SiNx) thin-films with thickness ranging from 200 to 500 nm from both experiments and complementary Monte Carlo simulations using the CASINO software package. There is good agreement about the thickness-dependent e-beam energy absorption of thin-film between modeling predictions and experiments. Using the absorption results, we then demonstrate adapting the e-beam as a quantitative heating source by measuring the thickness-dependent thermal conductivity of SiNx thin-films, with the results validated to within 7% by a separate Joule heating experiment. The results described here will open a new avenue for using SEM e-beams as a mobile heating source for advanced nanoscale thermal metrology development.

Applications such as solid-state waste-heat energy conversion, infrared sensing, and thermally-driven electron emission rely on pyroelectric materials (a subclass of dielectric piezoelectrics) which exhibit temperature-dependent changes in polarization. Although enhanced dielectric and piezoelectric responses are typically found at polarization instabilities such as temperature- and chemically induced phase boundaries, large pyroelectric effects have been primarily limited in study to temperature-induced phase boundaries. Here, we directly identify the magnitude and sign of the intrinsic, extrinsic, dielectric, and secondary pyroelectric contributions to the total pyroelectric response as a function of chemistry in thin films of the canonical ferroelectric PbZr1-xTixO3 (x = 0.40, 0.48, 0.60, and 0.80) across the morphotropic phase boundary. Using phase-sensitive frequency and applied dc-bias methods, the various pyroelectric contributions were measured. It is found that the total pyroelectric response decreases systematically as one moves from higher to lower titanium contents. This arises from a combination of decreasing intrinsic response (-232 to -97 μC m-2 K-1) and a sign inversion (+33 to -17 μC m-2 K-1) of the extrinsic contribution upon crossing the morphotropic phase boundary. Additionally, the measured secondary and dielectric contributions span between -70 and -29 and 10-115 μC m-2 K-1 under applied fields, respectively, following closely trends in the piezoelectric and dielectric susceptibility. These findings and methodologies provide novel insights into the understudied realm of pyroelectric response.

Rebuilding phonon mean free path (MFP) spectra from experimental data is integral to phonon MFP spectroscopy. However, being based on effective thermal conductivity, the current integral eq...

Considerable advances in manipulating heat flow in solids have been made through the innovation of artificial thermal structures such as thermal diodes, camouflages, and cloaks. Such thermal devices can be readily constructed only at the macroscale by mechanically assembling different materials with distinct values of thermal conductivity. Here, we extend these concepts to the microscale by demonstrating a monolithic material structure on which nearly arbitrary microscale thermal metamaterial patterns can be written and programmed. It is based on a single, suspended silicon membrane whose thermal conductivity is locally, continuously, and reversibly engineered over a wide range (between 2 and 65 W/m·K) and with fine spatial resolution (10-100 nm) by focused ion irradiation. Our thermal cloak demonstration shows how ion-write microthermotics can be used as a lithography-free platform to create thermal metamaterials that control heat flow at the microscale.

The need for efficient energy utilization is driving research into ways to harvest ubiquitous waste heat. Here, we explore pyroelectric energy conversion from low-grade thermal sources that exploits strong field- and temperature-induced polarization susceptibilities in the relaxor ferroelectric 0.68Pb(Mg1/3Nb2/3)O3–0.32PbTiO3. Electric-field-driven enhancement of the pyroelectric response (as large as −550 μC m−2 K−1) and suppression of the dielectric response (by 72%) yield substantial figures of merit for pyroelectric energy conversion. Field- and temperature-dependent pyroelectric measurements highlight the role of polarization rotation and field-induced polarization in mediating these effects. Solid-state, thin-film devices that convert low-grade heat into electrical energy are demonstrated using pyroelectric Ericsson cycles, and optimized to yield maximum energy density, power density and efficiency of 1.06 J cm−3, 526 W cm−3 and 19% of Carnot, respectively; the highest values reported to date and equivalent to the performance of a thermoelectric with an effective ZT ≈ 1.16 for a temperature change of 10 K. Our findings suggest that pyroelectric devices may be competitive with thermoelectric devices for low-grade thermal harvesting. Pyroelectric energy conversion in a thin-film relaxor ferroelectric is studied under an electric field, resulting in high energy and power densities. Performance is equivalent to a ZT = 1.16 thermoelectric, competitive for low-grade thermal harvesting.

Ferroelectric materials attract attention as potential solid-state thermal switches, due to various phenomena near their solid-state phase transition. In principle these phenomena could also be triggered by an external electric field, though recent experiments on thin films have shown only weak effects. The authors explore this issue by solving the linearized Boltzmann equation with first-principles force constants, to study the thermal conductivity of PbTiO${}_{3}$ as a function of electric field. The results emphasize the need for large-domain samples and lower temperatures, to have the best chance at large voltage-controlled thermal switching in this class of materials.

Many materials have anisotropic thermal conductivity, with diverse applications such as transistors, thermoelectrics, and laser gain media. Yet measuring the thermal conductivity tensor of such materials remains a challenge, particularly for materials lacking in-plane symmetry (i.e., transversely anisotropic materials). This paper demonstrates thermal conductivity tensor measurements for transversely anisotropic materials, by extending beam-offset frequency-domain thermoreflectance (BO-FDTR) methods which had previously been limited to transversely isotropic materials. Extensive sensitivity analysis is used to determine an appropriate range of heating frequencies and beam offsets to extract various tensor elements. This technique is demonstrated on a model transversely anisotropic material, x-cut quartz ( α-SiO2), by combining beam offset measurements from different sample orientations to reconstruct the full in-plane thermal conductivity tensor. The technique is also validated by measurements on two transversely isotropic materials, sapphire and highly oriented pyrolytic graphite (HOPG). The anisotropic measurements demonstrated very good self-consistency in correctly identifying isotropic directions when present, with residual anisotropy errors below 4% for sapphire and 2% for HOPG and quartz. Finally, a computational case study (simulated experiment) shows how the arbitrary in-plane thermal conductivity tensor of a fictitious material with high in-plane anisotropy can in principle be obtained from only a single sample orientation, rather than multiple orientations like the experiments on x-cut quartz.

The hot disk transient plane source (TPS) method is a widely used standard technique (ISO 22007–2) for characterizing the thermal properties of materials, especially the thermal conductivity, k. Despite its well-established reliability for a wide variety of common materials, the hot disk TPS method is also known to suffer from substantial systematic errors when applied to low-k thermal insulation materials, because of the discrepancies between the idealized model used for data analysis and the actual heat transfer process. Here, we present a combined numerical and experimental study of the influence of the geometry of the hot disk sensor on the measured k value of low-k materials. We demonstrate that the error is strongly affected by the finite thickness and thermal mass of the sensor's insulation layer as well as the corresponding increase of the effective heater size beyond the radius of the embedded metal heater itself. We further numerically investigate the dependence of the error on the sample thermal properties, confirming that the errors are worse in low-k samples. A simple polynomial correction function is provided based on the numerical error analysis, which converts the apparent (erroneous) result from a standard hot disk TPS measurement to a more accurate value of k. To experimentally validate the conclusions from numerical simulations, standard polyimide (Kapton) sensors are systematically optimized (thinned) by etching and used to measure low-k materials, including a standard polystyrene foam, a commercial Airloy® x56 aerogel, and a commercial Hydrophobic Silica Disk aerogel from Aerogel Technologies, LLC. The experimental results clearly demonstrate the strong influence of the sensor thickness. The k results of these samples obtained using either the optimized sensor or the pristine sensor then corrected with the corresponding polynomial correction functions are in good agreement with the values measured independently using a steady-state heat flowmeter (HFM) method: whereas the raw values measured with the pristine sensor are in error by 35% and 40% compared to the HFM reference values for the Airloy® x56 and the hydrophobic aerogel, respectively, the correction function greatly reduces those errors to

Temperature- and electric-field-induced structural transitions in a polydomain ferroelectric can have profound effects on its electrothermal susceptibilities. Here, the role of such ferroelastic domains on the pyroelectric and electrocaloric response is experimentally investigated in thin films of the tetragonal ferroelectric PbZr0.2 Ti0.8 O3 . By utilizing epitaxial strain, a rich set of ferroelastic polydomain states spanning a broad thermodynamic phase space are stabilized. Using temperature-dependent scanning-probe microscopy, X-ray diffraction, and high-frequency phase-sensitive pyroelectric measurements, the propensity of domains to reconfigure under a temperature perturbation is quantitatively studied. In turn, the "extrinsic" contributions to pyroelectricity exclusively due to changes between the ferroelastic domain population is elucidated as a function of epitaxial strain. Further, using highly sensitive thin-film resistive thermometry, direct electrocaloric temperature changes are measured on these polydomain thin films for the first time. The results demonstrate that temperature- and electric-field-driven domain interconversion under compressive strain diminish both the pyroelectric and the electrocaloric effects, while both these susceptibilities are enhanced due to the exact-opposite effect from the extrinsic contributions under tensile strain.

We quantify the tradeoff between ZT and materials cost for thermoelectric energy scavengers, considering 31 real materials. It is nearly always practical to aggressively miniaturize the legs until the overall system cost is limited by the heat exchangers and ceramic spreader plates. For thermoelectric materials costing less than C crit . ‴ ∼ 1 $/cm3 (∼100 $/kg), the material might as well be free, and even costs as high as ∼10 $/cm3 (∼1000 $/kg) may still be acceptable. Thus, the materials goal is maximizing ZT at (almost) any cost.

Simultaneous increases in electrical conductivity (up to 200%) and thermopower (up to 70%) are demonstrated by introducing native defects in Bi2 Te3 films, leading to a high power factor of 3.4 × 10(-3) W m(-1) K(-2). The maximum enhancement of the power factor occurs when the native defects act beneficially both as electron donors and energy filters to mobile electrons. They also act as effective phonon scatterers.

Thermal conductivity is estimated using a 3-omega technique for an individual bismuth nanowire (diameter: 595 nm, length: 2.24 mm) covered with a quartz template. To evaluate the thermal conductivity of the nanowire, we propose a simple model of thermal and electrical transfer functions for the nanowire that assumes a linear combination of that of the line heater on the substrate and a suspended wire. Since the out-of-phase third-harmonic component of the electrical transfer function depends only on the thermal diffusivity of the nanowire, measurement of the frequency dependence is carried out. A distinct extreme value of the frequency has been observed, as expected, and estimation of the thermal conductivity of the nanowire covered with the quartz is attempted. Although the thermal conductivity at 300 K is 9.8 W/mK, somewhat smaller than that of bulk bismuth, the temperature dependence of the thermal conductivity is quite different from that of bulk bismuth, and decreased linearly with decreasing temperature. In particular, this shows that the thermal conductivity obtained is suppressed in the low-temperature region by phonon confinement in the nanowire.

Phonons can display both wave-like and particle-like behaviour during thermal transport. While thermal transport in silicon nanomeshes has been previously interpreted by phonon wave effects due to interference with periodic structures, as well as phonon particle effects including backscattering, the dominant mechanism responsible for thermal conductivity reductions below classical predictions still remains unclear. Here we isolate the wave-related coherence effects by comparing periodic and aperiodic nanomeshes, and quantify the backscattering effect by comparing variable-pitch nanomeshes. We measure identical (within 6% uncertainty) thermal conductivities for periodic and aperiodic nanomeshes of the same average pitch, and reduced thermal conductivities for nanomeshes with smaller pitches. Ray tracing simulations support the measurement results. We conclude phonon coherence is unimportant for thermal transport in silicon nanomeshes with periodicities of 100 nm and higher and temperatures above 14 K, and phonon backscattering, as manifested in the classical size effect, is responsible for the thermal conductivity reduction., Low thermal conductivities in nanomeshes have been attributed to both wave-like and particle-like behaviour of phonons. Here, the authors use periodicity-controlled silicon nanomeshes to show that the particle backscattering effect dominates for periodicities above 100 nm and temperatures above 14 K.

The seventh U.S.–Japan Joint Seminar on Nanoscale Transport Phenomena was held in Shima, Japan, from December 11 to 14, 2011. The goals of this joint seminar were to provide a critical assessment of the state of the art and future directions in the field of nanoscale transport phenomena and energy conversion processes, to foster U.S.–Japan collaborations, and to provide international exposure to a new generation of scientists in this field. Issues discussed in the joint seminar were organized in 10 topical sessions, including (1) nanoscale thermophysical measurements; (2) optical characterization; (3) thermal and molecular transport; (4) phonon transport modeling; (5) energy storage and conversion; (6) nanoscale fluidics and phase change phenomena; (7) biological and organic systems; (8) interfacial thermal transport; (9) novel thermoelectric and thermal management materials; and (10) nanocarbon materials and devices. In addition to these topical sessions, the joint seminar featured an opening plenary ses...

Molecular dynamics simulations are performed to investigate the thermal transport properties of a three-dimensional (3D) anisotropic phononic crystal consisting of silicon nanowires and films. The calculation shows that the in-plane thermal conductivity is negatively correlated with the out-of-plane thermal conductivity upon making geometric changes, whether varying the nanowire diameter or the film thickness. This enables the anisotropy ratio of thermal conductivity to be tailored over a wide range, in some cases by more than a factor of 20. Similar trends in thermal conductivity are also observed from an independent phonon ray tracing simulation considering only diffuse boundary scattering effects, though the range of anisotropy ratios is smaller than that obtained in MD simulation. By analyzing the phonon dispersion relation with varied geometric parameters, it is found that increasing the nanowire diameter increases the out-of-plane acoustic phonon group velocities, but reduces the in-plane longitudinal and fast transverse acoustic phonon group velocities. The calculated phonon irradiation further verified the negative correlation between the in-plane and the out-of-plane thermal conductivity. The proposed 3D phononic crystal may find potential application in thermoelectrics, energy storage, catalysis and sensing applications owing to its widely tailorable thermal conductivity.

Decoupling charge and heat transport In metals, electrons carry both charge and heat. As a consequence, electrical conductivity and the electronic contribution to the thermal conductivity are typically proportional to each other. Lee et al. found a large violation of this so-called Wiedemann-Franz law near the insulator-metal transition in VO 2 nanobeams. In the metallic phase, the electronic contribution to thermal conductivity was much smaller than what would be expected from the Wiedemann-Franz law. The results can be explained in terms of independent propagation of charge and heat in a strongly correlated system. Science , this issue p. 371

Graphene is nature's thinnest elastic membrane, and its morphology has important impacts on its electrical, mechanical, and electromechanical properties. Here we report manipulation of the morphology of suspended graphene via electrostatic and thermal control. By measuring the out-of-plane deflection as a function of applied gate voltage and number of layers, we show that graphene adopts a parabolic profile at large gate voltages with inhomogeneous distribution of charge density and strain. Unclamped graphene sheets slide into the trench under tension; for doubly clamped devices, the results are well-accounted for by membrane deflection with effective Young's modulus E = 1.1 TPa. Upon cooling to 100 K, we observe buckling-induced ripples in the central portion and large upward buckling of the free edges, which arises from graphene's large negative thermal expansion coefficient.

The thermal conductivity reduction due to grain boundary scattering is widely interpreted using a scattering length assumed equal to the grain size and independent of the phonon frequency (gray). To assess these assumptions and decouple the contributions of porosity and grain size, five samples of undoped nanocrystalline silicon have been measured with average grain sizes ranging from 550 to 64 nm and porosities from 17% to less than 1%, at temperatures from 310 to 16 K. The samples were prepared using current activated, pressure assisted densification (CAPAD). At low temperature the thermal conductivities of all samples show a T(2) dependence which cannot be explained by any traditional gray model. The measurements are explained over the entire temperature range by a new frequency-dependent model in which the mean free path for grain boundary scattering is inversely proportional to the phonon frequency, which is shown to be consistent with asymptotic analysis of atomistic simulations from the literature. In all cases the recommended boundary scattering length is smaller than the average grain size. These results should prove useful for the integration of nanocrystalline materials in devices such as advanced thermoelectrics.

Graphene is nature's thinnest elastic material and displays exceptional mechanical and electronic properties. Ripples are an intrinsic feature of graphene sheets and are expected to strongly influence electronic properties by inducing effective magnetic fields and changing local potentials. The ability to control ripple structure in graphene could allow device design based on local strain and selective bandgap engineering. Here, we report the first direct observation and controlled creation of one- and two-dimensional periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains. We are able to control ripple orientation, wavelength and amplitude by controlling boundary conditions and making use of graphene's negative thermal expansion coefficient (TEC), which we measure to be much larger than that of graphite. These results elucidate the ripple formation process, which can be understood in terms of classical thin-film elasticity theory. This should lead to an improved understanding of suspended graphene devices, a controlled engineering of thermal stress in large-scale graphene electronics, and a systematic investigation of the effect of ripples on the electronic properties of graphene.

Nanostructures have a profound impact on the transport of heat and energy by electrons, phonons, and photons. In this paper, we will discuss some of the nanoscale heat transfer effects on phonon and photon transport and their implications for thermoelectric and thermophotovoltaic energy conversion technologies. For example, low thermal conductivity materials with good electrical properties are required in solid-state refrigerators and power generators to achieve high energy conversion efficiency. Various size effects on carrier transport in nanostructures can be utilized to engineer new structures with improved energy conversion efficiency. The thermal conductivity of superlattices will be used to illustrate the phonon transport characteristics in nanostructures. In another example, we will discuss some nanoscale thermal radiation phenomena, such as interference, tunneling, and surface waves, that can potentially be exploited to improve the efficiency of thermophotovoltaic power generation devices.

The net-radiation method of radiative heat transfer has been combined with the diffuse mismatch interface condition to develop a model for the phonon thermal conductivity of superlattice nanowires. The important size effect is increased classical scattering at interfaces and side walls, which is treated as diffuse and gray (frequency independent). Coherence and quantum confinement effects are neglected, which should be appropriate for typical nanowires at room temperature. An isotropic, sine-type dispersion relation is used which is a significant improvement over the common Debye dispersion. Without any adjustable parameters, the model captures the effects of diameter, segment length, and transmissivity. A simpler picture is offered in terms of Matthiessen’s rule and effective mean free paths. The limitations of the model are also discussed. For a model Si/Ge superlattice nanowire at 300 K, the thermal conductivity is reduced below the alloy limit (7.0 W/m-K) when the diameter is less than 15 nm and/or the segment length is less than 20 nm.Copyright © 2003 by ASME

A rigorous derivation is given for the thermal conductivity accumulation function and mean free path (MFP) spectrum of an isotropic bulk material. The key physical insight is to express the kinetic theory integral in terms of MFP rather than frequency. Extending this framework to incorporate boundary scattering in nanostructures leads to an integral equation that transforms a material's bulk MFP spectrum into the size-dependent thermal conductivity of the nanostructure. The kernel of this transform represents the boundary scattering rule for the particular type of nanostructure. The principal benefit of this transform is that it requires only a single function, the material's bulk MFP spectrum, or equivalently its accumulation function. Explicit knowledge of the material's dispersion relation and frequency-dependent bulk MFPs is not needed, nor is a summation over polarizations, because the bulk MFP spectrum already contains this information in exactly the form required to evaluate boundary scattering. The utility of this framework is demonstrated through a case study of six models for the phonon thermal conductivity of silicon: three analytical, one gray, and two numerical.

The thermal conductivity of graphene and ultrathin graphite (thickness from 1 to ∼20 layers) encased within silicon dioxide was measured using a heat spreader method. The thermal conductivity increases with the number of graphene layers, approaching the in-plane thermal conductivity of bulk graphite for the thickest samples, while showing suppression below 160 W/m-K at room temperature for single-layer graphene. These results show the strong effect of the encasing oxide in disrupting the thermal conductivity of adjacent graphene layers, an effect that penetrates a characteristic distance of approximately 2.5 nm (∼7 layers) into the core layers at room temperature.

A model has been established for the effective thermal conductivity of a bulk polycrystal made of randomly oriented superlattice grains with anisotropic thermal conductivity. The in-plane and cross-plane thermal conductivities of each superlattice grain are combined using an analytical averaging rule that is verified using finite element methods. The superlattice conductivities are calculated using frequency dependent solutions of the Boltzmann transport equation, which capture greater thermal conductivity reductions as compared to the simpler gray medium approximation. The model is applied to a PbTe/Sb_2Te_3 nanobulk material to investigate the effects of period, specularity, and temperature. The calculations show that the effective thermal conductivity of the polycrystal is most sensitive to the in-plane conductivity of each superlattice grain, which is generally four to five times larger than the cross-plane conductivity of a grain. The model is compared to experimental measurements of the same system for periods ranging from 287 to 1590 nm and temperatures from 300 to 500 K. The comparison suggests that the effective specularity increases with increasing annealing temperature and shows that these samples are in a mixed regime where both Umklapp and boundary scattering are important.

Using Raman spectroscopy, we measure the optical phonon energies of suspended graphene before, during, and after thermal cycling between 300 and 700 K. After cycling, we observe large upshifts ( approximately 25 cm(-1)) of the G band frequency in the graphene on the substrate region due to compression induced by the thermal contraction of the underlying substrate, while the G band in the suspended region remains unchanged. From these large upshifts, we estimate the compression in the substrate region to be approximately 0.4%. The large mismatch in compression between the substrate and suspended regions causes a rippling of the suspended graphene, which compensates for the change in lattice constant due to the compression. The amplitude (A) and wavelength (lambda) of the ripples, as measured by atomic force microscopy, correspond to an effective change in length Deltal/l that is consistent with the compression values determined from the Raman data.

In analogy to an electrical diode, a thermal rectifier transports heat more easily in one direction than in the reverse direction. Among various possible nanoscale rectification mechanisms, a ballistic rectifier relies on asymmetric scattering of energy carriers, as has been suggested for phonon transport in a sawtooth nanowire [S. Saha, L. Shi, & R. Prasher, IMECE 2006] or nanowire with special surface specularity function [N.A. Roberts and D.G. Walker, ITherm 2008]. We have used a Landauer-Buttiker method as well as a Monte Carlo method to model the asymmetric heat transport in such nanostructures, with careful attention to boundary conditions that satisfy the 2nd Law of Thermodynamics. The calculations show that ballistic rectification is only significant at relatively large “thermal bias,” which causes significant anisotropy in the distribution function of energy carriers emitted at each of the two thermal contacts. We also propose experiments to observe this phenomenon using either phonons or photons.Copyright © 2009 by ASME

In analogy to the asymmetric transport of electricity in a familiar electrical diode, a thermal rectifier transports heat more favorably in one direction than in the reverse direction. One approach to thermal rectification is asymmetric scattering of phonons and/or electrons, similar to suggestions in the literature for a sawtooth nanowire [1] or 2-dimensional electron gas with triangular scatterers [2]. To model the asymmetric heat transport in such nanostructures, we have used phonon ray-tracing, focusing on characteristic lengths that are small compared to the mean free path of phonons in bulk. To calculate the heat transfer we use a transmission-based (Landauer-Buttiker) method. The system geometry is described by a four-dimensional transfer function that depends on the position and angle of phonon emission and absorption from each of two contacts. At small temperature gradients, the phonon distribution function is very close to the usual isotropic equilibrium (Bose-Einstein) distribution, and there is no thermal rectification. In contrast, at large temperature gradients, the anisotropy in the phonon distribution function becomes significant, and the resulting heat flux vs. temperature curve (analogous to I-V curve of a diode) reveals large thermal rectification.Copyright © 2008 by ASME

The thermal conductivity is modeled with a spectral form of kinetic theory k = 13CωνLdω (1) where ω is the angular frequency, Cω is the specific heat per unit frequency, ν = ∂ω/∂q is the group velocity, and L is the effective mean free path (MFP) which combines bulk and boundary scattering using Matthiessen’s rule: Cω = ħω DOS ∂f/∂T (2)L−1 = Lbulk−1 + Lboundary−1. (3) Here q is the wavevector, DOS is the density of states (acoustic modes only), T is the temperature, and f is the Bose-Einstein distribution function.Copyright © 2008 by ASME

The Cahill-Pohl/Einstein model of minimum phonon thermal conductivity ( κmin), which assumes isotropic material properties, is widely successful as the lower limit for fully dense amorphous and disordered materials. However, measurements of disordered highly anisotropic layered WSe2 [Chiritescu et al., Science 315, 351 (2007)] fall below the isotropic κmin limit by at least a factor of four. Here, we generalize the isotropic κmin to be anisotropic, suitable for both layered and chain-like materials with any anisotropy ratio. We obtain compact algebraic expressions in limiting temperature regimes for heat transfer along both c-axis ( κmin−c) and ab-plane ( κmin−ab). Applying this framework to the disordered layered WSe2 with no free parameters brings the theoretical κmin−c back in line with the experimental results. The anisotropic corrections result from both a phonon focusing effect and a first Brillouin zone truncation effect.

We have calculated the mean free path (MFP) of phonons associated with grain boundary scattering in polycrystalline nanostructures, by developing a Monte Carlo ray tracing transmission model that can be applied to arbitrary geometries. The calculations for various log-normal grain-size distributions realized by Voronoi diagrams and genetic algorithms show that the boundary-scattering MFP in a polycrystalline nanostructure is 20%–30% longer than that in a simple cubic structure with the same average grain size (defined by matching grain volumes). The impact on thermal conductivity is quantified for nanocrystalline silicon by using Matthiessen's rule to combine boundary scattering with intrinsic phonon-phonon scattering. The result reveals that the thermal conductivity depends strongly on the average grain size but only weakly on the breadth of the grain-size distribution, and thus, the simple cubic structure is a reasonable approximation for the polydisperse grain structure of actual materials.

Thermoelectric effects enable direct energy conversion between heat and electricity. Various size effects can be explored to increase the thermoelectric performance of nanostructures compared to bulk. Boundary scattering reduces the phonon thermal conductivity, and quantum confinement and interface energy filtering can improve the electronic power factor. Theoretical and experimental results are described for thin films, nanowires, and nanocomposites.

For the effective use of nanowires and nanotubes in their many possible applications in sensing, computation and memory, optoelectronics, and energy conversion, it is important to understand their thermal properties, which may differ considerably from bulk [1]. For example, there is good agreement between theory and experiments on Si nanowires showing that the classical size effect of phonon boundary scattering may reduce the thermal conductivity by up to several orders of magnitude for diameters of 40 nm and up [2, 3, 12, 13]. However, more experiments are needed at 20 nm and smaller diameters. There is also a need for experiments on the specific heat of single nanowires, which is intimately related to thermal conductivity by kinetic theory, and may be altered by quantum confinement effects. We have previously measured the specific heat of a pellet of TiO2 nanotubes of ∼3 nm wall thickness and found it similar to the bulk material at temperatures above ∼80 K [4]; however, questions remain about the possible interactions between adjacent tubes, which single-tube studies would resolve.Copyright © 2005 by ASME

The large thermal conductivity reduction observed in superlattices has led to the reports of significantly increased thermoelectric figure-of-merit by several groups. The mechanisms of thermal conductivity reduction in superlattices were scrutinized from different angles over the last decade. This paper summarizes our current understanding on the heat conduction mechanisms in superlattices. Among several potential mechanisms, the interface scattering, particularly diffuse interface scattering, plays the most important role. Conclusions drawn from the studies on superlattices have implications to other nanostructured thermoelectric materials.

A Debye model is applied to a simple phonon radiation framework to predict the thermal conductivity of a SiGe segmented nanowire. A gray Matthiessen's rule is used to account for bulk scattering while phonon confinement and wave effects are neglected. When either the diameter D or segment length L is smaller than the bulk phonon mean free path the effective thermal conductivity is reduced significantly. In particular, combining diffuse side walls with the diffuse mismatch interface condition at room temperature the alloy limit of 8.5 W/m-K is surpassed for L

An incoherent particle model has been developed to predict the phonon thermal conductivity of nanowires and superlattice nanowires. It is argued that the surface roughness of most real nanowires prevents the formation of idealized confined dispersion relations for typical temperatures and diameters. Instead, the three-dimensional bulk dispersion is used, thus addressing only classical size effects. Four adjustable parameters capture the effects of diameter, superlattice, Umklapp, impurity, and alloy scattering. Predictions are compared with experimental data for nanowires and superlattice nanowires down to 22 nm diameter and 20 K, and are in good agreement above ∼40 nm diameter. The analysis suggests that ideal low thermal conductivity nanowires for thermoelectric applications would have small-diameter, alternating alloy segments that are acoustically dissimilar but electrically similar.

The thermal conductivity of pairs of boron nanoribbons can be switched between high and low values by wetting the interface between the nanoribbons with various solutions.

The effects of in-plane (IP) and cross-plane (CP) interatomic bonding strengths on the IP and CP thermal conductivities of a model layered material are investigated using molecular dynamics and lattice dynamics. Increasing the IP bonding strength while holding the CP bonding constant increases the IP thermal conductivity, but reduces the CP thermal conductivity. Analogous but weaker trends are seen when increasing the CP bonding strength while holding the IP bonding constant. These results show how both low- and high-symmetry directions must be considered to understand the effects of phonon focusing on the thermal conductivity tensor of highly anisotropic materials.

Wave packet dynamics is used to investigate the scattering of longitudinal (LA), transverse (TA), and bending-mode (ZA) phonons at the zigzag and armchair edges of suspended graphene. The interatomic forces are calculated using a linearized Tersoff potential. The strength of a boundary scattering event at impeding energy flow is described by a forward scattering coefficient, similar in spirit to a specularity parameter. For armchair boundaries, this scattering coefficient is found to depend strongly on the magnitude, direction, and polarization of the incident wavevector, while for zigzag boundaries, the forward scattering coefficient is found to always be unity regardless of wavevector and polarization. Wave packet splitting is observed for ZA phonons incident on armchair boundaries, while both splitting and mode conversion are observed for LA and TA phonons incident on both zigzag and armchair boundaries. These simulation results show that armchair boundaries impede the forward propagation of acoustic p...

Suspended shadow-mask evaporation is a simple, robust technique for fabricating Josephson-junction structures using scanning electron-beam lithography. The basic process entails the fabrication of an undercut structure in a resist bilayer to form a suspended “bridge,” followed by two angle evaporations of superconducting material with a brief oxidation step in between. The result is two overlapping wires separated by a thin layer of oxide. Josephson junctions with sub-50-nm diameters are of particular interest in quantum computing research. Unfortunately, standard shadow-mask fabrication techniques are highly variable at linewidths below 100nm, due to the difficulty of simultaneously fabricating a narrow line and a large undercut region. While most previous processes used poly(methylmethacrylate) (PMMA) for the top (imaging)layer and either lower-molecular-weight PMMA or a PMMA/methacrylic acid copolymer for the bottom (support) layer, the authors’ process uses a PMMA/poly(methylglutarimide) (PMGI) bilaye...