Ballistic Thermal Conductance Research Articles

Length-dependent thermal transport and ballistic thermal conduction

Probing length-dependent thermal conductivity of a given material has been considered as an important experimental method to determine the length of ballistic thermal conduction, or equivalently, the averaged phonon mean free path (l). However, many previous thermal transport measurements have focused on varying the lateral dimensions of samples, rendering the experimental interpretation indirect. Moreover, deducing l is model-dependent in many optical measurement techniques. In addition, finite contact thermal resistances and variations of sample qualities are very likely to obscure the effect in practice, leading to an overestimation of l. We point out that directly investigating one-dimensional length-dependent (normalized) thermal resistance is a better experimental method to determine l. In this regard, we find that no clear experimental data strongly support ballistic thermal conduction of Si or Ge at room temperature. On the other hand, data of both homogeneously-alloyed SiGe nanowires and heterogeneously-interfaced Si-Ge core-shell nanowires provide undisputed evidence for ballistic thermal conduction over several micrometers at room temperature.

Micron-scale ballistic thermal conduction and suppressed thermal conductivity in heterogeneously interfaced nanowires

By employing three different measurement methods, we rigorously show that micron-scale ballistic thermal conduction can be found in Si-Ge heterogeneously interfaced nanowires exhibiting low thermal conductivities. The heterogeneous interfaces localize most high-frequency phonons and suppress the total thermal conductivity below that of Si or Ge. Remarkably, the suppressed thermal conductivity is accompanied with an elongation of phonon mean free paths over 5 \ensuremath{\mu}m at room temperature, which is not only more than 25 times longer than that of Si or Ge but also longer than those of the best thermal conductors like diamond or graphene. We estimate that only 0.1% of the excited phonons carry out the heat transfer process, and, unlike phonon transport in Si or Ge, the low-frequency phonons in Si-Ge core-shell nanowires are found to be insensitive to twin boundaries, defects, and local strain. The ballistic thermal conduction persisting over 5 \ensuremath{\mu}m, along with the suppressed thermal conductivity, will enable wave engineering of phonons at room temperature and inspire new improvements of thermoelectric devices.

Ballistic thermal transport in a cylindrical semiconductor nanowire modulated with bridge contacts

Using the scattering-matrix method, we studied ballistic phonon transmission and thermal conductance at low temperatures in a cylindrical quantum wire with bridge contacts. The transmission coefficient exhibited a stepped profile, which became more evident as the bridge radius increased. When the dimensions of the bridge are identical to those of main wires, we observed a quantum platform of the thermal conductance, even in the presence of interface scattering. When the dimensions of the bridge are smaller than those of main wires, however, we could not observe the quantum platform. We also revealed other interesting physical properties, such as universal quantum thermal conductance and resonant transmission. A brief analysis of these results is given.

Role of atomic vacancies and boundary conditions on ballistic thermal transport in graphene nanoribbons

Quantum thermal transport in armchair and zigzag graphene nanoribbons is investigated in the presence of single atomic vacancies and subject to different boundary conditions. We start with a full comparison of the phonon polarizations and energy dispersions as given by a fifth-nearest-neighbor force-constant model (5NNFCM) and by elasticity theory of continuum membranes (ETCM). For free-edge ribbons, we discuss the behavior of an additional acoustic edge-localized flexural mode, known as fourth acoustic branch (4ZA), which has a small gap when it is obtained by the 5NNFCM. Then, we show that ribbons with supported edges have a sample-size dependent energy gap in the phonon spectrum which is particularly large for in-plane modes. Irrespective to the calculation method and the boundary condition, the dependence of the energy gap for the low-energy optical phonon modes against the ribbon width $W$ is found to be proportional to $1/W$ for in-plane, and $1/{W}^{2}$ for out-of-plane phonon modes. Using the 5NNFCM, the ballistic thermal conductance and its contributions from every single phonon mode are then obtained by the nonequilibrium Green's function technique. We found that, while edge and central localized single atomic vacancies do not affect the low-energy transmission function of in-plane phonon modes, they reduce considerably the contributions of the flexural modes. On the other hand, in-plane modes contributions are strongly dependent on the boundary conditions and at low temperatures can be highly reduced in supported-edge samples. These findings could open a route to engineer graphene based devices where it is possible to discriminate the relative contribution of polarized phonons and to tune the thermal transport on the nanoscale.

Thermal conductance associated with six types of vibration modes in quantum wire modulated with quantum dot

Abstract We study the ballistic phonon transport and thermal conductance of six low-lying vibration modes in quantum wire modulated with quantum dot at low temperatures. A comparative analysis is made among the six vibrational modes. The results show that the transmission rates of the six vibrational modes relative to reduced frequency display periodic or quasi-periodic oscillatory behavior. Among the four acoustic modes, the thermal conductance contributed by the torsional mode is the smallest, and the thermal conductances of other acoustic modes have adjacent values. It is also found that the thermal conductance of the optical mode increases from zero monotonously. Moreover, the total thermal conductance in concavity-shaped quantum structure is lower than that in convexity-shaped quantum structure. These thermal conductance values can be adjusted by changing the structural parameters of the quantum dot.

Tunable anisotropic thermal conduction in graphane nanoribbons

Graphane and graphene are both two-dimensional materials but of different bonding configurations, which can result in distinct thermal conduction properties. We simulate thermal conduction in graphane nanoribbons (GANRs) using the nonequilibrium Green's function method. We find anisotropic thermal conduction in GANRs, with zigzag GANRs giving higher thermal conductance than armchair ones. Compared to the graphene counterparts, GANRs show lower ballistic thermal conductance and stronger thermal conductance anisotropy. Furthermore, hydrogen vacancies of GANRs considerably suppress thermal conduction, accompanied by enhanced thermal conductance anisotropy. The tunable thermal conduction, realized by controlling the ribbon width, edge shape, and hydrogen vacancy concentration of GANRs, could be useful for thermal management and thermoelectric applications.

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.

Ballistic thermal conductance by phonons through superlattice quantum-waveguides

Ballistic thermal conductances (BTCs) by phonons through superlattice quantum-waveguides are investigated by using the scattering-matrix method and the elastic continuum theory. A comparison for the cylindrical model (CM) and the rectangular model (RM) is addressed. We find that for these two models, the quantum thermal conductance can be observed even when the superlattices exist in quantum-waveguides. At low temperature, BTCs for the CM and the RM present almost the same behaviors regardless of the periodic length of superlattices. However, at higher temperature, BTCs for the RM are larger than those for the CM stemming from lower cutoff frequencies of high order modes for the RM. We also find that BTCs undergo a noticeable transformation from the monotonic decrease to constant with increasing the periodic number of superlattices. A brief analysis of these results is given.

Thermal and Thermoelectric Properties of Graphene

The subject of thermal transport at the mesoscopic scale and in low-dimensional systems is interesting for both fundamental research and practical applications. As the first example of truly two-dimensional materials, graphene has exceptionally high thermal conductivity, and thus provides an ideal platform for the research. Here we review recent studies on thermal and thermoelectric properties of graphene, with an emphasis on experimental progresses. A general physical picture based on the Landauer transport formalism is introduced to understand underlying mechanisms. We show that the superior thermal conductivity of graphene is contributed not only by large ballistic thermal conductance but also by very long phonon mean free path (MFP). The long phonon MFP, explained by the low-dimensional nature and high sample purity of graphene, results in important isotope effects and size effects on thermal conduction. In terms of various scattering mechanisms in graphene, several approaches are suggested to control thermal conductivity. Among them, introducing rough boundaries and weakly-coupled interfaces are promising ways to suppress thermal conduction effectively. We also discuss the Seebeck effect of graphene. Graphene itself might not be a good thermoelectric material. However, the concepts developed by graphene research might be applied to improve thermoelectric performance of other materials.

Ballistic phonon thermal conductance in graphene nanoribbons

Phonon dispersions for graphene nanoribbons (GNRs) have been derived from the first-principles calculations, and ballistic phonon thermal conductances have been evaluated using the Landauer theory. The phonon thermal conductance per unit width for GNR is larger than that for graphene and increases with decreasing ribbon width. The normalized thermal conductance with a unit of thermal quantum for the zigzag GNR is higher than that for the single-walled carbon nanotube that has a circumferential length corresponding to the width of GNR.

Observation of room-temperature ballistic thermal conduction persisting over 8.3 µm in SiGe nanowires

In ballistic thermal conduction, the wave characteristics of phonons allow the transmission of energy without dissipation. However, the observation of ballistic heat transport at room temperature is challenging because of the short phonon mean free path. Here we show that ballistic thermal conduction persisting over 8.3µm can be observed in SiGe nanowires with low thermal conductivity for a wide range of structural variations and alloy concentrations. We find that an unexpectedly low percentage (∼0.04%) of phonons carry out the heat conduction process in SiGe nanowires, and that the ballistic phonons display properties including non-additive thermal resistances in series, unconventional contact thermal resistance, and unusual robustness against external perturbations. These results, obtained in a model semiconductor, could enable wave-engineering of phonons and help to realize heat waveguides, terahertz phononic crystals and quantum phononic/thermoelectric devices ready to be integrated into existing silicon-based electronics.

Ballistic phonon transport in ultra-thin silicon layers: Effects of confinement and orientation

We investigate the effect of confinement and orientation on the phonon transport properties of ultra-thin silicon layers of thicknesses between 1 nm and 16 nm. We employ the modified valence force field method to model the lattice dynamics and the ballistic Landauer transport formalism to calculate the thermal conductance. We consider the major thin layer surface orientations {100}, {110}, {111}, and {112}. For every surface orientation, we study thermal conductance as a function of the transport direction within the corresponding surface plane. We find that the ballistic thermal conductance in the thin layers is anisotropic, with the {110}/⟨110⟩ channels exhibiting the highest and the {112}/⟨111⟩ channels the lowest thermal conductance with a ratio of about two. We find that in the case of the {110} and {112} surfaces, different transport orientations can result in ∼50% anisotropy in thermal conductance. The thermal conductance of different transport orientations in the {100} and {111} layers, on the other hand, is mostly isotropic. These observations are invariant under different temperatures and layer thicknesses. We show that this behavior originates from the differences in the phonon group velocities, whereas the phonon density of states is very similar for all the thin layers examined. We finally show how the phonon velocities can be understood from the phonon spectrum of each channel. Our findings could be useful in the design of the thermal properties of ultra-thin Si layers for thermoelectric and thermal management applications.

Ballistic to diffusive crossover of heat flow in graphene ribbons

Heat flow in nanomaterials is an important area of study, with both fundamental and technological implications. However, little is known about heat flow in two-dimensional devices or interconnects with dimensions comparable to the phonon mean free path. Here we find that short, quarter-micron graphene samples reach ~35% of the ballistic thermal conductance limit up to room temperature, enabled by the relatively large phonon mean free path (~100 nm) in substrate-supported graphene. In contrast, patterning similar samples into nanoribbons leads to a diffusive heat-flow regime that is controlled by ribbon width and edge disorder. In the edge-controlled regime, the graphene nanoribbon thermal conductivity scales with width approximately as ~W(1.8)(0.3), being about 100 W m(-1) K(-1) in 65-nm-wide graphene nanoribbons, at room temperature. These results show how manipulation of two-dimensional device dimensions and edges can be used to achieve full control of their heat-carrying properties, approaching fundamentally limited upper or lower bounds.

Calculation of Confined Phonon Spectrum in Narrow Silicon Nanowires Using the Valence Force Field Method

We study the effect of confinement on the phonon properties of ultra-narrow silicon nanowires of side sizes of 1-10nm . We use the modified valence force field method to compute the phononic dispersion, and extract the density of states, the transmission function, the sound velocity, the ballistic thermal conductance and boundary scattering-limited diffusive thermal conductivity. We find that the phononic dispersion and the ballistic thermal conductance are functions of the geometrical features of the structures, i.e. the transport orientation and confinement dimension. The phonon group velocity and thermal conductance can vary by a factor of two depending on the geometrical features of the channel. The <110> nanowire has the highest group velocity and thermal conductance, whereas the <111> the lowest. The <111> channel is thus the most suitable orientation for thermoelectric devices based on Si nanowires since it also has a large power factor. Our findings could be useful in the thermal transport design of silicon-based devices for thermoelectric and thermal management applications.

Impact of Isotope Doping on Phonon Thermal Transport in Silicon Nanowires

Phonon transport in silicon nanowires (Si NWs) doped with isotopes is investigated theoretically. The ballistic thermal conductance and diffusive thermal conductivity are calculated at room temperature using the phonon dispersion relations derived through a semiempirical atomistic approach. The thermal conductance and conductivity in 28Si NWs randomly doped with 29Si are smaller than those in the corresponding pure 28Si NW, which can be fully explained by the effect of isotope impurities on the dispersion relations. In [001]-oriented 28Si NWs having a square cross section with a side length of 1.086 nm and randomly doped with 29Si, the maximum reduction in thermal conductivity reaches more than 20%. This reduction leads directly to an improvement in the thermoelectric figure of merit by more than 25%. It is also found that the impact of isotope impurities on phonon transport becomes large with increasing mass difference between the constituent and impurity isotopes or with increasing wire cross-sectional area. Phonon transport in isotopic core–shell Si NWs is also investigated. Some of these Si NWs show increased thermal conductance and conductivity although the increase is very small.

Enhancement of ballistic thermal conductance in three dimensional double stub structures

Abstract We investigate ballistic thermal conductance in three dimensional double stub structures by using the scattering-matrix method. It is found that in such structures the thermal conductance can be clearly enhanced by inhomogeneities despite of the phonon scattering. When the stress-free boundary condition is employed, the enhancement can be observed only at very low temperature, and such the enhancement is strongly sensitive to the coupling length between two stubs. However, when the hall-wall boundary condition is employed, the enhancement can be observed in all explored temperature range, and becomes insensitive to the coupling length. A brief analysis of these results is given.

Effect of grain boundaries on thermal transport in graphene

We investigate the influence of grain boundaries (GBs), line defects (LDs), and chirality on thermal transport in graphene using non-equilibrium Green's functions. At room temperature, the ballistic thermal conductance is ∼4.2 GW m−2 K−1, and single GBs or LDs yield transmission from 50% to 80% of this value. LDs with carbon atom octagon defects have lower thermal transmission than that of GBs with pentagon and heptagon defects. We apply our findings to study the thermal conductivity of polycrystalline graphene for practical applications, and find that the type and size of GBs play an important role when grain sizes are smaller than a few hundred nanometers.

Enhanced low-temperature thermal conductance by quantum dot made of material with high sound velocity in a three-dimensional semiconductor nanowire

We investigate ballistic phonon transport and thermal conductance in a three-dimensional semiconductor nanowire modulated with different materials in a single quantum dot using elastic wave continuum model. In general, the acoustic discontinuities at such system cause the decrease of the thermal conductance. However, at very low temperatures, the material with higher sound velocity in quantum dot do enhance the thermal transport, despite that phonons are scattered due to the acoustic mismatch at the interfaces. The enhancement originates from the longer wavelength of the mode (0,0) in the material with higher sound velocity.

Strain dependence of the heat transport properties of graphene nanoribbons

Using a combination of accurate density-functional theory and a nonequilibrium Green’s function method, we calculate the ballistic thermal conductance characteristics of tensile-strained armchair (AGNR) and zigzag (ZGNR) edge graphene nanoribbons, with widths between 3 and 50 Å. The optimized lateral lattice constants for AGNRs of different widths display a three-family behavior when the ribbons are grouped according to N modulo 3, where N represents the number of carbon atoms across the width of the ribbon. Two lowest-frequency out-of-plane acoustic modes play a decisive role in increasing the thermal conductance of AGNR-N at low temperatures. At high temperatures the effect of tensile strain is to reduce the thermal conductance of AGNR-N and ZGNR-N. These results could be explained by the changes in force constants in the in-plane and out-of-plane directions with the application of strain. This fundamental atomistic understanding of the heat transport in graphene nanoribbons paves a way to effect changes in their thermal properties via strain at various temperatures.

The effect of the modulation shape in the ballistic thermal conductance of modulated nanowires

We report on calculations of the ballistic thermal conductance of nanowires with modulated width along their length. We discuss the effect of the shape of the modulation in the thermal conductance of the nanowires. The ballistic thermal conductance is determined by the phonon transmission coefficient. It is shown that the thermal conductance of the modulated wires is lower than that of the corresponding straight wires. The phonon conductance decreases with increasing number of modulating periods and saturates to the infinite superlattice value. It decreases below this value when the modulation profile is non-periodic. It is shown that the thermal conductance can be tuned by changing the shape of the modulation profile. This behavior could lead to structures of nanowires with enhanced thermoelectric efficiency.