Ballistic Thermal Transport Research Articles

Ballistic Thermal Transport in Carbyne and Cumulene with Micron-Scale Spectral Acoustic Phonon Mean Free Path.

The elastic modulus of carbyne, a one-dimensional carbon chain, was recently predicted to be much higher than graphene. Inspired by this discovery and the fundamental correlation between elastic modulus and thermal conductivity, we investigate the intrinsic thermal transport in two carbon allotropes: carbyne and cumulene. Using molecular dynamics simulations, we discover that thermal conductivities of carbyne and cumulene at the quantum-corrected room temperature can exceed 54 and 148 kW/m/K, respectively, much higher than that for graphene. Such conductivity is attributed to high phonon energies and group velocities, as well as reduced scattering from non-overlapped acoustic and optical phonon modes. The prolonged spectral acoustic phonon lifetime of 30–110 ps and mean free path of 0.5–2.5 μm exceed those for graphene, and allow ballistic phonon transport along micron-length carbon chains. Tensile extensions can enhance the thermal conductivity of carbyne due to the increased phonon density of states in the acoustic modes and the increased phonon lifetime from phonon bandgap opening. These findings provide fundamental insights into phonon transport and band structure engineering through tensile deformation in low-dimensional materials, and will inspire studies on carbyne, cumulene, and boron nitride chains for their practical deployments in nano-devices.

Comparison on thermal transport properties of graphene and phosphorene nanoribbons.

We investigate ballistic thermal transport at low temperatures in graphene and phosphorene nanoribbons (PNRS) modulated with a double-cavity quantum structure. A comparative analysis for thermal transport in these two kinds of nanomaterials is made. The results show that the thermal conductance in PNRS is greater than that in graphene nanoribbons (GNRS). The ratio kG/kP (kG is the thermal conductivity in GNRS and kP is the thermal conductivity in PNRS) decreases with lower temperature or for narrower nanoribbons, and increases with higher temperature or for wider nanoribbons. The greater thermal conductance and thermal conductivity in PNRS originate from the lower cutoff frequencies of the acoustic modes.

Material properties dependent on the thermal transport in a cylindrical nanowire**Project supported by the National Natural Science Foundation of China (Grant No. 11404110), the Natural Science Foundation of Hunan Province, China (Grant Nos. 14JJ3139, 2015JJ6027, and 2015JJ6030), the Outstanding Young Program from the Education Department of Hunan Province, China (Grant No. 14B046), and the Doctoral Activation Foundation of Hunan Institute

Using the elastic wave continuum model, we investigate the effect of material properties on ballistic thermal transport in a cylindrical nanowire. A comparative analysis for the convexity-shaped and concavity-shaped structure is made. It is found that in the convexity-shaped structure, the material with higher wave velocity in the convexity region can increase the thermal conductance at the lower temperature range; the thermal conductance of the nanowire with higher wave velocity in the convexity region is lower than that of the nanowire with lower wave velocity in the convexity region at the higher temperature range. However, in the concavity-shaped structure, the material properties of the concavity region have less effect on the thermal conductance at the lower temperature range; the material with higher wave velocity in the concavity region can reduce the thermal conductance at the higher temperature range. A brief analysis of these results is given.

Ballistic thermal transport by phonons in three dimensional periodic nanostructures

Ballistic thermal transport properties by phonons in three dimensional (3D) periodic nanostructures is investigated. Results show that thermal transport properties in 3D periodic nanostructures can be efficiently tuned by modulating structural parameters of systems. When the incident frequency is below the first cutoff frequency, the quasi/formal-periodic oscillations of the transmission coefficient versus the periodic number/length can be observed. When the incident frequency is above the first cutoff frequency, however, these quasi/formal-periodic oscillations cannot be observed. As the periodic number is increased, the thermal conductance undergoes a prominent transition from the decrease to the constant. We also observe other intriguing physics properties such as stop-frequency gaps and quantum thermal conductance in 3D periodic nanostructures. Some similarities and differences between 2D and 3D periodic systems are identified.

Strong Thermal Transport Anisotropy and Strain Modulation in Single-Layer Phosphorene

Using first-principles calculations and non-equilibrium Green's function method, we investigate the ballistic thermal transport in single-layer phosphorene. A significant crystallographic orientation dependence of thermal conductance is observed, with room temperature thermal conductance along zigzag direction being 40 percent higher than that along armchair direction. Furthermore, we find that the thermal conductance anisotropy with the orientation can be tuned by applying strain. In particular, the zigzag-oriented thermal conductance is enhanced when a zigzag-oriented strain is applied but decreases when an armchair-oriented strain is applied; whereas the armchair-oriented thermal conductance always decreases when either a zigzag- or an armchair-oriented strain is applied. The present work suggests that the remarkable thermal transport anisotropy and its strain-modulated effect in single-layer phosphorene may be used for thermal management in phosphorene-based electronics and optoelectronic 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.

Phonon scattering and thermal conductivity of pillared graphene structures with carbon nanotube-graphene intramolecular junctions

We present results of a reverse non-equilibrium molecular dynamics study of thermal transport in single-walled carbon nanotube (SWCNT)-graphene junctions comprised of carbon-carbon (C-C) bonds with either sp2 or mixed sp2/sp3 hybridization. In both cases, a finite interfacial thermal resistance is observed at the SWCNT-graphene junctions for thermal transport in the out-of-plane direction. The interfacial thermal resistance at the junctions is attributed to the combined effects of scattering of the phonons at the SWCNT-graphene junctions due to the presence of distorted sp2 bonds in the junction region and the change in dimensionality of the medium along the phonon transport path as the phonons propagate from SWCNT pillars (quasi-1D) to graphene sheet (2D) and then again to SWCNTs. Moreover, the thermal resistance is found to depend on the C-C bond hybridization at the intramolecular junctions with mixed sp2/sp3 hybridization showing a higher interfacial resistance when compared to pure sp2 bonding. Thermal conductivity of typical SWCNT-graphene unit cells was observed to increase nearly linearly with an increase in cell dimensions, and then reaches a plateau as the pillar height and the inter-pillar distance approach the critical length for ballistic thermal transport in SWCNT and single layer graphene. These results indicate that the thermal transport characteristics of the three-dimensional SWCNT-graphene (hybrid) structures can be tuned by controlling the unit cell size.

Thermal Transport in Graphene Oxide – From Ballistic Extreme to Amorphous Limit

Graphene oxide is being used in energy, optical, electronic and sensor devices due to its unique properties. However, unlike its counterpart – graphene – the thermal transport properties of graphene oxide remain unknown. In this work, we use large-scale molecular dynamics simulations with reactive potentials to systematically study the role of oxygen adatoms on the thermal transport in graphene oxide. For pristine graphene, highly ballistic thermal transport is observed. As the oxygen coverage increases, the thermal conductivity is significantly reduced. An oxygen coverage of 5% can reduce the graphene thermal conductivity by ~90% and a coverage of 20% lower it to ~8.8 W/mK. This value is even lower than the calculated amorphous limit (~11.6 W/mK for graphene), which is usually regarded as the minimal possible thermal conductivity of a solid. Analyses show that the large reduction in thermal conductivity is due to the significantly enhanced phonon scattering induced by the oxygen defects which introduce dramatic structural deformations. These results provide important insight to the thermal transport physics in graphene oxide and offer valuable information for the design of graphene oxide-based materials and devices.

Thermal Resistance across Interfaces Comprising Dimensionally Mismatched Carbon Nanotube‐Graphene Junctions in 3D Carbon Nanomaterials

In the present study, reverse nonequilibrium molecular dynamics is employed to study thermal resistance across interfaces comprising dimensionally mismatched junctions of single layer graphene floors with (6,6) single‐walled carbon nanotube (SWCNT) pillars in 3D carbon nanomaterials. Results obtained from unit cell analysis indicate the presence of notable interfacial thermal resistance in the out‐of‐plane direction (along the longitudinal axis of the SWCNTs) but negligible resistance in the in‐plane direction along the graphene floor. The interfacial thermal resistance in the out‐of‐plane direction is understood to be due to the change in dimensionality as well as phonon spectra mismatch as the phonons propagate from SWCNTs to the graphene sheet and then back again to the SWCNTs. The thermal conductivity of the unit cells was observed to increase nearly linearly with an increase in cell size, that is, pillar height as well as interpillar distance, and approaches a plateau as the pillar height and the interpillar distance approach the critical lengths for ballistic thermal transport in SWCNT and single layer graphene. The results indicate that the thermal transport characteristics of these SWCNT‐graphene hybrid structures can be tuned by controlling the SWCNT‐graphene junction characteristics as well as the unit cell dimensions.

Ballistic thermal transport in a cylindrical quantum structure modulated with double quantum dots

Ballistic thermal transport properties in a cylindrical quantum structure modulated with double quantum dots (DQDs) are investigated. Results show that the transmission coefficients exhibit the irregular oscillation. Some resonant transmission peaks and stop-frequency gaps can be observed, and the number and positions of these peaks and gaps are sensitive to the sizes of DQDs. With increasing the temperature, the thermal conductance undergoes a transition from the decrease to increase, and can be efficiently tuned by modulating the radius, length of DQDs as well as the interval between DQDs. In addition, at low temperatures, the enhancement of the thermal conductance can be also observed in this case. Some similarities and differences between the cylindrical and rectangular structures are identified.

Ballistic thermal transport in multi-terminal graphene junctions

Ballistic thermal transport properties in Y-branch three-terminal and H-branch four-terminal graphene junctions are systematically investigated by using nonequilibrium Green’s function method. A comparative analysis for the Y-branch and H-branch quantum structure models is made. The results show that the increased junction in H-branch four-terminal graphene junctions can obviously reduce the thermal conductance of the adjacent quantum channel and slightly influence the thermal conductance of the farside quantum channel. The total thermal conductance displays almost the same thermal conductance property in both Y-branch and H-branch quantum structures.

Ballistic thermal transport contributed by the in-plane waves in a quantum wire modulated with an acoustic nanocavity

We investigate ballistic thermal transport contributed by the in-plane waves in a quantum wire modulated with an acoustic nanocavity. Here, the numerical calculations for two transmitted components (P wave and SV wave) are made to consider the mode conversion. Results show for the P wave component that the universal quantum thermal conductance can be observed in spite of structural details in the low temperature limit, and then the thermal conductance decreases with increasing temperature. However, for the SV wave component, the thermal conductance increases from zero monotonically with temperature. These indicate the mode conversion is directly proportional to the temperature. In addition, it is found that the mode conversion sensitively depend upon the incident frequency, the index of the modes as well as structural parameters. A brief analysis of these results is given.

Transition between ballistic and diffusive heat transport regimes in silicon materials

We study the extent of ballistic and diffusive thermal transport and the range of application of the Casimir and Fourier theories in semiconductor materials by using a theoretical model based on the Boltzmann transport equation. We show that combined effects of length scale, temperature, and boundary roughness are responsible for thermal transport transitions in silicon nanowires and thin films. We also introduce a more accurate principle for ballistic transport that considers the balance between internal and surface scattering. Phonon quantum confinement effects as well as the conditions for phonon wave interference in nanoscale heat transport are discussed.

Statistical phonon transport model for multiscale simulation of thermal transport in silicon: Part II – Model verification and validation

In Part I, the statistical phonon transport (SPT) model for solving the phonon Boltzmann transport equation in a statistical framework was presented. In this part, verification and validation of the SPT model is performed. The three-phonon scattering model is evaluated by considering populations of phonons interacting within an enclosed volume of silicon. The capability of the SPT model to capture the unique aspects of phonon transport from the diffuse to the ballistic thermal transport regimes is verified. Steady-state and transient results are validated against analytical solutions, results from Monte Carlo models, and experimental data for homogeneous silicon.

Direct Nanoscale Imaging of Ballistic and Diffusive Thermal Transport in Graphene Nanostructures

We report direct imaging of nanoscale thermal transport in single and few-layer graphene with approximately 50 nm lateral resolution using high vacuum scanning thermal microscopy. We observed increased heat transport in suspended graphene where heat is conducted by ballistic phonons, compared to adjacent areas of supported graphene, and observed decreasing thermal conductance of supported graphene with increased layer number. Our nanothermal images suggest a mean-free-path of thermal phonons in supported graphene below 100 nm.

Ballistic phonon thermal transport in a cylindrical semiconductor nanowire modulated with nanocavity

By developing the mode matching numerical technique, we investigate the ballistic phonon thermal transport through a cylindrical semiconductor nanowire modulated with a coupling nanocavity. It is found that the phonon transmission exhibits the periodical transmission properties in low frequency region. The resonant transmission and reflection behaviors of acoustic phonon modes at particular energy can be observed. In the limit T → 0, the thermal conductance approaches the universal quantum value π2kB2T/3h, and such a quantum is robust against all geometrical parameters. However, the thermal conductance exhibits nonmonotonic behaviors with increasing temperature and can be modulated by adjusting geometrical parameters of the nanocavity.

Noncontact Sub-10 nm Temperature Measurement in Near-Field Laser Heating

An extremely focused optical field down to sub-10 nm in an apertureless near-field scanning optical microscope has been used widely in surface nanostructuring and structure characterization. The involved sub-10 nm near-field heating has not been characterized quantitatively due to the extremely small heating region. In this work, we present the first noncontact thermal probing of silicon under nanotip focused laser heating at a sub-10 nm scale. A more than 200 °C temperature rise is observed under an incident laser of 1.2 × 10(7) W/m(2), while the laser polarization is well aligned with the tip axis. To explore the mechanism of heating and thermal transport at sub-10 nm scale, a simulation is conducted on the enhanced optical field by the AFM tip. The high intensity of the optical field generated in this region results in nonlinear photon absorption. The optical field intensity under low polarization angles (∼10(14) W/m(2) within 1 nm region for 15° and 30°) exceeds the threshold for avalanche breakdown in silicon. The measured high-temperature rise is a combined effect of the low thermal conductivity due to ballistic thermal transport and the nonlinear photon absorption in the enhanced optical field. Quantitative analysis reveals that under the experimental conditions the temperature rise can be about 235 and 105 °C for 15° and 30° laser polarization angles, agreeing well with the measurement result. Evaluation of the thermal resistances of the tip-substrate system concludes that little heat in the substrate can be transferred to the tip because of the very large thermal contact resistance between them.

Interfacial thermal transport in atomic junctions

We study ballistic interfacial thermal transport across atomic junctions. Exact expressions for phonon transmission coefficients are derived for thermal transport in one-junction and two-junction chains, and verified by numerical calculation based on a nonequilibrium Green's function method. For a single-junction case, we find that the phonon transmission coefficient typically decreases monotonically with increasing freqency. However, in the range between the point of equal frequency spectrum and that of equal acoustic impedance, it first increases then decreases, which explains why the Kapitza resistance calculated from the acoustic mismatch model is far larger than the experimental values at low temperatures. The junction thermal conductance reaches a maximum when the interfacial coupling equals the harmonic average of the spring constants of the two semi-infinite chains. For three-dimensional junctions, in the weak coupling limit, we find that the conductance is proportional to the square of the interfacial coupling, while for a intermediate coupling strength the conductance is approximately proportional to the interfacial coupling strength. For two-junction chains, the transmission coefficient oscillates with the frequency due to interference effects. The oscillations between the two envelope lines can be understood analytically, thus providing guidelines for designing phonon frequency filters.

Ballistic thermal transport in quantum wire modulated with trapeziform quantum structures

We investigate ballistic thermal transport property in quantum wire modulated with trapeziform quantum structures at low temperatures. A comparative analysis for two different trapeziform quantum structure models is made. It is found that the transmission probability and thermal conductance sensitively depend on the figure of the quantum scattering structures. The thermal conductance K T is always bigger than the thermal conductance K O in the trapeziform quantum structures and the thermal-conductance ratio K T / K O is increased with the enlarging difference of the bottom side-length of the trapeziform quantum structures. A brief analysis of these results is given.