Ballistic Thermal Transport Research Articles

Probing ballistic thermal conduction in segmented silicon nanowires.

Ballistic heat conduction in semiconductors is a remarkable but controversial nanoscale phenomenon, which implies that nanostructures can conduct thermal energy without dissipation. Here, we experimentally probed ballistic thermal transport at distances of 400-800 nm and temperatures of 4-250 K. Measuring thermal properties of straight and serpentine silicon nanowires, we found that at 4 K heat conduction is quasi-ballistic with stronger ballisticity at shorter length scales. As we increased the temperature, quasi-ballistic heat conduction weakened and gradually turned into diffusive regime at temperatures above 150 K. Our Monte Carlo simulations illustrate how this transition is driven by different scattering processes and linked to the surface roughness and the temperature. These results demonstrate the length and temperature limits of quasi-ballistic heat conduction in silicon nanostructures, knowledge of which is essential for thermal management in microelectronics.

Heat conduction measurements in ballistic 1D phonon waveguides indicate breakdown of the thermal conductance quantization

Emerging quantum technologies require mastering thermal management, especially at the nanoscale. It is now accepted that thermal metamaterial-based phonon manipulation is possible, especially at sub-kelvin temperatures. In these extreme limits of low temperatures and dimensions, heat conduction enters a quantum regime where phonon exchange obeys the Landauer formalism. Phonon transport is then governed by the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here we report on ultra-sensitive thermal experiments made on ballistic 1D phonon conductors using a micro-platform suspended sensor. Our thermal conductance measurements attain a power sensitivity of 15 attoWatts sqrt {{mathrm{Hz}}} ,^{ - 1} around 100 mK. Ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. This limitation of heat transport in the quantum regime may have a significant impact on modern thermal management and thermal circuit design.

Superconducting transition edge sensors with phononic thermal isolation

The sensitivity of a low-noise superconducting transition edge sensor (TES) is determined by the thermal conductance of the support structure that connects the active elements of the device to the heat bath. Low-noise devices require conductances in the range 0.1 to 10 pW K−1 and so have to rely on diffusive phonon scattering in long, narrow, amorphous SiNx legs. We show that it is possible to manufacture and operate TESs having short, ballistic low-dimensional legs (cross section 0.5 × 0.2 μm) that contain multi-element phononic interferometers and ring resonators. These legs transport heat in effectively just 5 elastic modes at the TES’s operating temperature (<150 mK), which is close to the quantised limit of 4. The phononic filters then reduce the thermal flux further by frequency-domain filtering. For example, a micromachined 3-element ring resonator reduced the flux to 19% of a straight-legged ballistic device operating at the quantised limit and 38% of a straight-legged diffusive reference device. This work opens the way to manufacturing TESs where performance is determined entirely by filtered, few-mode, ballistic thermal transport in short, low-heat capacity legs, free from the artifacts of two level systems.

Thermal conductivity of Si nanowires with δ-modulated dopant distribution by self-heated 3ω method and its length dependence

Here, we report the thermal conductivity measurement of B-doped Si nanowires with δ dopant modulation on the surface using the self-heated 3ω method, which resembles the thermal dissipation in operating electronic devices. The thermal conductivity for δ-modulated Si nanowires of 45 nm diameter (∼23 W/m K) is found to agree well with that of non-doped Si nanowires reported previously, which is attributed to the dominant surface boundary scattering and the highly confined dopant distribution at the surface. Furthermore, through a length dependent study of the thermal conductivity (κ) from 400 nm to 4 μm, we found an apparent length dependence of κ at L < 2 μm. The phenomenon could not be simply interpreted by solely considering the ballistic effect in thermal transport, but can be accounted for by including the additional resistive processes that are associated with the thermalization of joule-heating emitted phonons, which opts in to suppress the thermal conductivity of nano-systems under the ballistic thermal transport regime.

Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons

The recent observation of a half-integer quantized thermal Hall effect in $\alpha$-RuCl$_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity $\kappa_xy$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity focusing on the edge theory. As an example we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge-picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue, that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, $\Delta \kappa_{xy}/T \sim \text{sign(B)} \, T^2$, arises from a intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.

Significantly High Thermal Rectification in an Asymmetric Polymer Molecule Driven by Diffusive versus Ballistic Transport.

Tapered bottlebrush polymers have novel nanoscale polymer architecture. Using nonequilibrium molecular dynamics simulations, we showed that these polymers have the unique ability to generate thermal rectification in a single polymer molecule and offer an exceptional platform for unveiling different heat conduction regimes. In sharp contrast to all other reported asymmetric nanostructures, we observed that the heat current from the wide end to the narrow end (the forward direction) in tapered bottlebrush polymers is smaller than that in the opposite direction (the backward direction). We found that a more disordered to less disordered structural transition within tapered bottlebrush polymers is essential for generating nonlinearity in heat conduction for thermal rectification. Moreover, the thermal rectification ratio increased with device length, reaching as high as ∼70% with a device length of 28.5 nm. This large thermal rectification with strong length dependence uncovered an unprecedented phenomenon-diffusive thermal transport in the forward direction and ballistic thermal transport in the backward direction. This is the first observation of radically different transport mechanisms when heat flow direction changes in the same system. The fundamentally new knowledge gained from this study can guide exciting research into nanoscale organic thermal diodes.

Ballistic-diffusive phonon heat transport across grain boundaries

The propagation of a heat pulse in a single crystal and across grain boundaries (GBs) is simulated using a concurrent atomistic-continuum method furnished with a coherent phonon pulse model. With a heat pulse constructed based on a Bose-Einstein distribution of phonons, this work has reproduced the phenomenon of phonon focusing in single and polycrystalline materials. Simulation results provide visual evidence that the propagation of a heat pulse in crystalline solids with or without GBs is partially ballistic and partially diffusive, i.e., there is a co-existence of ballistic and diffusive thermal transport, with the long-wavelength phonons traveling ballistically while the short-wavelength phonons scatter with each other and travel diffusively. To gain a quantitative understanding of GB thermal resistance, the kinetic energy transmitted across GBs is monitored on the fly and the time-dependent energy transmission for each specimen is measured; the contributions of coherent and incoherent phonon transport to the energy transmission are estimated. Simulation results reveal that the presence of GBs modifies the nature of thermal transport, with the coherent long-wavelength phonons dominating the heat conduction in materials with GBs. In addition, it is found that phonon-GB interactions can result in reconstruction of GBs.

Assessment of Self‐Assembled Monolayers as High‐Performance Thermal Interface Materials

Thermal interface materials (TIMs) are highly desirable for efficient thermal transfer or dissipation in a wide range of material and device applications. The self‐assembled monolayers (SAMs) are promising candidates for these applications due to their high thermal transparency and structural flexibility. In this work, the performance of SAMs as practical TIMs is assessed by performing atomistic simulations. The mixed nature of diffusive and ballistic thermal transport is identified across the monolayers from signatures of coherent energy propagation and strong phonon scattering processes, respectively. The interfacial thermal conductance (ITC), G, displays remarkable dependence on the length, N, packing density, n and stretch of alkane chains. The nonmonotonic G–N relation features a peak at N = 4 that corresponds to maximum overlap of the vibrational density of states between molecular chains and substrate. When n > 0.98 mols/nm2, phonon scattering between neighboring chains reduces the ITC. The ITC can be reduced by 32.9% under tensile strain of 23.9%, but remains almost unchanged under compression. Compared to other TIMs such as polymers, graphene, and carbon nanotubes, SAMs demonstrate simultaneously high thermal transparency and structural flexibility that can be further tailored through their molecular structures and mechanical loading conditions.

Nonequilibrium thermal transport and vacuum expansion in the Hubbard model

One of the most straightforward ways to study thermal properties beyond linear response is to monitor the relaxation of an arbitrarily large left-right temperature gradient $T_L-T_R$. In one-dimensional systems which support ballistic thermal transport, the local energy currents $\langle j(t)\rangle$ acquire a non-zero value at long times, and it was recently investigated whether or not this steady state fulfills a simple additive relation $\langle j(t\to\infty)\rangle=f(T_L)-f(T_R)$ in integrable models. In this paper, we probe the non-equilibrium dynamics of the Hubbard chain using density matrix renormalization group (DMRG) numerics. We show that the above form provides an effective description of thermal transport in this model; violations are below the finite-time accuracy of the DMRG. As a second setup, we study how an initially equilibrated system radiates into different non-thermal states (such as the vacuum).

Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions.

We study the thermal transport properties of the one-dimensional Fermi-Pasta-Ulam model (β type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as distance^{-δ}, where δ≥0. Two Langevin heat baths at unequal temperatures are connected to the ends of the one-dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity, and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity κ has an interesting nonmonotonic dependence with δ with a maximum at δ=2.0 for this model. Moreover, at δ=2.0,κ diverges almost linearly with system size N and the temperature profile has a negligible slope, as one expects in ballistic transport for an integrable system. We demonstrate that the nonmonotonic behavior of the conductivity and the nearly ballistic thermal transport at δ=2.0 obtained under nonequilibrium conditions can be explained consistently by studying the variation of largest Lyapunov exponent λ_{max} with δ, and excess energy diffusion in the equilibrium microcanonical system.

Ballistic phonon thermal transport across topologically structured nanojunctions on Gold wires

We investigate the coherent phonon thermal transport at low temperatures in Gold nanowires, in order to study the effects of scattering on the lattice thermal conductivity. Three types of shaped joint nanostructures are employed in our calculation. We present a detailed study of the thermal conductance as a function of the temperature for different shaped joint. This is done by solving the phonon Boltzmann transport equation in the ballistic regime and calculating the transmission rates of the vibration modes through the consideration of the phonon group velocity modification in the system. The transmission properties are calculated by use of the matching method in the harmonic approximation with nearest and next nearest neighbor force constants. The results show that the transmission probabilities depend on the type of joint nanostructure. The pronounced fluctuations of the transmission spectra as a function of the frequency can be understood as Fano resonances. It is also found that the behavior of the thermal conductance versus temperature is qualitatively different for different nanostructures and depends sensitively on the width of the shaped joint.

Evidence of ballistic thermal transport in lithium niobate at room temperature

In ballistic transport, heat carriers such as phonons travel through the solid without any scattering or interaction. Therefore, there is no temperature gradient in the solid, suggesting zero thermal conductivity by Fourier's law. Ballistic transport is typically seen in high purity crystals at either temperatures below ~10K, or physical size below ~100nm, where the mean free path of the carrier is larger than the solid itself. In this letter, we show evidence of ballistic transport at room temperature in lithium niobate wafers in the in-plane and cross-plane directions under both steady state and high frequency heating that are monitored using both infrared and resistance thermometry. We report phonon mean free path in lithium niobate around 425μm, which is about 50 times higher than the largest phonon mean free path in the literature at room temperature.

Lattice thermal conductivities and thermoelectric performances of binary tin-based sheets: A computational study

Thermal transport properties of nanomaterials are essential for their nanodevices and nano-energy applications. Here, utilizing first-principles calculation with the Boltzmann transport equation, we investigate the lattice thermal conductivities and thermoelectric performances of SnSi and SnGe sheets. Their room-temperature lattice thermal conductivities (κlat) are found in the magnitude of 5–12W/mK, which are smaller than the values in elemental silicene, germanene, and stanene sheets. A long phonon mean free path limitation is found for the SnSi system, which causes a ballistic thermal transport in its finite micro-scale samples, while for the SnGe one, it will still exhibit a diffusive feature instead. Accompanied with the low κlat, their figures of merit are estimated to exceed one in the wide temperature range of 350–800K, where the peak value can arrive at 1.47 and 1.64 for SnSi and SnGe sheets, respectively. Those merits of thermal transport properties will enable intriguing thermoelectric and other sustain-energy applications for binary SnSi and SnGe systems.

Thermal Conductivity of the One-Dimensional Fermi-Hubbard Model.

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials.

Ballistic phonon and thermal radiation transport across a minute vacuum gap in between aluminum and silicon thin films: Effect of laser repetitive pulses on transport characteristics

Short-pulse laser heating of aluminum and silicon thin films pair with presence of a minute vacuum gap in between them is considered and energy transfer across the thin films pair is predicted. The frequency dependent Boltzmann equation is used to predict the phonon intensity distribution along the films pair for three cycles of the repetitive short-pulse laser irradiation on the aluminum film surface. Since the gap size considered is within the Casimir limit, thermal radiation and ballistic phonon contributions to energy transfer across the vacuum gap is incorporated. The laser irradiated field is formulated in line with the Lambert's Beer law and it is considered as the volumetric source in the governing equations of energy transport. In order to assess the phonon intensity distribution in the films pair, equivalent equilibrium temperature is introduced. It is demonstrated that thermal separation of electron and lattice sub-systems in the aluminum film, due to the short-pulse laser irradiation, takes place and electron temperature remains high in the aluminum film while equivalent equilibrium temperature for phonons decays sharply in the close region of the aluminum film interface. This behavior is attributed to the phonon boundary scattering at the interface and the ballistic phonon transfer to the silicon film across the vacuum gap. Energy transfer due to the ballistic phonon contribution is significantly higher than that of the thermal radiation across the vacuum gap.

Ballistic thermal transport properties at low temperatures in semiconductor nanowires-based heterojunctions

In this paper, we study ballistic thermal transport properties at low temperatures in semiconductor nanowires-based heterojunctions under hard-wall boundary conditions (HWBCs) and stress-free boundary conditions (SFBCs). Here, the numerical calculations for the asymmetric heterojunction (ASHJ) and symmetric heterojunction (SHJ) are done. When SFBCs are employed, the transmission coefficient exhibits different behaviors between ASHJ and SHJ especially at low frequency, but when HWBCs are employed, the transmission coefficient displays similar smooth platforms in both heterojunctions. In low temperature limit, the quantized thermal conductance can be observed in SHJ under SFBCs regardless of the structural details. However, this quantization cannot be observed in ASHJ under SFBCs, and the thermal conductance is strongly sensitive to the transverse width ratio rather than the slant angle. With increasing the transverse width ratio, the thermal conductance in both heterojunctions gradually increases especially, and such the increasing degree is more evident at higher temperatures. A brief analysis of these results is given.

Axial strain effects on ballistic phonon thermal transport in silicon nanowires

We study the effects of axial strain on phonon thermal transport in silicon nanowires (Si NWs). The thermal conductance of strained Si NWs in the ballistic regime is evaluated with the phonon dispersion relation derived through an atomistic approach. Compressive strain increases the ballistic thermal conductance of [100]-oriented Si NWs having a square cross section with a side length of about 3 nm. In contrast, tensile strain reduces it. These strain effects mainly result from two factors: a change in the phonon energy per unit length of a NW directly due to the length change of the NW, and a change in the phonon group velocity. We also investigate the relationships of the strain effects with the wire size, surface orientation, and wire orientation. Among the three factors, the wire orientation has the most significant effect on the strain effects.

Enhancing the ballistic thermal transport of silicene through smooth interface coupling

We have performed nonequilibrium molecular dynamics calculations on the length () dependence of thermal conductivity () of silicene both supported on and sandwiched between the smooth surfaces, i.e. h-BN, at room temperature. We find that of silicene follows a power law , with increasing from about 0.3–0.4 under the effect of interface coupling, showing an enhancement of the ballistic thermal transport of silicene. We also find that can be further increased to about 0.6 by increasing the interface coupling strength for the silicene sandwiched between h-BN. The increase of for the supported case is found to come from the variation of the flexural acoustic (ZA) phonon mode and the first optical phonon mode induced by the substrate, whereas the unusual increase of for the sandwiched case is attributed to the increment of velocities of all three acoustic phonon modes. These findings provide an interesting route for manipulating the ballistic energy flow in nanomaterials.

Ballistic thermal transport in monolayer transition-metal dichalcogenides: Role of atomic mass

We investigate the ballistic thermal transport of monolayer transition-metal dichalcogenides (TMDs), which is crucial for the thermal management of their potential applications in nanoelectronics. We find the thermal conductance is mainly affected by the atomic masses of TMDs. As a consequence, the temperature dependences of thermal conductances of different TMDs cross: At low temperatures below ∼50 K, the thermal conductance increases with the atomic mass, while it exhibits the opposite trend at high temperatures. The crossing behavior of temperature dependent thermal conductance is characteristic of the atomic mass effect, and TMDs provide a model system demonstrating that the thermal conductance can be effectively manipulated via the atomic mass by selecting appropriate atom. In addition, we clarify that in any two dimensional system such as monolayer TMDs and graphene, due to quadratic dispersion of the out-of-plane modes, the thermal conductance and specific heat in the low temperature limit are proportional to T3∕2 and T, respectively. Mainly because of much smaller group velocities of in-plane acoustic phonons, the high temperature thermal conductances of monolayer TMDs are much smaller than graphene. However, due to comparable group velocities of out-of-plane acoustic phonons, below 100 K thermal conductances of monolayer TMDs are rather comparable to graphene if taking the same layer thickness for comparison.

Thermal Transport of Flexural and In-Plane Phonons Modulated by Bended Graphene Nanoribbons

Ballistic thermal transport properties are investigated comparatively for out-of-plane phonon modes (FPMs) and in-plane phonon modes (IPMs) in bended graphene nanoribbons (GNRs). Results show that the phonon modes transports can be modulated separately by the phonon dispersion mismatch between armchair and zigzag GNRs in considered system. The contribution of FPMs to total thermal conductance is larger than 50% in low temperature for perfect GNRs. But it becomes less than 20% in the bended GNRs. Furthermore, this contribution can be modulated by changing the structural parameters of the bended GNRs. The result is useful for the design of thermal or thermoelectric nanodevices in future.