Ballistic Phonons in Ultrathin Nanowires

TEM-compatible microdevice for the complete thermoelectric characterization of epitaxially integrated Si-based nanowires

Nanostructured materials present improved thermoelectric properties due to non-trivial effects at the nanoscale. However, the characterization of individual nanostructures, especially from the thermal point of view, is still an unsolved topic. This work presents the complete structural, morphological, and thermoelectrical evaluation of the selfsame individual bottom-up integrated nanowire employing an innovative micro-machined device compatible with transmission electron microscopy whose fabrication is also discussed. Thanks to a design that arranges the nanostructured samples completely suspended, detailed structural analysis using transmission electron microscopy is enabled. In the same device architecture, electrical collectors and isolated heaters are available at both ends of the trenches for thermoelectrical measurements of the nanowire i.e. thermal and electrical properties simultaneously. This allows the direct measurement of the nanowire power factor. Furthermore, micro-Raman thermometry measurements were performed to evaluate the thermal conductivity of the same suspended silicon nanowire. A thermal profile of the self-heating nanowire could be spatially resolved and used to compute the thermal conductivity. In this work, heavily-doped silicon nanowires were grown on this microdevices yielding a thermal conductivity of 30.8 ± 1.7 W Km-1 and a power factor of 2.8 mW mK-2 at an average nanowire temperature of 400 K. Notably, no thermal contact resistance was observed between the nanowire and the bulk, confirming the epitaxial attachment. The device presented here shows remarkable utility in the challenging thermoelectrical characterization of integrated nanostructures and in the development of multiple devices such as thermoelectric generators.

Temperature and Thickness Dependence of the Thermal Conductivity in 2D Ferromagnet Fe3GeTe2

The emergence of symmetry-breaking orders such as ferromagnetism and the weak interlayer bonding in van der Waals materials offers a unique platform to engineer novel heterostructures and tune transport properties like thermal conductivity. Here, we report the experimental and theoretical study of the cross-plane thermal conductivity, κ⊥, of the van der Waals two-dimensional (2D) ferromagnet Fe3GeTe2. We observe an increase in κ⊥ with thickness, indicating a diffusive transport regime with ballistic contributions. These results are supported by the theoretical analyses of the accumulated thermal conductivity, which show an important contribution of phonons with mean free paths between 10 and 200 nm. Moreover, our experiments show a reduction of κ⊥ in the low-temperature ferromagnetic phase occurring at the magnetic transition. The calculations show that this reduction in κ⊥ is associated with a decrease in the group velocities of the acoustic phonons and an increase in the phonon-phonon scattering of the Raman modes that couple to the magnetic phase. These results demonstrate the potential of van der Waals ferromagnets for thermal transport engineering.

Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects

In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects.

Super-Ballistic Width Dependence of Thermal Conductivity in Graphite Nanoribbons and Microribbons

The super-ballistic temperature dependence of thermal conductivity, facilitated by collective phonons, has been widely studied. It has been claimed to be unambiguous evidence for hydrodynamic phonon transport in solids. Alternatively, hydrodynamic thermal conduction is predicted to be as strongly dependent on the width of the structure as is fluid flow, while its direct demonstration remains an unexplored challenge. In this work, we experimentally measured thermal conductivity in several graphite ribbon structures with different widths, from 300 nm to 1.2 µm, and studied its width dependence in a wide temperature range of 10-300 K. We observed enhanced width dependence of the thermal conductivity in the hydrodynamic window of 75 K compared to that in the ballistic limit, which provides indispensable evidence for phonon hydrodynamic transport from the perspective of peculiar width dependence. This will help to find the missing piece to complete the puzzle of phonon hydrodynamics, and guide future attempts at efficient heat dissipation in advanced electronic devices.

Observation of phonon Poiseuille flow in isotopically purified graphite ribbons

In recent times, the unique collective transport physics of phonon hydrodynamics motivates theoreticians and experimentalists to explore it in micro- and nanoscale and at elevated temperatures. Graphitic materials have been predicted to facilitate hydrodynamic heat transport with their intrinsically strong normal scattering. However, owing to the experimental difficulties and vague theoretical understanding, the observation of phonon Poiseuille flow in graphitic systems remains challenging. In this study, based on a microscale experimental platform and the pertinent occurrence criterion in anisotropic solids, we demonstrate the existence of the phonon Poiseuille flow in a 5.5 μm-wide, suspended and isotopically purified graphite ribbon up to a temperature of 90 K. Our observation is well supported by our theoretical model based on a kinetic theory with fully first-principles inputs. Thus, this study paves the way for deeper insight into phonon hydrodynamics and cutting-edge heat manipulating applications.

Isotope doping-induced crossover shift in the thermal conductivity of thin silicon nanowires

Here, using homogeneous nonequilibrium molecular dynamics simulations, we report the thermal transport characteristics of thin Si nanowires (NWs) with varying size and isotope doping ratio. It is identified that crossover in the thermal conductivity (κ) of both isotope doping-free and isotope doped Si-NWs appears at critical sizes, below whichκis enlarged with decreasing size because the hydrodynamic phonon flow predominates, above which, due to the dominant phonon boundary scattering, opposite behavior is observed. With increasing isotope doping, however, the critical size in minimizing theκis moved to small values because the phonon impurity scattering caused by isotope doping is critically involved. Moreover, there is a critical isotope doping (<50%) in the critical size motion, originating from that, above which, the critical size no longer moves due to the persistence of hydrodynamic phonon flow. This study provides new insights into the thermal transport behaviors of quasi-1D structures.

Lévy walk of quasiballistic phonons in nanowires

Phonon transport in square-cross-section nanowires is studied using spectral Monte Carlo simulations. Our results show the evolution of the different transport regimes described by Lévy statistics as a function of the surface roughness-to-thermal wavelength ratio σ/λ. More precisely, the relationship between the Lévy index γ describing the mean free path distribution Ψ(Λ) and σ/λ is established for the classical diffusive regime, the superdiffusive regime, and the ballistic regime in the nanowire. Besides the conventional superdiffusive regime that is marked by Ψ(Λ) with a single heavy-tailed peak, we reveal an unconventional superdiffusive subregime featuring Ψ(Λ) with sawtooth oscillations when σ/λ∼0.01. Investigation of the direction of propagation of phonons shows a significant narrowing of the angular distribution around the long axis of the nanowire due to the diffuse scattering at rough boundaries when σ/λ>0.1. These results shed light on the transport mechanisms of quasiballistic phonons and will help in nanowire design for specific applications.

Optimization and Fabrication of MEMS suspended structures for nanoscale thermoelectric devices

By eliminating the influence of the substrate on parasitic thermal resistance, MEMS suspended structures become one of the accurate nanoscale thermoelectric performance evaluation devices. However, the process of MEMS suspended thermoelectric devices is complex, and its multilayer suspended structure is easy to fracture due to large stress. As a result, optimizing the design of suspended structures is critical in order to reduce manufacturing complexity and increase yield. In this study, finite element simulation is used to investigate the impacts of varying structures and sizes on the stress of MEMS suspended devices. The maximum stress and average stress of silicon nanomaterials are lowered by 90.89% and 92.35%, respectively, by optimizing the structure and size of the beams and nanobelt. Moreover, MEMS suspended devices of various structures are successfully manufactured. It not only increases the yield to more than 70% but also decreases the impact of strain on thermoelectric performance and can be used to create suspended devices with integrated silicon microstrips.

Violation of Boltzmann Equipartition Theorem in Angular Phonon Phase Space Slows down Nanoscale Heat Transfer in Ultrathin Heterofilms

Heat transfer through heterointerfaces is intrinsically hampered by a thermal boundary resistance originating from the discontinuity of the elastic properties. Here, we show that with shrinking dimensions the heat flow from an ultrathin epitaxial film through atomically flat interfaces into a single crystalline substrate is significantly reduced due to violation of Boltzmann equipartition theorem in the angular phonon phase space. For films thinner than the phonons mean free path, we find phonons trapped in the film by total internal reflection, thus suppressing heat transfer. Repopulation of those phonon states, which can escape the film through the interface by transmission and refraction, becomes the bottleneck for cooling. The resulting nonequipartition in the angular phonon phase space slows down the cooling by more than a factor of 2 compared to films governed by phonons diffuse scattering. These allow tailoring of the thermal interface conductance via manipulation of the interface.

Observation of superdiffusive phonon transport in aligned atomic chains

Fascinating phenomena can occur as charge and/or energy carriers are confined in one dimension^1-4. One such example is the divergent thermal conductivity (κ) of one-dimensional lattices, even in the presence of anharmonic interatomic interactions-a direct consequence of the Fermi-Pasta-Ulam-Tsingou paradox proposed in 1955⁵. This length dependence of κ, also known as superdiffusive phonon transport, presents a classical anomaly of continued interest^6-9. So far the concept has remained purely theoretical, because isolated single atomic chains of sufficient length have been experimentally unattainable. Here we report on the observation of a length-dependent κ extending over 42.5 µm at room temperature for ultrathin van der Waals crystal NbSe₃ nanowires. We found that κ follows a 1/3 power law with wire length, which provides experimental evidence pointing towards superdiffusive phonon transport. Contrary to the classical size effect due to phonon-boundary scattering, the observed κ shows a 25-fold enhancement as the characteristic size of the nanowires decreases from 26 to 6.8 nm while displaying a normal-superdiffusive transition. Our analysis indicates that these intriguing observations stem from the transport of one-dimensional phonons excited as a result of elastic stiffening with a fivefold enhancement of Young's modulus. The persistent divergent trend of the observed thermal conductivity with sample length reveals a real possibility of creating novel van der Waals crystal-based thermal superconductors with κ values higher than those of any known materials.

Heat Transport Control and Thermal Characterization of Low-Dimensional Materials: A Review

Heat dissipation and thermal management are central challenges in various areas of science and technology and are critical issues for the majority of nanoelectronic devices. In this review, we focus on experimental advances in thermal characterization and phonon engineering that have drastically increased the understanding of heat transport and demonstrated efficient ways to control heat propagation in nanomaterials. We summarize the latest device-relevant methodologies of phonon engineering in semiconductor nanostructures and 2D materials, including graphene and transition metal dichalcogenides. Then, we review recent advances in thermal characterization techniques, and discuss their main challenges and limitations.

Mean Free Path Suppression of Low-Frequency Phonons in SiGe Nanowires

Accurate measurements of the size-dependent lattice thermal conductivity (κ_l) of alloy nanostructures are challenging but help to address outstanding questions on the effects of atomic disorder and surface roughness on low-frequency vibrational modes in functional materials. Here, we report sensitive κ_l measurements of multiple segments of the same individual SiGe nanowires. In contrast to a previous report of ballistic thermal transport over several microns in SiGe nanowires, the obtained κ_l are nearly independent of the segment length from 2 to 10 μm and the temperature between 150 and 300 K. The results are in agreement with a theoretical calculation based on the virtual crystal approximation of the vibrational modes as phonons with mean free paths suppressed by purely diffuse surface scattering. The findings inform continuing theoretical efforts for understanding the roles of different types of vibrational modes in thermal transport in disordered thermoelectric and electronic materials.

Heat conduction in polymer chains with controlled end-to-end distance

The low thermal conductance of polymers is one of the major drawbacks for many polymer-based products. However, a single polymer chain when stretched can have high thermal conductivities. We use non-equilibrium molecular dynamics simulations to study the steady-state thermal conductance along finite macromolecules under mechanical control of the end-to-end distance. We find that the nature of heat transport along such chains strongly depends on mechanical tuning, leading to significantly different heat conductions and temperature profiles along the chain in the compressed-chain and stretched-chain limits. This transition between modes of behaviors appears to be a threshold phenomenon: at relatively small end-to-end distances, the thermal conductance remains almost constant as one stretches the polymer chain. At given critical end-to-end distances, thermal conductances start to increase, reaching the fully extended chain values. Correlated with this behavior are two observations: first, the temperature bias falls mostly at contacts in the fully stretched chain, while part of it falls along the molecule in the compressed limit. Second, the heat conduction does not change significantly with the chain length in the stretched-chain limit but decreases dramatically when this length increases in the compressed molecule. This suggests that heat transfer along stretched chains is mostly ballistic, while in the compressed chain, heat is transferred by diffusive mechanisms. Significantly, these trends persist also for a large range of molecular structures and force fields, and the changing behavior correlates well with mode localization properties. Similar studies conducted with disordered chains and bundles of several chains show remnants of the same behavior.

Spatially resolved thermoelectric effects in operando semiconductor-metal nanowire heterostructures

The thermoelectric properties of a nanoscale germanium segment connected by aluminium nanowires are studied using scanning thermal microscopy. The germanium segment of 168 nm length features atomically sharp interfaces to the aluminium wires and is surrounded by an Al2O3 shell. The temperature distribution along the self-heated nanowire is measured as a function of the applied electrical current, for both Joule and Peltier effects. An analysis is developed that is able to extract the thermal and thermoelectric properties including thermal conductivity, the thermal boundary resistance to the substrate and the Peltier coefficient from a single measurement. Our investigations demonstrate the potential of quantitative measurements of temperature around self-heated devices and structures down to the scattering length of heat carriers.