Investigation of phonon coherence and backscattering using silicon nanomeshes

Physics mechanisms underlying the optimization of coherent heat transfer across width-modulated nanowaveguides with calculations and machine learning

Optimization of heat transfer at the nanoscale is necessary for efficient modern technology applications in nanoelectronics, energy conversion, and quantum technologies. In such applications, phonons dominate thermal transport and optimal performance requires minimum phonon conduction. Coherent phonon conduction is minimized by maximum disorder in the aperiodic modulation profile of width-modulated nanowaveguides, according to a physics rule. It is minimized for moderate disorder against physics intuition in composite nanostructures. Such counter behaviors call for a better understanding of the optimization of phonon transport in non-uniform nanostructures. We have explored mechanisms underlying the optimization of width-modulated nanowaveguides with calculations and machine learning, and we report on generic behavior. We show that the distribution of the thermal conductance among the aperiodic width-modulation configurations is controlled by the modulation degree irrespective of choices of constituent material, width-modulation-geometry, and composition constraints. The efficiency of Bayesian optimization is evaluated against increasing temperature and sample size. It is found that it decreases with increasing temperature due to thermal broadening of the thermal conductance distribution. It shows weak dependence on temperature in samples with high discreteness in the distribution spectrum. Our work provides new physics insight and indicates research pathways to optimize heat transfer in non-uniform nanostructures.

Nonequilibrium thermal rectification at the junction of harmonic chains

A thermal diode or rectifier is a system that transmits heat or energy in one direction better than in the opposite direction. We investigate the influence of the distribution of energy among wave numbers on the diode effect for the junction of two dissimilar harmonic chains. An analytical expression for the diode coefficient, characterizing the difference between heat fluxes through the junction in two directions, is derived. It is shown that the diode coefficient depends on the distribution of energy among wave numbers. For an equilibrium energy distribution, the diode effect is absent, while for non-equilibrium energy distributions the diode effect is observed even though the system is harmonic. We show that the diode effect can be maximized by varying the energy distribution and relative position of spectra of the two harmonic chains. Conditions are formulated under which the system acts as an ideal thermal rectifier, i.e., transmits heat only in one direction. The results obtained are important for understanding the heat transfer in heterogeneous low-dimensional nanomaterials.

Heat Flow Guiding and Modulation by Kinks in a Silicon Nanoribbon

Tailoring heat flow in solids has profound implications for the innovation of functional thermal devices. However, the current methods face technological challenges related to system complexity, material stability, and operating temperature. In this study, we demonstrated efficient heat flow modulation in a single material without a phase transition, using a simple and entirely material-independent strategy, kinked nanostructure patterning, at near-ambient temperature. By carefully controlling the kink arm length and kink angle of the Si nanoribbons, we achieved a thermal conductivity modulation of up to ∼20%. Our theoretical modeling showed that this modulation results from the competing roles of phonon backscattering and open view channels on heat transport. We also build a regime map based on the existence of an open view channel and provide concrete design guidelines for thermal conductivity modulation considering the kink angle and arm length. This study opens up new opportunities for efficient heat flow manipulation through nanostructure patterning.

Universal Behavior of Highly Confined Heat Flow in Semiconductor Nanosystems: From Nanomeshes to Metalattices

Nanostructuring on length scales corresponding to phonon mean free paths provides control over heat flow in semiconductors and makes it possible to engineer their thermal properties. However, the influence of boundaries limits the validity of bulk models, while first-principles calculations are too computationally expensive to model real devices. Here we use extreme ultraviolet beams to study phonon transport dynamics in a 3D nanostructured silicon metalattice with deep nanoscale feature size and observe dramatically reduced thermal conductivity relative to bulk. To explain this behavior, we develop a predictive theory wherein thermal conduction separates into a geometric permeability component and an intrinsic viscous contribution, arising from a new and universal effect of nanoscale confinement on phonon flow. Using experiments and atomistic simulations, we show that our theory applies to a general set of highly confined silicon nanosystems, from metalattices, nanomeshes, porous nanowires, to nanowire networks, of great interest for next-generation energy-efficient devices.

Efficient modulation of thermal transport in two-dimensional materials for thermal management in device applications

With the development of chip technology, the density of transistors on integrated circuits is increasing and the size is gradually shrinking to the micro-/nanoscale, with the consequent problem of heat dissipation on chips becoming increasingly serious. For device applications, efficient heat dissipation and thermal management play a key role in ensuring device operation reliability. In this review, we summarize the thermal management applications based on 2D materials from both theoretical and experimental perspectives. The regulation approaches of thermal transport can be divided into two main types: intrinsic structure engineering (acting on the intrinsic structure) and non-structure engineering (applying external fields). On one hand, the thermal transport properties of 2D materials can be modulated by defects and disorders, size effect (including length, width, and the number of layers), heterostructures, structure regulation, doping, alloy, functionalizing, and isotope purity. On the other hand, strain engineering, electric field, and substrate can also modulate thermal transport efficiently without changing the intrinsic structure of the materials. Furthermore, we propose a perspective on the topic of using magnetism and light field to modulate the thermal transport properties of 2D materials. In short, we comprehensively review the existing thermal management modulation applications as well as the latest research progress, and conclude with a discussion and perspective on the applications of 2D materials in thermal management, which will be of great significance to the development of next-generation nanoelectronic devices.

Engineering thermal transport within Si thin films: The impact of nanoslot alignment and ion implantation

In recent years, nanoporous Si films have been intensively studied for their potential applications in thermoelectrics and the thermal management of devices. To minimize the thermal conductivity, ultrafine nanoporous patterns are required but the smallest structure size is largely limited by the spatial resolution of the employed nanofabrication techniques. Along this line, an effectively smaller characteristic length of a nanoporous film can be achieved with offset nanoslot patterns. Compared with periodic circular pores, the nanoslot pattern can achieve an even lower thermal conductivity, where a much smaller porosity is required using ultra-narrow nanoslots. The obtained low thermal conductivity can be understood from the thermally dead volume revealed by phonon Monte Carlo simulations. To further minimize the contribution from short-wavelength phonons, an additional 25% thermal conductivity reduction can be achieved with Ga ions implanted using a focused ion beam.

Preparation of mesoporous nitrogen-doped titania comprising large crystallites with low thermal conductivity

Reducing the thermal conductivity (κ) of mesoporous N-doped titania (TiO2) is crucial for the development of TiO2-based materials that exhibit excellent electronic, photochemical, and thermoelectric properties. Mesopores can contribute to the reduction of κ via phonon scattering, and the scattering effect due to the randomness of crystal interfaces should be significantly reduced to clarify the role of mesopores in reducing thermal conductivity. Highly ordered mesoporous N-doped TiO2 comprising large crystallites was prepared with silica colloidal crystals as a template into which a Ti source was introduced, followed by calcination with urea. N-doped samples comprising large crystallites exhibiting random mesopores were also prepared and used for the investigation of the effects of the shape and arrangement of the mesopore on phonon scattering. The mesostructures of the two separately prepared N-doped TiO2 samples were retained after sintering at 873 K and 80 MPa to fabricate pellets. Furthermore, the effective suppression of the long mean-free-path phonon conduction by the thin pore walls at a nanometer scale thickness significantly reduced the thermal conductivities of both samples. The presence of ordered mesopores further contributed to the reduction of κ, which was probably due to the enhanced contribution of the backscattering of phonons caused by ordered pore wall surfaces.

Impact of Porosity and Boundary Scattering on Thermal Transport in Diameter-Modulated Nanowires

We study the thermal conductivity of diameter-modulated Si nanowires to understand the impact of different nanoscale transport mechanisms as a function of nanowire morphology. Our investigation couples transient suspended microbridge measurements of diameter-modulated Si nanowires synthesized via vapor-liquid-solid growth and dopant-selective etching with predictive Boltzmann transport modeling. We show that the presence of a low thermal conductivity phase (i.e., porosity) dominates the reduction in effective thermal conductivity and is supplemented by increased phonon-boundary scattering. The relative contributions of both mechanisms depend on the details of the nanoscale morphology. Our findings provide valuable insights into the factors that govern thermal conduction in complex nanoscale materials.

Concentrated radiative cooling and its constraint from reciprocity

Concentrated radiative cooling, an analogous concept of the concentrated solar power technology, has the potential of amplifying both the cooling power and the temperature reduction. However, concentrators have not yet been systematically optimized. Moreover, a widely used theoretical approach to analyze such systems has neglected a fundamental constraint from reciprocity, which can lead to an overestimate of cooling performance and unclarified limits of amplification factors. Here we develop a theoretical framework addressing these shortcomings. Modeling suggests the optimized shape and geometric dimensions of concentrators, as well as the limiting cooling power and temperature reduction. Using an electroplated Al₂O₃ emitter and an optimized conical concentrator, we experimentally amplify the nighttime radiative cooling by 26%.

Structural optimization of silicon thin film for thermoelectric materials

The method to optimize nanostructures of silicon thin films as thermoelectric materials is developed. The simulated annealing method is utilized for predicting the optimized structure. The mean free path and thermal conductivity of thin films, which are the objective function of optimization, is evaluated by using phonon transport simulations and lattice dynamics calculations. In small systems composed of square lattices, the simulated annealing method successfully predicts optimized structure corroborated by an exhaustive search. This fact indicates that the simulated annealing method is an effective tool for optimizing nanostructured thin films as thermoelectric materials.

Phonon transport in the nano-system of Si and SiGe films with Ge nanodots and approach to ultralow thermal conductivity

Phonon transport in the nano-system has been studied using well-designed nanostructured materials to observe and control the interesting phonon behaviors like ballistic phonon transport. Recently, we observed drastic thermal conductivity reduction in the films containing well-controlled nanodots. Here, we investigate whether this comes from the interference effect in ballistic phonon transport by comparing the thermal properties of the Si or Si0.75Ge0.25 films containing Ge nanodots. The experimentally-obtained thermal resistance of the nanodot layer shows peculiar nanodot size dependence in the Si films and a constant value in the SiGe films. From the phonon simulation results, interestingly, it is clearly found that in the nanostructured Si film, phonons travel in a non-diffusive way (ballistic phonon transport). On the other hand, in the nanostructured SiGe film, although simple diffusive phonon transport occurs, extremely-low thermal conductivity (∼0.81 W m-1 K-1) close to that of amorphous Si0.7Ge0.3 (∼0.7 W m-1 K-1) is achieved due to the combination of the alloy phonon scattering and Ge nanodot scattering.

Small-Nanostructure-Size-Limited Phonon Transport within Composite Films Made of Single-Wall Carbon Nanotubes and Reduced Graphene Oxides

Nanocarbon materials have been widely used for nanoelectronics and energy-related applications. In this work, composite films consisting of reduced graphene oxides (rGOs) and single-wall carbon nanotubes (SWCNTs) are synthesized and studied for their in-plane thermal conductivities. Different from pristine carbon nanotubes or graphene with decreased thermal conductivities above 300 K, the in-plane thermal conductivities of these composite films are found to follow the trend of the specific heat of graphene from 100 to 400 K, i.e., monotonously increasing at elevated temperatures. Such a trend can often be found within amorphous solids but has seldom been observed for nanocarbon. This unique temperature dependence of thermal conductivities is attributed to the largely restricted phonon mean free paths within the graphene sheets that mainly contribute to the in-plane thermal transport. The highest in-plane thermal conductivity among samples with different synthesis conditions is 62.8 W/(m·K) at 300 K. Such a high thermal conductivity, combined with its unique temperature dependency, can be ideal for applications such as flexible film-like thermal diodes based on the junction between two materials with a large contrast for their temperature dependence of the thermal conductivity.

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.

Development of a rigid suspended micro-island device and robust measurement method for thermal transport measurements

One of the most versatile techniques to study thermal transport in low dimensional materials utilizes a suspended micro-island device integrated with resistance thermometers. Advancements in experimental techniques with suspended micro-island devices resulted in increasing capabilities such as enhancing temperature resolution and expanding a measurable range of sample thermal conductance. In this work, we further improve the suspended micro-island based technique. Specifically, we present a rigid structure of the suspended micro-island device and robust measurement method for sequential heating. The rigid structure enabled by T-shaped beams prevents the displacement of suspended micro-islands, thus increasing the success rates of sample transfer especially for samples with a large cross-sectional area and short length. Besides, thermal isolation of micro-islands is maintained at a similar level through the T-shaped beams compared to conventional flat beams. Next, we introduce an advanced experimental approach that enables sequential heating to measure sample thermal conductance. Sequential heating in micro-islands can be used either to measure accurate sample thermal conductance even under unexpected asymmetric supporting beam configuration or to study thermal transport dependence on heat flow directions. Using a switch matrix for sequential heating eliminates the need for experimental reconfigurations during the experiment. We demonstrate the experimental method with thermal conductivity measurements of the Si nanowire under both the ideal symmetric beam configuration and replicated asymmetric beam configuration scenarios. The results show that the developed experimental method effectively eliminates potential experimental errors that can arise from the asymmetry in beam configurations.

Thermal Metamaterial: Fundamental, Application, and Outlook

Thermal metamaterials have amazing properties in heat transfer beyond naturally occurring materials owing to their well-designed artificial structures. The idea of thermal metamaterial has completely subverted the design of thermal functional devices and makes it possible to manipulate heat flow at will. In this perspective, we review the up-to-date progress of thermal metamaterials starting from 2008. We focus on both the key theoretical fundamentals and techniques for applications and give a perspective of scale-based classification on thermal metamaterials' theories and applications. We also discuss the junction between macroscale and microscale design methods and propose some prospects for the future trend of this field.

Enhanced Reduction of Thermal Conductivity in Amorphous Silicon Nitride-Containing Phononic Crystals Fabricated Using Directed Self-Assembly of Block Copolymers

Studies have demonstrated that the thermal conductivity (κ) of crystalline semiconductor materials can be reduced by phonon scattering in periodic nanostructures formed using templates fabricated from self-assembled block copolymers (BCPs). Compared to crystalline materials, the heat transport mechanisms in amorphous inorganic materials differ significantly and have been explored far less extensively. However, thermal management of amorphous inorganic solids is crucial for a broad range of semiconductor devices. Here we present the fabrication of freestanding amorphous silicon nitride (SiN_x) membranes for studying κ in an amorphous solid. To form a periodic nanostructure, directed self-assembly of cylinder-forming BCPs is used to pattern in the SiN_x highly ordered, hexagonally close packed nanopores with pitch and neck width down to 37.5 and 12 nm, respectively. The κ of the nanoporous SiN_x membranes is 60% smaller than the classically predicted value based on just the membrane porosity. In comparison, holes with much larger neck widths and pitches patterned by e-beam lithography lead to only a slight reduction in κ, which is closer to the classical porosity-based prediction. These results demonstrate that κ of amorphous SiN_x can be reduced by introducing periodic nanostructures that behave as a phononic crystal, where the relationship between the smallest dimension of the nanostructure and the length scale of the mean-free paths of the dominant, heat-carrying phonons is critical. Additionally, changing the orientation of the hexagonal array of nanopores relative to the primary direction of heat flow has a smaller impact on amorphous SiN_x than was previously observed in silicon.

Coherent and Incoherent Impacts of Nanopillars on the Thermal Conductivity in Silicon Nanomembranes

Nanostructuring is the dominant approach for effective thermal conduction control in nanomaterials. In the past decade, researchers have been interested in thermal conduction control by the coherent effects in phononic crystal (PnC) systems. Recent theoretical works predicted that nanopillars on the surface of silicon membranes could cause a dramatic thermal conductivity reduction due to the phonon local resonances. However, this remarkable prediction has not been experimentally verified yet with the deep-nanoscale pillar-based PnCs. Here, we fabricate nanopillars on suspended silicon membranes using damageless neutral-beam etching and investigate the impact of nanopillars on the thermal conductivity of the membranes in the 4-300 K range. We found that thermal conductivity reduction caused by the nanopillars does not exceed 16%, which is much weaker than that predicted by the theoretical works. Moreover, this reduction remains temperature independent. These facts make the coherence an unlikely reason for the observed reduction. Indeed, our Monte Carlo simulations can reproduce the experimental results under a purely incoherent approximation. Our study shows that the coherent control of heat conduction by PnC nanostructures is more challenging to observe experimentally in reality than predicted in near-ideal modeling.

Designing bistability or multistability in macroscopic diffusive systems

We theoretically design a kind of diffusion bistability (and even multistability) in the macroscopic scale, which has a similar phenomenon but different underlying mechanism from its microscopic counterpart [Phys. Rev. Lett. 101, 267203 (2008)10.1103/PhysRevLett.101.267203]; the latter has been extensively investigated in literature, e.g., for building nanometer-scale memory components. By introducing second- and third-order nonlinear terms (that opposite in sign) into diffusion coefficient matrices, a bistable energy or mass diffusion occurs with two different steady states identified as "0" and "1." In particular, we study heat conduction in a two-terminal three-body system and show that this bistable system exhibits a macroscale thermal memory effect with tailored nonlinear thermal conductivities. The theoretical analysis is confirmed by finite-element simulations. Also, we suggest experiments with metamaterials based on shape memory alloys. This theoretical framework blazes a trail on constructing intrinsic bistability or multistability in diffusive systems for macroscopic energy or mass management.

Recent Progress of Two-Dimensional Thermoelectric Materials

Thermoelectric generators have attracted a wide research interest owing to their ability to directly convert heat into electrical power. Moreover, the thermoelectric properties of traditional inorganic and organic materials have been significantly improved over the past few decades. Among these compounds, layered two-dimensional (2D) materials, such as graphene, black phosphorus, transition metal dichalcogenides, IVA-VIA compounds, and MXenes, have generated a large research attention as a group of potentially high-performance thermoelectric materials. Due to their unique electronic, mechanical, thermal, and optoelectronic properties, thermoelectric devices based on such materials can be applied in a variety of applications. Herein, a comprehensive review on the development of 2D materials for thermoelectric applications, as well as theoretical simulations and experimental preparation, is presented. In addition, nanodevice and new applications of 2D thermoelectric materials are also introduced. At last, current challenges are discussed and several prospects in this field are proposed.

Radiative metasurface for thermal camouflage, illusion and messaging

Thanks to the conductive thermal metamaterials, novel functionalities like thermal cloak, camouflage and illusion have been achieved, but conductive metamaterials can only control the in-plane heat conduction. The radiative thermal metamaterials can control the out-of-plane thermal emission, which are more promising and applicable but have not been studied as comprehensively as the conductive counterparts. In this paper, we theoretically investigate the surface emissivity of metal/insulator/metal (MIM, i.e., Au/Ge/Au here) microstructures, by the rigorous coupled-wave algorithm, and utilize the excitation of the magnetic polaritons to realize thermal camouflage through designing the grating width distribution by minimizing the temperature standard deviation of the overall plate. Through this strategy, the hot spot in the original temperature field is removed and a uniform temperature field is observed in the infrared camera instead, demonstrating the thermal camouflage functionality. Furthermore, thermal illusion and thermal messaging functionalities are also demonstrated by resorting to using such an emissivity-structured radiative metasurface. The present MIM-based radiative metasurface may open avenues for developing novel thermal functionalities via thermal metasurface and metamaterials.

Phonon transport and thermal conductivity of diamond superlattice nanowires: a comparative study with SiGe superlattice nanowires

Due to the coupling of a superlattice's longitudinal periodicity to a nanowire's radial confinement, the phonon transport properties of superlattice nanowires (SLNWs) are expected to be radically different from those of pristine nanowires. In this work, we present the comparative investigation of phonon transport and thermal conductivity between diamond SLNWs and SiGe SLNWs by using molecular dynamics simulations. In the case of period length ∼ 25 Å, the thermal conductivities of diamond SLNWs and SiGe SLNWs both increase linearly with increasing the period number, which implies the wave-like coherent phonons dominate the heat transport of SLNWs. In the case of period length ∼ 103 Å, the thermal conductivity of SiGe SLNWs is length-independent with increasing the period number, indicating that the particle-like incoherent phonons in SiGe SLNWs control the heat transport, because the phonon–phonon scattering causes phonons to not retain their phases and the coherence is destroyed before the reflection at interfaces. However in diamond SLNWs the coherent phonons still dominate heat conduction and the thermal conductivity is length-dependent, because the mean free path of phonon–phonon scattering in diamond SLNWs is much longer. The spatial distribution of phonon localized modes further supports these opinions. These results are helpful not only to understand the coherent and incoherent phonon transport, but also to modulate the thermal conductivity of SLNWs.

We present the comparative investigation of phonon transport and thermal conductivity between diamond SLNWs and SiGe SLNWs by molecular dynamics simulations.

Tailoring Nanoporous Structures in Bi2Te3 Thin Films for Improved Thermoelectric Performance

Thin-film thermoelectrics (TEs) with unique advantages have triggered great interest in thermal management and energy harvesting technology for ambient temperature microscale systems. Although they have exhibited a good prospect, their unsatisfactory performances still seriously hamper their widespread application. Tailoring the porous structure has been demonstrated to be a facile strategy to significantly reduce thermal conductivity and enhance the figure of merit (ZT) of bulk TE materials; however, it is challenging for thin-film TEs. Here, the nanoporous Bi₂Te₃ thin films with faceted pore shapes and various porosities, pore sizes, and pore intervals are carefully designed and fabricated by evacuating the over-stoichiometry Te atoms. The dependence of the carrier mobility and lattice thermal conductivity on the pore characteristics is investigated. In the case of the pore interval longer than the electron mean free path, the porous structure greatly reduces the lattice thermal conductivity without affecting the electrical conductivity obviously. Phonon specular backscattering that is highly related to the pore characteristics is suggested to be mainly responsible for thermal conductivity reduction, resulting in ∼60% enhancement in ZT at room temperature, that is, from ∼0.42 for the dense film to ∼0.67 for the nanoporous film. The enhanced ZT value is comparable to that of commercial bulk TEs and can be further improved by optimizing the carrier concentrations. This work provides a general approach to fabricate high-performance chalcogenide TE thin-film materials.

Thermal Conductivity Reduction in a Silicon Thin Film with Nanocones

Modern thermoelectric devices incline toward inexpensive, environmentally friendly, and CMOS-compatible materials, such as silicon. To improve the thermoelectric performance of silicon, researchers try to decrease its thermal conductivity using various nanostructuring methods. However, most of these methods have limited efficiency because they are costly and damaging for the internal structure of silicon. Here, we propose a cost-effective, large-area, and maskless nanofabrication method that creates external nanocones on the silicon surface while preserving its interior. Our experiments show that these nanocones reduce the thermal conductivity of thin silicon membranes by more than 40%. Using a modified Callaway-Holland model, we study how the thermal conductivity is affected by various phonon scattering processes in the 4-295 K temperature range. We conclude that the nanocones generate additional surface scattering, which causes the thermal conductivity reduction. The proposed nanocones and their simple fabrication method are promising for the planar thermoelectric devices based on silicon.

Ion Write Microthermotics: Programing Thermal Metamaterials at the Microscale

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.

Thermal transport through fishbone silicon nanoribbons: unraveling the role of Sharvin resistance

Heat conduction has been shown to be greatly suppressed in Si nanomeshes, which has attracted extensive attention for potential thermoelectric applications, yet the precise suppression mechanism remains to be fully understood. Attempting to further disclose the underlying mechanisms, we report on the thermal conductivity of the building block for nanomeshes, i.e., Si nanoribbons with fins attached to the two opposite sides. By expanding only the fin width while keeping both the period length and the backbone size constant, we observed an unexpected non-monotonic trend of the effective thermal conductivity normalized with the backbone cross-section. Further analysis showed that the corrected thermal conductivity extracted with appropriate consideration of the geometrical effect on diffusion followed a monotonically decreasing trend, reaching a maximum thermal conductivity reduction of 18% at 300 K for a ribbon with the maximum explored fin width of 430 nm, as compared to that of the straight ribbon of 66 nm backbone width. We attribute the thermal conductivity reduction to the thermal constriction resistance induced by the cross-section reduction between the fin and backbone sections. For ribbons with a larger fin width, the effective phonon mean free path is longer for phonons arriving at the constriction, which boosts the ballistic constriction resistance, i.e., Sharvin resistance, and leads to a lower thermal conductivity.

Thermoelectrics of Nanowires

The field of thermoelectric research has undergone a renaissance and boom in the past two and a half decades, largely fueled by the prospect of engineering electronic and phononic properties in nanostructures, among which semiconductor nanowires (NWs) have served both as an important platform to investigate fundamental thermoelectric transport phenomena and as a promising route for high thermoelectric performance for diverse applications. In this Review, we provide a comprehensive look at various aspects of thermoelectrics of NWs. We start with a brief introduction of basic thermoelectric phenomena, followed by synthetic methods for thermoelectric NWs and a summary of their thermoelectric figures of merit (ZT). We then focus our discussion on charge and heat transport, which dictate thermoelectric power factor and thermal conductivity, respectively. For charge transport, we cover the basic principles governing the power factor and then review several strategies using NWs to enhance it, including earlier theoretical and experimental work on quantum confinement effects and semimetal-to-semiconductor transition, surface engineering and complex heterostructures to enhance the carrier mobility and power factor, and the recent emergence of topological insulator NWs. For phonon transport, we broadly categorize the work on thermal conductivity of NWs into five different effects: classic size effect, acoustic softening, surface roughness, complex NW morphology, and dimensional crossover. Finally, we discuss the integration of NWs for device applications for thermoelectric power generation and cooling. We conclude our review with some outlooks for future research.

TSV-integrated thermoelectric cooling by holey silicon for hot spot thermal management

The trends toward higher power, higher frequency, and smaller scale electronics are making heat dissipation ever more challenging. Passive thermal management based on high thermal conductivity materials or through-silicon vias (TSVs) may not provide sufficient cooling for hot spots reaching 1 kW cm^-2, and active thermal management by thermoelectric cooling (TEC) may require large power consumption or suffer from a large off-state thermal resistance of thermoelectric materials. Here we address these issues by integrating a holey silicon-based TEC with a TSV that directly draws heat from a hot spot to combine active and passive cooling approaches. Our simulations of the TSV-integrated TEC demonstrate exceptional cooling performance, which reduces the hot spot temperature from 154 °C to 68 °C while dissipating a heat flux of 1 k W cm^-2 and consuming 0.5 W for TEC operation. The off-state hot spot temperature, 154 °C, is 24 °C lower than that of the same TEC with no TSV, and the on-state hot spot temperature, 68 °C, is 67 °C lower than that of the same TEC with no TSV. We also investigate the cooling prospects of metal-filled holey silicon by modeling the electron-phonon coupling and size dependent transport phenomena, which can further increase the thermal conductivity anisotropy and improve the TEC performance depending on the metal-to-silicon interfacial resistance. These results show the combined passive and active cooling in TSV-integrated TEC offers effective hot spot thermal management solutions for advanced electronics.

Phonon and heat transport control using pillar-based phononic crystals

Phononic crystals have been studied for the past decades as a tool to control the propagation of acoustic and mechanical waves. Recently, researchers proposed that nanosized phononic crystals can also control heat conduction and improve the thermoelectric efficiency of silicon by phonon dispersion engineering. In this review, we focus on recent theoretical and experimental advances in phonon and thermal transport engineering using pillar-based phononic crystals. First, we explain the principles of the phonon dispersion engineering and summarize early proof-of-concept experiments. Next, we review recent simulations of thermal transport in pillar-based phononic crystals and seek to uncover the origin of the observed reduction in the thermal conductivity. Finally, we discuss first experimental attempts to observe the predicted thermal conductivity reduction and suggest the directions for future research.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt {{\mathrm{Hz}}} \,^{ - 1}$$\end{document}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.

At low temperatures and dimensionality it has become possible to probe the quantum limits of heat transport. Tavakoli et al. show that heat transport through a one-dimensional device can be dominated by non-ideal transmission instead of reaching the regime of thermal conductance quantization.

Impact of thermally dead volume on phonon conduction along silicon nanoladders

Thermal conduction in complex periodic nanostructures remains a key area of open questions and research, and a particularly provocative and challenging detail is the impact of nanoscale material volumes that do not lie along the optimal line of sight for conduction. Here, we experimentally study thermal transport in silicon nanoladders, which feature two orthogonal heat conduction paths: unobstructed line-of-sight channels in the axial direction and interconnecting bridges between them. The nanoladders feature an array of rectangular holes in a 10 μm long straight beam with a 970 nm wide and 75 nm thick cross-section. We vary the pitch of these holes from 200 nm to 1100 nm to modulate the contribution of bridges to the net transport of heat in the axial direction. The effective thermal conductivity, corresponding to reduced heat flux, decreases from ∼45 W m-1 K-1 to ∼31 W m-1 K-1 with decreasing pitch. By solving the Boltzmann transport equation using phonon mean free paths taken from ab initio calculations, we model thermal transport in the nanoladders, and experimental results show excellent agreement with the predictions to within ∼11%. A combination of experiments and calculations shows that with decreasing pitch, thermal transport in nanoladders approaches the counterpart in a straight beam equivalent to the line-of-sight channels, indicating that the bridges constitute a thermally dead volume. This study suggests that ballistic effects are dictated by the line-of-sight channels, providing key insights into thermal conduction in nanostructured metamaterials.

Thermal Studies of Nanoporous Si Films with Pitches on the Order of 100 nm -Comparison between Different Pore-Drilling Techniques

In recent years, nanoporous Si films have been widely studied for thermoelectric applications due to the low cost and earth abundance of Si. Despite many encouraging results, inconsistency still exists among experimental and theoretical studies of reduced lattice thermal conductivity for varied nanoporous patterns. In addition, divergence can also be found among reported data, due to the difference in sample preparation and measurement setups. In this work, systematic measurements are carried out on nanoporous Si thin films with pore pitches on the order of 100 nm, where pores are drilled either by dry etching or a focused ion beam. In addition to thermal conductivity measurements, the specific heat of the nanoporous films is simultaneously measured and agrees with the estimation using bulk values, indicating a negligible change in the phonon dispersion. Without considering coherent phonon transport, the measured thermal conductivity values agree with predictions by frequency-dependent phonon Monte Carlo simulations assuming diffusive pore-edge phonon scattering. In Monte Carlo simulations, an expanded effective pore diameter is used to account for the amorphization and oxidation on real pore edges.

Thermal Transport in Supported Graphene Nanomesh

Graphene is considered as a promising candidate material to replace silicon for the next-generation nanoelectronics because of its superb carrier mobility. To evaluate its thermal dissipation capability as electronic materials, the thermal transport in monolayer graphene was extensively explored over the past decade. However, the supported chemical vapor deposition (CVD) grown monolayer graphene with submicron structures were seldom studied, which is important for practical nanoelectronics. Here we investigate the thermal transport properties in a series of CVD graphene nanomeshes patterned by a hard-template-assisted etching method. The experimental and numerical results uncovered the phonon backscattering at hole boundary (<100 nm neck width) and its substantial contribution to the thermal conductivity reduction.

Electron-phonon scattering effect on the lattice thermal conductivity of silicon nanostructures

Nanostructuring technology has been widely employed to reduce the thermal conductivity of thermoelectric materials because of the strong phonon-boundary scattering. Optimizing the carrier concentration can not only improve the electrical properties, but also affect the lattice thermal conductivity significantly due to the electron-phonon scattering. The lattice thermal conductivity of silicon nanostructures considering electron-phonon scattering is investigated for comparing the lattice thermal conductivity reductions resulting from nanostructuring technology and the carrier concentration optimization. We performed frequency-dependent simulations of thermal transport systematically in nanowires, solid thin films and nanoporous thin films by solving the phonon Boltzmann transport equation using the discrete ordinate method. All the phonon properties are based on the first-principles calculations. The results show that the lattice thermal conductivity reduction due to the electron-phonon scattering decreases as the feature size of nanostructures goes down and could be ignored at low feature sizes (50 nm for n-type nanowires and 20 nm for p-type nanowires and n-type solid thin films) or a high porosity (0.6 for n-type 500 nm-thick nanoporous thin films) even when the carrier concentration is as high as 10²¹ cm^-3. Similarly, the size effect due to the phonon-boundary scattering also becomes less significant with the increase of carrier concentration. The findings provide a fundamental understanding of electron and phonon transports in nanostructures, which is important for the optimization of nanostructured thermoelectric materials.

Enhancing Thermal Transport in Layered Nanomaterials

A comprehensive rational thermal material design paradigm requires the ability to reduce and enhance the thermal conductivities of nanomaterials. In contrast to the existing ability to reduce the thermal conductivity, methods that allow to enhance heat conduction are currently limited. Enhancing the nanoscale thermal conductivity could bring radical improvements in the performance of electronics, optoelectronics, and photovoltaic systems. Here, we show that enhanced thermal conductivities can be achieved in semiconductor nanostructures by rationally engineering phonon spectral coupling between materials. By embedding a germanium film between silicon layers, we show that its thermal conductivity can be increased by more than 100% at room temperature in contrast to a free standing thin-film. The injection of phonons from the cladding silicon layers creates the observed enhancement in thermal conductivity. We study the key factors underlying the phonon injection mechanism and find that the surface conditions and layer thicknesses play a determining role. The findings presented here will allow for the creation of nanomaterials with an increased thermal conductivity.

Thermal conductivity anisotropy in holey silicon nanostructures and its impact on thermoelectric cooling

Artificial nanostructures have improved prospects of thermoelectric systems by enabling selective scattering of phonons and demonstrating significant thermal conductivity reductions. While the low thermal conductivity provides necessary temperature gradients for thermoelectric conversion, the heat generation is detrimental to electronic systems where high thermal conductivity are preferred. The contrasting needs of thermal conductivity are evident in thermoelectric cooling systems, which call for a fundamental breakthrough. Here we show a silicon nanostructure with vertically etched holes, or holey silicon, uniquely combines the low thermal conductivity in the in-plane direction and the high thermal conductivity in the cross-plane direction, and that the anisotropy is ideal for lateral thermoelectric cooling. The low in-plane thermal conductivity due to substantial phonon boundary scattering in small necks sustains large temperature gradients for lateral Peltier junctions. The high cross-plane thermal conductivity due to persistent long-wavelength phonons effectively dissipates heat from a hot spot to the on-chip cooling system. Our scaling analysis based on spectral phonon properties captures the anisotropic size effects in holey silicon and predicts the thermal conductivity anisotropy ratio up to 20. Our numerical simulations demonstrate the thermoelectric cooling effectiveness of holey silicon is at least 30% greater than that of high-thermal-conductivity bulk silicon and 400% greater than that of low-thermal-conductivity chalcogenides; these results contrast with the conventional perception preferring either high or low thermal conductivity materials. The thermal conductivity anisotropy is even more favorable in laterally confined systems and will provide effective thermal management solutions for advanced electronics.

Reduction of thermal conductivity in silicene nanomesh: insights from coherent and incoherent phonon transport

Investigation of heat transfer reduction of silicene nanomesh considering the mechanisms of both coherent and incoherent phonon transport.

Aluminium nanopillars reduce thermal conductivity of silicon nanobeams

In search of efficient thermoelectric nanostructures, many theoretical works predicted that nanopillars, placed on the surface of silicon membranes, nanobeams, or nanowires, can reduce the thermal conductivity of these nanostructures. To verify these predictions, we experimentally investigate heat conduction in suspended silicon nanobeams with periodic arrays of aluminium nanopillars. Our room temperature time-domain thermoreflectance experiments show that the nanobeams with nanopillars have 20% lower thermal conductivity as compared to pristine nanobeams. We discuss possible explanations of these data, including coherent effects, and conclude that the thermal conductivity is reduced mainly by phonon scattering at the pillar/beam interface due to the intermixing of aluminium and silicon atoms, as supported by the transmission electron microscopy. As this intermixing does not only reduce thermal conductivity but may also increase electrical conductivity, these nanostructures are exceptionally promising for thermoelectric applications.

Heat conduction tuning by wave nature of phonons

The world communicates to our senses of vision, hearing, and touch in the language of waves, because light, sound, and even heat essentially consist of microscopic vibrations of different media. The wave nature of light and sound has been extensively investigated over the past century and is now widely used in modern technology. However, the wave nature of heat has been the subject of mostly theoretical studies because its experimental demonstration, let alone practical use, remains challenging due to its extremely short wavelengths. We show a possibility to use the wave nature of heat for thermal conductivity tuning via spatial short-range order in phononic crystal nanostructures. Our experimental and theoretical results suggest that interference of thermal phonons occurs in strictly periodic nanostructures and slows the propagation of heat. This finding expands the methodology of heat transfer engineering to the wave nature of heat.

Phonon Conduction in Silicon Nanobeam Labyrinths

Here we study single-crystalline silicon nanobeams having 470 nm width and 80 nm thickness cross section, where we produce tortuous thermal paths (i.e. labyrinths) by introducing slits to control the impact of the unobstructed "line-of-sight" (LOS) between the heat source and heat sink. The labyrinths range from straight nanobeams with a complete LOS along the entire length to nanobeams in which the LOS ranges from partially to entirely blocked by introducing slits, s = 95, 195, 245, 295 and 395 nm. The measured thermal conductivity of the samples decreases monotonically from ~47 W m^-1 K^-1 for straight beam to ~31 W m^-1 K^-1 for slit width of 395 nm. A model prediction through a combination of the Boltzmann transport equation and ab initio calculations shows an excellent agreement with the experimental data to within ~8%. The model prediction for the most tortuous path (s = 395 nm) is reduced by ~14% compared to a straight beam of equivalent cross section. This study suggests that LOS is an important metric for characterizing and interpreting phonon propagation in nanostructures.