Thermal Rectification by Design in Telescopic Si Nanowires

Room temperature thermal rectification in suspended asymmetric graphene ribbon

Thermal rectifiers are essential in optimizing heat dissipation in solid-state devices to enhance energy efficiency, reliability, and overall performance. In this study, we experimentally investigate the thermal rectification phenomenon in suspended asymmetric graphene ribbons (GRs). The asymmetry within the graphene is introduced by incorporating periodic parallel nanoribbons on one side of the GR while maintaining the other side in a pristine form. Our findings reveal a substantial thermal rectification effect in these asymmetric graphene devices, reaching up to 45% at room temperature and increasing further at lower environmental temperatures. This effect is attributed to a significant thermal conductivity contrast between pristine graphene and nanoribbon graphene within the asymmetric structure. We observe that the incorporation of nanoribbons leads to a notable reduction in thermal conductivity, primarily due to phonon scattering and bottleneck effects near the nanoribbon edges. These findings suggest that graphene structures exhibiting asymmetry, facilitated by parallel nanoribbons, hold promise for effective heat management at the nanoscale level and the development of practical phononic devices.

Thermal rectification through the topological states of asymmetrical length armchair graphene nanoribbons heterostructures with vacancies

We present a theoretical investigation of electron heat current in asymmetrical length armchair graphene nanoribbon (AGNR) heterostructures with vacancies, focusing on the topological states (TSs). In particular, we examine the 9-7-9 AGNR heterostructures where the TSs are well-isolated from the conduction and valence subbands. This isolation effectively mitigates thermal noise of subbands arising from temperature fluctuations during charge transport. Moreover, when the TSs exhibit an orbital off-set, intriguing electron heat rectification phenomena are observed, primarily attributed to inter-TS electron Coulomb interactions. To enhance the heat rectification ratio (ηQ), we manipulate the coupling strengths between the heat sources and the TSs by introducing asymmetrical lengths in the 9-AGNRs. This approach offers control over the rectification properties, enabling significant enhancements. Additionally, we introduce vacancies strategically positioned between the heat sources and the TSs to suppress phonon heat current. This arrangement effectively reduces the overall phonon heat current, while leaving the TSs unaffected. Our findings provide valuable insights into the behavior of electron heat current in AGNR heterostructures, highlighting the role of topological states, inter-TS electron Coulomb interactions, and the impact of structural modifications such as asymmetrical lengths and vacancy positioning. These results pave the way for the design and optimization of graphene-based devices with improved thermal management and efficient control of electron heat transport.

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.

Thermal rectification in ultra-narrow hydrogen functionalized graphene: a non-equilibrium molecular dynamics study

In this study, the non-equilibrium molecular dynamics simulation (NEMD) has been used to evaluate the thermal properties, especially the rectification of ultra-narrow edge-functionalized graphene with hydrogen atoms. The system's small width equals 4.91 Å (equivalent to two hexagonal rings). The dependence of the thermal rectification on the mean temperature, hydrogen concentration, and temperature difference between the two baths was investigated. Results reveal that the thermal rectification increases to 100% at 550 K by increasing the mean temperature. Also, it is disclosed that hydrogen concentration plays a vibrant role in thermal rectification. As a result of maximum phonon scattering at the interface, a thorough rectification is obtained in a half-fully hydrogenated system. As well, the effects of temperature difference of baths ΔT on thermal rectification has been calculated. As a result, the thermal rectification decreases even though the current heat increases with ΔT. Finally, the thermal resistance at the interface using a mismatching factor between the two-phonon density of states (DOS) on both sides of the interface has been explained.

Tunable Thermal Switch via Order-Order Transition in Liquid Crystalline Block Copolymer

Organic material-based thermal switch is drawing much attention as one of the key thermal management devices in organic electronic devices. This study aims at tuning the switching temperature (T_S) of thermal conductivity by using liquid crystalline block copolymers (BCs) with different order-order transition temperature (T_tr) related to the types of mesogens in the side chain. The BC films with low T_tr of 363 K and high T_tr of 395 K exhibit reversible thermal conductivity switching behaviors at T_S of ∼360 K and ∼390 K, respectively. The BC films also exhibit thermal conductivity variation originating from the anisotropy of the internal structures: poly(ethylene oxide) domains and liquid crystals. These results demonstrate that the switching behavior is attributed to an order-order transition between BC films with vertically arranged cylinder domains and the ones with ordered sphere domains. This highlights that BCs become a promising thermal conductivity switching material with tailored T_S.

Thermal rectification in polytelescopic Ge nanowires

Herein we served non-equilibrium molecular dynamics (NEMD) approach to simulate thermal rectification in the mono- and polytelescopic Ge nanowires (GeNWs). We considered mono-telescopic structures with different Fat-Thin configurations (15-10 nm-nm or Type (I); 15-5 nm-nm or Type (II); and 10-5 or Type (III) nm-nm) as generic models. We simulated the variation of thermal conductivity against interfacial cross-sectional temperature as well as the direction of heat transfer, where a higher thermal conductivity correlating to thicker nanowires, and a more significant drop (or discontinuity) in the average interface temperature in the positive (or negative) direction were detected. Noticeably, interfacial thermal resistance followed the order of Type (II) (48 K/μW, maximal) ˃ Type (III) ˃ Type (I) (5 K/μW, minimal). In the second stage, a series of polytelescopic nanostructures of GeNWs were born with consecutive cross-sectional interfaces. Surprisingly, larger interfacial cross-sectional areas equivalent to smaller diameter changes along the GeNWs were responsible for higher temperature rectification. This led to a very limited thermal conductivity loss or a very high unidirectional heat transfer along the polytelescopic structures - the key for manufacturing next generation high-performance thermal diodes.

Thermal conduction and rectification phenomena in nanoporous silicon membranes

Non-equilibrium molecular dynamics simulations have been applied to study thermal transport properties, such as thermal conductivity and rectification, in nanoporous Si membranes. Cylindrical pores have been generated in crystalline Si membranes with different configurations, including step-like, ordered and random pore distributions. The effect of interface and overall porosity on thermal transport properties has been investigated as well as the impact of the porosity profile on the direction of the heat current. The lowest thermal conductivity and highest thermal rectification for equal porosity have been found for a step-like pore distribution. Increasing interface porosity resulted in an increase of thermal rectification, which has been found to be systematically higher for random pore distribution with respect to an ordered one. Furthermore, a maximum in rectification of 5.5% has been found for a specific overall porosity (Φ_tot = 0.02) in samples with constant interface porosity and ordered pore distribution. This has been attributed to an increased effect of asymmetric interface boundary resistance resulting from increased fluctuations of the latter with altering temperature. The average value of the interface boundary resistance has been found to decrease with increasing porosity for samples with ordered pore distribution leading to a decrease in thermal rectification.

Experimental evaluation of thermal rectification in a ballistic nanobeam with asymmetric mass gradient

Practical applications of heat transport control with artificial metamaterials will heavily depend on the realization of thermal diodes/rectifiers, in which thermal conductivity depends on the heat flux direction. Whereas various macroscale implementations have been made experimentally, nanoscales realizations remain challenging and efficient rectification still requires a better fundamental understanding of heat carriers’ transport and nonlinear mechanisms. Here, we propose an experimental realization of a thermal rectifier based on two leads with asymmetric mass gradients separated by a ballistic spacer, as proposed in a recent numerical investigation, and measure its thermal properties electrically with the microbridge technique. We use a Si\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{4}$$\end{document}4 nanobeam on which an asymmetric mass gradient has been engineered and demonstrate that in its current form, this structure does not allow for thermal rectification. We explain this by a combination of too weak asymmetry and non-linearities. Our experimental observations provide important information towards fabricating rigorous thermal rectifiers in the ballistic phonon transport regime, which are expected to open new possibilities for applications in thermal management and quantum thermal devices.

Graphene-carbon nitride interface-geometry effects on thermal rectification: a molecular dynamics simulation

In this paper we expand our previous study on phonon thermal rectification (TR) exhibited in a hybrid graphene-carbon nitride system (G-C3N) to investigate the system's behavior under a wider range of temperature differences, between the two employed baths, and the effects of media-interface geometry on the rectification factor. Our simulation results reveal a sigmoid relation between TR and temperature difference, with a sample-size depending upper asymptote occurring at generally large temperature differences. The achieved TR values are significant and go up to around 120% for ΔT = 150 K. Furthermore, the consideration of varying media-interface geometries yields a non-negligible effect on TR and highlights areas for further investigation. Finally, calculations of Kapitza resistance at the G-C3N interface are performed for assisting us in the understanding of interface-geometry effects on TR.

Phonon thermal rectification in hybrid graphene-[Formula: see text]: a molecular dynamics simulation

We apply the non-equilibrium molecular dynamics approach (NEMD) to study thermal rectification in a hybrid graphene-carbon nitride system ([Formula: see text]) under a series of positive and negative temperature gradients. In this study, the effects of temperature difference, between two baths (ΔT), and sample size on thermal rectification are investigated. Our simulation results indicate positive correlation between thermal rectification and temperature difference for ΔT > 60 K, and high thermal rectification values, up to around 50% for ΔT = 100 K. Furthermore, this behavior remains practically consistent among different sample lengths. The underlying mechanism leading to a preferable direction for phonons is calculated using phonon density of states (DOS) on both sides of the [Formula: see text] interface, and the contributions of in-plane and out-of-plane phonon modes in total thermal rectification are also explored.

Net negative contributions of free electrons to the thermal conductivity of NbSe3 nanowires

Understanding transport mechanisms of electrons and phonons, two major energy carriers in solids, are crucial for various engineering applications. It is widely believed that more free electrons in a material should correspond to a higher thermal conductivity; however, free electrons also scatter phonons to lower the lattice thermal conductivity. The net contribution of free electrons has been rarely studied because the effects of electron-phonon (e-ph) interactions on lattice thermal conductivity have not been well investigated. Here an experimental study of e-ph scattering in quasi-one-dimensional NbSe3 nanowires is reported, taking advantage of the spontaneous free carrier concentration change during charge density wave (CDW) phase transition. Contrary to the common wisdom that more free electrons would lead to a higher thermal conductivity, results show that during the depinning process of the condensed electrons, while the released electrons enhance the electronic thermal conductivity, the overall thermal conductivity decreases due to the escalated e-ph scattering. This study discloses how competing effects of free electrons result in unexpected trends and provides solid experimental data to dissect the contribution of e-ph scattering on lattice thermal conductivity. Lastly, an active thermal switch design is demonstrated based on tuning electron concentration through electric field.

Thermal rectification and interfacial thermal resistance in hybrid pillared-graphene and graphene: a molecular dynamics and continuum approach

We investigate thermal rectification and thermal resistance in a hybrid pillared-graphene and graphene (PGG) system by both molecular dynamics (MD) simulation and a continuum model. First, the thermal conductivity of both pillared-graphene and graphene is calculated by employing MD simulation and Fourier's law. Our results show that the thermal conductivity of the pillared-graphene is much smaller than that of graphene by one order of magnitude. Next, by applying positive and negative temperature gradients along the longitudinal direction of the PGG, the thermal rectification is examined. The MD results indicate that for the lengths in the range of 3686 nm, the thermal rectification remains almost constant (~3%-5%). We have also studied the phonon density of states (DOS) on both sides of the interface of PGG. The DOS curves show that there is phonon scattering at low frequencies that depends on the imposed temperature gradient direction in the system. Therefore, we can introduce the PGG as a thermal rectifier at room temperature. Furthermore, next, we also explore the temperature distribution over the PGG by using the continuum model. The results obtained from the continuum model predict the MD results, such as the temperature distribution in the upper half-layer and lower full-layer graphene, the temperature gap, and also the thermal resistance at the interface. This study could help in the design of chip coolers, and phononic devices such as thermal nanodiodes.

Green function, quasi-classical Langevin and Kubo-Greenwood methods in quantum thermal transport

With the advances in fabrication of materials with feature sizes at the order of nanometers, it has been possible to alter their thermal transport properties dramatically. Miniaturization of device size increases the power density in general, hence faster electronics require better thermal transport, whereas better thermoelectric applications require the opposite. Such diverse needs bring new challenges for material design. Shrinkage of length scales has also changed the experimental and theoretical methods to study thermal transport. Unsurprisingly, novel approaches have emerged to control phonon flow. Besides, ever increasing computational power is another driving force for developing new computational methods. In this review, we discuss three methods developed for computing vibrational thermal transport properties of nano-structured systems, namely Green function, quasi-classical Langevin, and Kubo-Green methods. The Green function methods are explained using both nonequilibrium expressions and the Landauer-type formula. The partitioning scheme, decimation techniques and surface Green functions are reviewed, and a simple model for reservoir Green functions is shown. The expressions for the Kubo-Greenwood method are derived, and Lanczos tridiagonalization, continued fraction and Chebyshev polynomial expansion methods are discussed. Additionally, the quasi-classical Langevin approach, which is useful for incorporating phonon-phonon and other scatterings is summarized.

The effect of structural asymmetry on thermal rectification in nanostructures

Three SWCNT-graphene nanostructure-based models are designed to probe the thermal rectification caused by the structural asymmetry in the boundary thermal contacts, the device, and the whole system, respectively. We find that both the asymmetry of entire system and the asymmetry of the device are not necessary condition for the existence of thermal rectification, and the asymmetry in boundary thermal contacts is more important than the asymmetry in device toward determining both the magnitude and the direction of thermal rectification. Interestingly, notable thermal rectification can exist in the systems with overall structural symmetry when the boundary thermal contacts are structurally asymmetric. Moreover, nanostructures with a structurally symmetric device and structurally asymmetric boundary thermal contacts can still display significant thermal rectification. These findings could offer insight into the future design and performance improvement of nanostructured thermal rectifiers.

Reduction of Thermal Conductivity in Nanowires by Combined Engineering of Crystal Phase and Isotope Disorder

Nanowires are a versatile platform to investigate and harness phonon and thermal transport phenomena in nanoscale systems. With this perspective, we demonstrate herein the use of crystal phase and mass disorder as effective degrees of freedom to manipulate the behavior of phonons and control the flow of local heat in silicon nanowires. The investigated nanowires consist of isotopically pure and isotopically mixed nanowires bearing either a pure diamond cubic or a cubic-rhombohedral polytypic crystal phase. The nanowires with tailor-made isotopic compositions were grown using isotopically enriched silane precursors ²⁸SiH₄, ²⁹SiH₄, and ³⁰SiH₄ with purities better than 99.9%. The analysis of polytypic nanowires revealed ordered and modulated inclusions of lamellar rhombohedral silicon phases toward the center in otherwise diamond-cubic lattice with negligible interphase biaxial strain. Raman nanothermometry was employed to investigate the rate at which the local temperature of single suspended nanowires evolves in response to locally generated heat. Our analysis shows that the lattice thermal conductivity in nanowires can be tuned over a broad range by combining the effects of isotope disorder and the nature and degree of polytypism on phonon scattering. We found that the thermal conductivity can be reduced by up to ∼40% relative to that of isotopically pure nanowires, with the lowest value being recorded for the rhombohedral phase in isotopically mixed ²⁸Si _x³⁰Si_{1- x} nanowires with composition close to the highest mass disorder ( x ∼ 0.5). These results shed new light on the fundamentals of nanoscale thermal transport and lay the groundwork to design innovative phononic devices.

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.

Experimental study of thermal rectification in suspended monolayer graphene

Thermal rectification is a fundamental phenomenon for active heat flow control. Significant thermal rectification is expected to exist in the asymmetric nanostructures, such as nanowires and thin films. As a one-atom-thick membrane, graphene has attracted much attention for realizing thermal rectification as shown by many molecular dynamics simulations. Here, we experimentally demonstrate thermal rectification in various asymmetric monolayer graphene nanostructures. A large thermal rectification factor of 26% is achieved in a defect-engineered monolayer graphene with nanopores on one side. A thermal rectification factor of 10% is achieved in a pristine monolayer graphene with nanoparticles deposited on one side or with a tapered width. The results indicate that the monolayer graphene has great potential to be used for designing high-performance thermal rectifiers for heat flow control and energy harvesting.

Thermal rectification is instrumental to achieving active heat flow control and energy harvesting in nanoscale devices. Here, the authors demonstrate thermal rectification in asymmetric graphene nanostructures, achieving a large rectification factor up to 26%.

High Temperature Near-Field NanoThermoMechanical Rectification

Limited performance and reliability of electronic devices at extreme temperatures, intensive electromagnetic fields, and radiation found in space exploration missions (i.e., Venus &Jupiter planetary exploration, and heliophysics missions) and earth-based applications requires the development of alternative computing technologies. In the pursuit of alternative technologies, research efforts have looked into developing thermal memory and logic devices that use heat instead of electricity to perform computations. However, most of the proposed technologies operate at room or cryogenic temperatures, due to their dependence on material's temperature-dependent properties. Here in this research, we show experimentally-for the first time-the use of near-field thermal radiation (NFTR) to achieve thermal rectification at high temperatures, which can be used to build high-temperature thermal diodes for performing logic operations in harsh environments. We achieved rectification through the coupling between NFTR and the size of a micro/nano gap separating two terminals, engineered to be a function of heat flow direction. We fabricated and tested a proof-of-concept NanoThermoMechanical device that has shown a maximum rectification of 10.9% at terminals' temperatures of 375 and 530 K. Experimentally, we operated the microdevice in temperatures as high as about 600 K, demonstrating this technology's suitability to operate at high temperatures.

Ultrahigh Thermal Rectification in Pillared Graphene Structure with Carbon Nanotube-Graphene Intramolecular Junctions

In this letter, graded pillared graphene structures with carbon nanotube-graphene intramolecular junctions are demonstrated to exhibit ultrahigh thermal rectification. The designed graded two-stage pillared graphene structures are shown to have rectification values of 790.8 and 1173.0% at average temperatures 300 and 200 K, respectively. The ultrahigh thermal rectification is found to be a result of the obvious phonon spectra mismatch before and after reversing the applied thermal bias. This outcome is attributed to both the device shape asymmetry and the size asymmetric boundary thermal contacts. We also find that the significant and stable standing waves that exist in graded two-stage pillared graphene structures play an important role in this kind of thermal rectifier, and are responsible for the ultrahigh thermal rectification of the two-stage ones as well. Our work demonstrates that pillared graphene structure with SWCNT-graphene intramolecular junctions is an excellent and promising phononic device.

Microscale solid-state thermal diodes enabling ambient temperature thermal circuits for energy applications

A micro-scale phase change thermal diode capable of ambient and solid-state operation is developed and incorporated into a thermal diode bridge circuit.

Bidirectional negative differential thermal resistance in three-segment Frenkel-Kontorova lattices

By coupling three nonlinear 1D lattice segments, we demonstrate a thermal insulator model, where the system acts like an insulator for large temperature bias and a conductor for very small temperature bias. We numerically investigate the parameter range of the thermal insulator and find that the nonlinear response (the role of on-site potential), the weakly coupling interaction between each segment, and the small system size collectively contribute to the appearance of bidirectional negative differential thermal resistance (BNDTR). The corresponding exhibition of BNDTR can be explained in terms of effective phonon-band shifts. Our results can provide a new perspective for understanding the microscopic mechanism of negative differential thermal resistance and also would be conducive to further developments in designing and fabricating thermal devices and functional materials.

Plateau-Rayleigh Crystal Growth of Nanowire Heterostructures: Strain-Modified Surface Chemistry and Morphological Control in One, Two, and Three Dimensions

One-dimensional (1D) structures offer unique opportunities for materials synthesis since crystal phases and morphologies that are difficult or impossible to achieve in macroscopic crystals can be synthesized as 1D nanowires (NWs). Recently, we demonstrated one such phenomenon unique to growth on a 1D substrate, termed Plateau-Rayleigh (P-R) crystal growth, where periodic shells develop along a NW core to form diameter-modulated NW homostructures with tunable morphologies. Here we report a novel extension of the P-R crystal growth concept with the synthesis of heterostructures in which Ge (Si) is deposited on Si (Ge) 1D cores to generate complex NW morphologies in 1, 2, or 3D. Depositing Ge on 50 nm Si cores with a constant GeH4 pressure yields a single set of periodic shells, while sequential variation of GeH4 pressure can yield multimodulated 1D NWs with two distinct sets of shell periodicities. P-R crystal growth on 30 nm cores also produces 2D loop structures, where Ge (Si) shells lie primarily on the outside (inside) of a highly curved Si (Ge) core. Systematic investigation of shell morphology as a function of growth time indicates that Ge shells grow in length along positive curvature Si cores faster than along straight Si cores by an order of magnitude. Short Ge deposition times reveal that shells develop on opposite sides of 50 and 100 nm Si cores to form straight 1D morphologies but that shells develop on the same side of 20 nm cores to produce 2D loop and 3D spring structures. These results suggest that strain mediates the formation of 2 and 3D morphologies by altering the NW's surface chemistry and that surface diffusion of heteroatoms on flexible freestanding 1D substrates can facilitate this strain-mediated mechanism.

Heat transport through a solid–solid junction: the interface as an autonomous thermodynamic system

We perform computational experiments using nonequilibrium molecular dynamics simulations, showing that the interface between two solid materials can be described as an autonomous thermodynamic system.