Cross-plane Thermal Transport Research Articles

Twist-Dependent Anisotropic Thermal Conductivity in Homogeneous MoS2 Stacks

Thermal transport property of homogeneous twisted molybdenum disulfide (MoS2) is investigated using non-equilibrium molecular dynamics simulations with the state-of-art force fields. The simulation results demonstrate that the cross-plane thermal conductivity strongly depends on the interfacial twist angle, while it has only a minor effect on the in-plane thermal conductivity, exhibiting a highly anisotropic nature. A frequency-decomposed phonon analysis showed that the cross-plane and in-plane thermal conductivity of MoS2 are dominated by the phonons with frequencies below 12.5 THz and 7.5 THz, respectively. As the interfacial twist angle increases, these low-frequency phonons significantly attenuate the phonon transport across the interface, leading to impeded cross-plane thermal transport. However, the in-plane phonon transport is almost unaffected, which allows for maintaining high in-plane thermal conductivity. Furthermore, our study revealed a strong size dependence for both cross-plane and in-plane thermal conductivities due to the influence of low-frequency phonons in MoS2. The maximum thermal conductivity anisotropy ratio is estimated as ∼400 for twisted MoS2 from our simulation, which is in the same order of magnitude as recent experimental results (∼900). Our study highlights the potential of twist engineering as a tool for tailoring the thermal transport properties of layered materials.

Comprehensive characterization of thermal and mechanical properties in thin metal film-glass substrate system by ultrafast laser pump-probe method.

Picosecond ultrasonics (PU), time-domain Brillouin scattering (TDBS), and time-domain thermo-reflectance (TDTR) are all in-situ, non-destructive, and non-contact experimental techniques based on the ultrafast laser pump-probe method, which can generate and detect coherent acoustic phonons (CAP) and thermal transport in thin metal film-glass substrate system. However, these techniques are generally considered different experimental methods to characterize the thermal or mechanical properties of metal nano-objects or transparent materials. Here we present a comprehensive characterization of the generation, propagation, and attenuation of high-frequency CAP and cross-plane thermal transport in the thin Cr film-glass substrate system by PU, TDBS, and TDTR. To investigate the key factors of characterizations, two kinds of thin Cr film-glass substrate systems were measured on the film side and substrate side. The measured thermal and mechanical properties show that boundary conditions and film thickness have significantly affected the characterization.

The dual role of interlayer crosslinks leads to an abnormal behavior of interlayer thermal resistance in multilayer graphene

Understanding and controlling the interlayer thermal resistance (ITR) are crucial to the cross-plane thermal transport in multilayer graphene (MLG). Using non-equilibrium molecular dynamics simulations, we show that the ITR of MLG can be effectively tuned by in-plane defects, sp2 and sp3 C–C bond crosslinks. Specifically, with the increase of the in-plane defect density, the ITR initially increases sharply and then almost saturates; while with the increase of the crosslink density, the ITR initially also increases sharply, then peaks and subsequently decreases rapidly to a level that can be even lower than that of pristine MLG. The underlying mechanism for this unexpected variation of ITR with crosslink density is explored through the analyses of the phonon density of states (DOS) and spectral transmission function. It was found that the crosslinks play a dual role: the crosslink-generated in-plane defect enhances phonon scattering and leads to an increase in the ITR, while the interlayer bonding gives rise to a fast phonon transmission pathway and decreases the ITR. An effective medium approximation (EMA) model was proposed to describe the dual role of the crosslinks. This work provides new insight into the thermal transport behavior of crosslinks, which is useful for modulating the cross-plane thermal transport of MLG for the thermal management of MLG-based nanodevices.

Thermal and electrical cross-plane conductivity at the nanoscale in poly(3,4-ethylenedioxythiophene):trifluoromethanesulfonate thin films.

Cross-plane electrical and thermal transport in thin films of a conducting polymer (poly(3,4-ethylenedioxythiophene), PEDOT) stabilized with trifluoromethanesulfonate (OTf) is investigated in this study. We explore their electrical properties by conductive atomic force microscopy (C-AFM), which reveals the presence of highly conductive nano-domains. Thermal conductivity in the cross-plane direction is measured by null-point scanning thermal microscopy (NP-SThM). PEDOT:OTf indeed demonstrates a non-negligible electronic contribution to the thermal transport. We further investigate the correlation between electrical and thermal conductivity by applying post-treatment: chemical reduction (de-doping) to lower charge carrier concentration and hence, electrical conductivity and acid treatment (over-doping) to increase the latter. From our measurements, we find a vibrational thermal conductivity of 0.34 ± 0.04 W m-1 K-1. From the linear dependence or the electronic contribution of thermal conductivity vs. the electronic conductivity (Wiedemann-Franz law), we infer a Lorenz number 6 times larger than the classical Sommerfeld value as also observed in many organic materials for in-plane thermal transport. By applying the recently proposed molecular Wiedemann-Franz law, we deduced a reorganization energy of 0.53 ± 0.06 eV.

Cross-plane thermal transport in MoS2

We study the cross-plane thermal transport in ${\text{MoS}}_{2}$ using density functional theory by adequately accounting for the effect of widespread van der Waals (vdW) forces. We show that past studies report a large variation in the reported values of cross-plane thermal conductivity due to no or limited benchmarking of vdW functionals in computations and variations in sample sizes in experiments. In particular, we show that the validation of the considered vdW functionals based on the correct reproduction of harmonic properties (structural parameters, heat capacity) only is insufficient for the correct description of the thermal transport physics. Further, after having validated the suitability of different functionals, we find that the phonons contributing to cross-plane conductivity have an order of magnitude larger mean free path than that for the basal-plane thermal transport in ${\text{MoS}}_{2}$ at room temperature. The cross-plane transport is quasiballistic with a more than 80% contribution coming from phonons having mean free paths larger than 500 nm. Furthermore, we demonstrate that four-phonon scattering lowers the cross-plane thermal conductivity by more than 35% at room temperature and is required for a correct description of cross-plane thermal transport physics in layered materials.

Experimental Validation of Formula for Calculation Thermal Diffusivity in Superlattices Performed Using a Combination of Two Frequency-Domain Methods: Photothermal Infrared Radiometry and Thermoreflectance

In this paper, we validate two theoretical formula used to characterize thermal transport of superlattices at different temperatures. These formulas are used to measure cross-plane thermal conductivity and thermal boundary resistance, when it is not possible to obtain heat capacity or thermal diffusivity and in-plane thermal conductivity. We find that the most common formula for calculating thermal diffusivity and heat capacity (and density) can be used in a temperature range of −50 °C to 50 °C. This confirms that the heat capacity in the very thin silicon membranes is the same as in bulk silicon, as was preliminary investigated using an elastic continuum model. Based on the obtained thermal parameters, we can fully characterize the sample using a new procedure for characterization of the in-plane and cross-plane thermal transport properties of thin-layer and superlattice semiconductor samples.

High-Throughput Computations of Cross-Plane Thermal Conductivity in Multilayer Stanene

Computational materials science based on data-driven approach has gained increasing interest in recent years. The capability of trained machine learning (ML) models, such as an artificial neural network (ANN), to predict the material properties without repetitive calculations is an appealing idea to save computational time. Thermal conductivity in single or multilayer structure is a quintessential property that plays a pivotal role in electronic applications. In this work, we exemplified a data-driven approach based on ML and high-throughput computation (HTC) to investigate the cross-plane thermal transport in multilayer stanene. Stanene has attracted considerable attention due to its novel electronic properties such as topological insulating features with a wide bandgap, making it an appealing candidate to ferry current in electronic devices. Classical molecular dynamics simulations are performed to extract the lattice thermal conductivities (κL). The calculated cross-plane κL is orders of magnitude lower than its lateral counterparts. Impact factors such as layer number, system temperature, interlayer coupling strength, and compressive/tensile strains are explored. It is found that κL of multilayer stanene in the cross-plane direction can be diminished by 86.7% with weakened coupling strength, or 66.6% with tensile strains. A total of 2700 κL data are generated using HTC, which are fed into 9 different ANN models for training and testing. The best prediction performance is given by the 2-layer ANN with 30 neurons in each layer.

Effects of mass and interaction mismatches on in-plane and cross-plane thermal transport of Si-doped graphene

The effects of silicon (Si) doping on the in-plane and cross-plane thermal transport of suspended and silicon dioxide (SiO2) supported graphene were investigated via molecular dynamics simulations. Due to the large mismatch in atomic mass and interaction with neighboring carbon atoms, Si can act as an effective phonon scatterer, thus suppressing the thermal transport. In this study, we evaluated the contributions of mass and interaction mismatches of Si dopants to the reduction in the in-plane thermal conductivity and the cross-plane thermal resistance through systematic control of the dopant's properties. 2% Si doping reduces the in-plane transport of suspended graphene by ~94% due to the increased scattering, while the SiO2-supported graphene is less affected. The phonon scattering by Si linearly increases with the Si content, and the interaction mismatch has a greater influence on the phonon kinetics during in-plane transport than the mass mismatch. In contrast, the cross-plane transport is enhanced by Si doping, decreasing the interfacial thermal resistance by ~30%, because of the stronger interfacial interactions by weaker in-plane bonding and the smaller atomic mass mismatch with the substrate material. The enhanced understanding of doping effects on thermal transport from this research is expected to provide insights for effective thermal transport control in various graphene structures.

Effects of alloying on in-plane thermal conductivity and thermal boundary conductance in transition metal dichalcogenide monolayers

Two-dimensional 1H transition metal dichalcogenides (TMDs) provide a platform, analogous to group IV cubic semiconductor alloys (${\mathrm{Si}}_{1\ensuremath{-}x}\mathrm{Ge}$), that enables systematic investigations on the effects of alloying in 2D material systems. The existing literature on TMD alloys explores their electrical, magnetic, and optical properties, but lacks a comprehensive analysis of thermal transport in supported and nanostructured systems. Here we employ first-principles-driven phonon Boltzmann transport formalism and a 2D-3D thermal boundary conductance model to systematically study in-plane and cross-plane phonon transport of suspended and ${\mathrm{SiO}}_{2}$ supported single-layer TMD alloys. We find that the thermal conductivity of alloyed TMDs is dependent on system size up to tens of microns and that the combination of mass-difference and substrate scattering can significantly reduce thermal transport even in large systems ($g500$ nm). Beyond in-plane transport, we find that the thermal boundary conductance displays a qualitatively different trend and significantly weaker modulation with alloy composition as compared to the thermal conductivity. Our results help shed light on the in-plane and cross-plane thermal transport properties of 2D single-layer TMD alloys and further their applications in nanoelectronics, sensing, and energy devices.

Intercalated ion tuning of the cross-plane thermal transport properties of graphite

The effects of the intercalated ion concentration on the cross-plane thermal conductivity and the thermal boundary conductance in the graphite/lithiated graphite interface are investigated from molecular dynamics simulations. At low ion concentration, the cross-plane thermal conductivity of the lithiated graphite is lower than that of the pristine graphite. However, as the intercalated ion concentration increases, the cross-plane thermal conductivity increases rapidly, even exceeding that of the pristine graphite at high ion concentration. By analyzing the variations of the cross-plane elastic constants and phonon dispersion relation with the intercalated ion concentration, it is found that the intercalated ions significantly increase the phonon irradiation heat flux along the cross-plane direction. Our study further shows that the variation of the intercalated ion concentrations can also modulate the thermal boundary conductance in the graphite/lithiated graphite interface. The non-equilibrium molecular dynamics simulations show that the thermal boundary conductance between graphite and lithiated graphite decreases as the lithiation level increases, which would worsen the thermal performance of Li-ion batteries. A one-dimensional atomic chain model is proposed to elaborate on how the effective spring stiffness of material influences the interfacial transmission of phonons with different frequencies. This work provides a quantitative calculation of the cross-plane thermal conductivity and thermal boundary conductance in intercalated graphite samples and is also extremely important for the thermal management and structural design of lithium-ion batteries.

Cross-plane thermal conductivity in amorphous Si/SiO2 superlattices

Heat conduction in superlattices demonstrates various atomic-scale effects, one of which is the ultra-low thermal conductivity. Remarkably, theoretical works even promise sub-amorphous thermal conductivity in superlattices made of amorphous materials. Yet, these predictions were not tested experimentally. Here, we experimentally study the cross-plane thermal transport in amorphous Si/SiO2 superlattices at room temperature. Using the micro time-domain thermoreflectance technique, we measured the thermal conductivity of superlattices with periods of 6.6, 11.8, and 25.7 nm. The thermal conductivity values are in the range of 1.1–1.5 W m−1 K−1 and generally agree with the values reported for amorphous Si and SiO2. However, the superlattice with the highest density of interfaces seems to have the thermal conductivity slightly below the amorphous limit. These data suggest that heat conduction below the amorphous limit might be possible in amorphous superlattices with a periodicity shorter than 6.6 nm.

Covalent-bonding-induced strong phonon scattering in the atomically thin WSe2 layer

In nano-device applications using two-dimensional (2D) van der Waals materials, a heat dissipation through nano-scale interfaces can be a critical issue for optimizing device performances. By using a time-domain thermoreflectance measurement technique, we examine a cross-plane thermal transport through mono-layered (n = 1) and bi-layered (n = 2) WSe2 flakes which are sandwiched by top metal layers of Al, Au, and Ti and the bottom Al2O3 substrate. In these nanoscale structures with hetero- and homo-junctions, we observe that the thermal boundary resistance (TBR) is significantly enhanced as the number of WSe2 layers increases. In particular, as the metal is changed from Al, to Au, and to Ti, we find an interesting trend of TBR depending on the WSe2 thickness; when referenced to TBR for a system without WSe2, TBR for n = 1 decreases, but that for n = 2 increases. This result clearly demonstrates that the stronger bonding for Ti leads to a better thermal conduction between the metal and the WSe2 layer, but in return gives rise to a large mismatch in the phonon density of states between the first and second WSe2 layers so that the WSe2-WSe2 interface becomes a major thermal resistance for n = 2. By using photoemission spectroscopy and optical second harmonic generation technique, we confirm that the metallization induces a change in the valence state of W-ions, and also recovers a non-centrosymmetry for the bi-layered WSe2.

Cross-plane thermal transport measurements across CVD grown few layer graphene films on a silicon substrate

Room-temperature time-domain thermoreflectance technique (TDTR) measurements of cross-plane heat conduction across gold-graphene-silicon interfaces are presented. The graphene layers are originally grown on a copper substrate by chemical vapor deposition and later transferred to a silicon substrate in layer-by-layer fashion. We estimate the thermal boundary conductance (TBC) as a function of number of graphene layers, by fitting a layered heat conduction model that accounts for heat accumulation in the gold layer to the TDTR data, using the TBC as a free fitting parameter. The estimated TBC was found to decrease with number of graphene layers at the interface, as observed in previous TDTR measurements reported in the literature. The decrease in TBC with number of graphene layers matches the trends in the transmission coefficient of low frequency (25 GHz) coherent acoustic phonons across the interface, indicating that the interface elastic stiffness decreases with the number of graphene layers due to poor bonding between the gold film and silicon substrate.

How interlayer twist angles affect in-plane and cross-plane thermal conduction of multilayer graphene: A non-equilibrium molecular dynamics study

Graphene, a kind of emerging low dimensional carbon material, has admirable thermal properties with potential applications in the thermal management of aerospace and microelectronics fields. In recent studies, thermal properties of both conventional single-layer and multilayer graphene were extensively studied. However, few studies focused on that of multilayer graphene with twist angles, whose thermal properties are different from that of conventional graphene because of the existence of interlayer twist angles. Such knowledge gap hinders the potential applications. Therefore, the thermal conductivity of bilayer, 4-layers and 6-layer zigzag graphene with various twist angles is investigated utilizing non-equilibrium molecular dynamics at the typical temperature region in this study, and both in- and cross-plane thermal conductivity are investigated. The size of the studied graphene is 10 nm × 22 nm in the x-y plane, and the size in the z-direction depends on the number of layers. Moreover, the phonon vibrational density of state is also analyzed for mechanisms behind the thermal transport. The result indicates that a local maximum value can be found with the twist angle of 30° for in-plane thermal conduction. The results also suggest that the highest thermal conductivity could be reached without any twist angles for both in and cross-plane conduction. The observation would provide an opportunity to study the characteristics of in-plane and cross-plane thermal transport of twisted multilayer graphene.

Using Mosaicity to Tune Thermal Transport in Polycrystalline Aluminum Nitride Thin Films.

The effect of controlling the c-axis alignment (mosaicity) to the cross-plane thermal transport in textured polycrystalline aluminum nitride (AlN) thin films is experimentally and theoretically investigated. We show that by controlling the sputtering conditions we are able to deposit AlN thin films with varying c-axis grain tilt (mosaicity) from 10° to 0°. Microstructural characterization shows that the films are nearly identical in thickness and grain size, and the difference in mosaicity alters the grain interface quality. This has a significant effect to thermal transport where a thermal conductivity of 4.22 vs 8.09 W/mK are measured for samples with tilt angles of 10° versus 0° respectively. The modified Callaway model was used to fit the theoretical curves to the experimental results using various phonon scattering mechanisms at the grain interface. It was found that using a non-gray model gives an overview of the phonon scattering at the grain boundaries, whereas treating the grain boundary as an array of dislocation lines with varying angle relative to the heat flow, best describes the mechanism of the thermal transport. Lastly, our results show that controlling the quality of the grain interface provides a tuning knob to control thermal transport in polycrystalline materials.

Significantly reduced c-axis thermal diffusivity of graphene-based papers

Owing to their very high thermal conductivity as well as large surface-to-volume ratio, graphene-based films/papers have been proposed as promising candidates of lightweight thermal interface materials and lateral heat spreaders. In this work, we study the cross-plane (c-axis) thermal conductivity (kc) and diffusivity (αc) of two typical graphene-based papers, which are partially reduced graphene paper (PRGP) and graphene oxide paper (GOP), and compare their thermal properties with highly-reduced graphene paper and graphite. The determined αc of PRGP varies from (1.02 ± 0.09) × 10−7 m2 s−1 at 295 K to (2.31 ± 0.18) × 10−7 m2 s−1 at 12 K. This low αc is mainly attributed to the strong phonon scattering at the grain boundaries and defect centers due to the small grain sizes and high-level defects. For GOP, αc varies from (1.52 ± 0.05) × 10−7 m2 s−1 at 295 K to (2.28 ± 0.08) × 10−7 m2 s−1 at 12.5 K. The cross-plane thermal transport of GOP is attributed to the high density of functional groups between carbon layers which provide weak thermal transport tunnels across the layers in the absence of direct energy coupling among layers. This work sheds light on the understanding and optimizing of nanostructure of graphene-based paper-like materials for desired thermal performance.

Enhanced thermal transport across monolayer MoS2

Characterizing the thermal properties of MoS2 is important for the design of electronic devices based on this material. We used frequency domain thermoreflectance to study the cross-plane thermal transport in mechanically exfoliated MoS2 samples supported on SiO2 and muscovite mica substrates. The thickness of MoS2 ranged between one and five layers, and the MoS2 layers were sandwiched between a metal layer and the substrate. In the case of mica, heat transport into the substrate remained the same whether or not a monolayer of MoS2 was present, whereas, for SiO2, heat transport was reduced by surface roughness. We observed a significant improvement in heat transport across monolayer MoS2 as compared to few layer MoS2. For MoS2 on SiO2, the effective thermal interface conductance was improved by more than three times if a monolayer was used. For MoS2 on mica, the thermal interface conductance was approximately two times better for monolayer MoS2. This implies that monolayer MoS2 has superior thermal properties and can be used in electronic devices as an intermediate layer between two materials. Additionally, we also report on the measurement of anisotropic thermal conductivity in bulk MoS2 and mica.

Native-oxide limited cross-plane thermal transport in suspended silicon membranes revealed by scanning thermal microscopy

By thermally characterizing nanometer-thin suspended silicon membranes with various micrometric lengths in ambient conditions, we determine simultaneously the spatial resolution of our Wollaston-probe scanning thermal microscopy experiment, which probes an area of (285 nm)2, and the effective thermal conductivity of the membranes of 40 W.m−1.K−1. This value is smaller than the in-plane thermal conductivity measured using other techniques in vacuum (∼60 W.m−1.K−1), revealing that both cross-plane and in-plane heat conduction are strongly affected by the native oxide in ambient conditions. This work also underlines that high-thermal conductivity samples can be characterized by scanning thermal microscopy when micro-patterned.

Heat flow diversion in supported graphene nanomesh

Redirection of energy carrier propagation by geometric confinement is studied through the analysis of in-plane and cross-plane thermal transport within various graphene nanomesh (GNM) configurations using molecular dynamics (MD) simulations. As the transport channel width decreases with an increase in porosity, the effect of redirection increases; thus, the in-plane thermal conductivity of large-porosity GNM is more dependent on hole arrangement. Since higher porosities weaken the GNM structure due to a larger population of broken bonds, carbon atoms within the graphene structures are more easily influenced by interactions with the substrate silicon (Si) block. Subsequently, increase in porosity leads to the decrease of interfacial thermal resistance. At higher porosities, lower interfacial resistance and in-plane thermal conductivity cause diversions (and redirections) in heat flow from the GNM to the underlying Si substrate. Our study suggests that this method of heat flow redirection can be applied as an effective means to control and manage heat transfer within numerous applications; extension to the improved conductivity calculation accuracy can also be achieved through the inclusion of this diversion analysis.

Magnetic and thermal transport properties of SrFe12O19 permanent magnets with anisotropic grain structure

Permanent magnets are gaining increasing interest and importance for applications such as generators and motors. Thermal management is a key concern since performance of magnets decreases with temperature. We investigate the magnetic and thermal transport properties of rare earth-free, fine-grained SrFe12O19 magnets produced by the current activated pressure assisted densification. We propose a cooling scheme based on an anisotropic grain structure that can help retain magnetic performance under high temperature conditions. The synthesized magnets have aligned grains such that their magnetic easy axis is perpendicular to their largest surface area to maximize their magnetic performance. The SrFe12O19 magnets have fine grain sizes in the cross-plane direction and substantially larger grain sizes in the in-plane direction. This microstructure results in approximately a factor of two higher thermal conductivity in the in-plane direction, providing an opportunity for effective cooling. The phonons are the dominant heat carriers near room temperature. Temperature and direction dependent thermal conductivity measurements indicate that both Umklapp and grain boundary scattering are important in the in-plane direction, while grain boundary scattering dominates the cross-plane thermal transport. The proposed design strategy should translate well to other material systems and has important implications for thermal management of nanostructured permanent magnets.