Optical phonon modes can be overpopulated because of larger generation rate than decay during various energy conversions and resistive processes (e.g., in electric circuits). These overpopulated optical phonons (i.e. hot phonons) hinder the energy relaxation and transport in devices, and they are finally thermalized converting their energy to waste heat by generating entropy. Thus, utilizing the hot phonons before thermalization is expected to improve the efficiency and the performance mitigating heat generation. We suggest the direct energy conversion from hot phonon to electron potential using semiconductor heterobarrier structures.
Here, we employ a heterojunction structure composed of GaAs and Al_xGa_1minus;xAs (x or x_Al is the Al content), which has a band edge discontinuity in the conduction and valence bands depending on x_Al. With electrons as the main charge carriers, conduction band edge discontinuity is regarded as a barrier with a height phi;_b depending x_Al. Potential barriers impose an adverse current by the potential change, and to compensate this adverse effect, large, forward local electric field (e_e,HPAB) formed by x_Al grading is introduced in the barrier. Electrons in the suggested hot-phonon absorbing barrier (HPAB) structure absorb phonon thus increasing their kinetic energy, and this energy is in turn converted to electric potential through the barrier transition.
Hot phonons can be decayed by their downconversion to acoustic phonons in addition to the interactions with electrons. The kinetics of all the interactions (phonon-electron and phonon-phonon) is central in this study, and it can be calculated through the quantum mechanical perturbation theory, i.e. the Fermi golden rule. In order to pass through barriers, electrons require sufficient E_e, or the less energetic electrons need to increase their energy through phonon absorption. Since high-energy carriers are emission-favorable and less populated and from the kinetics multiphonon absorption for low-energy electron transition is not probable enough, then tandem of barrier structures with phi;_b le; E_p,LO (only absorption available) rather than a single barrier with a large height is employed for large potential gain.
Based on the phonon and electron interaction kinetics from the first principle, self-consistent ensemble Monte Carlo (MC) method is employed to show the electric potential/power gain by phonon absorption in HPAB. MC simulations demonstrate that the HPAB produces electric potential gain without current loss through a proper combination of e_e,HPAB, phi;_b and hot phonon population. We found the favorable conditions for unassisted absorption of hot phonons and an optimized GaAs/Al_xGa_1minus;xAs barrier structure which can harvest 19% of hot phonons. By integrating HPAB in electronic devices, reduced heat dissipation by effective removal of excess phonons, as well as additional electric power generation (or recovery) will be achieved.

Quantum Cascade Lasers (QCLs) produce coherent radiation in the mid IR to THz frequency range with applications for defense, medicine and communication. QCL operation relies on intersubband electronic transitions within confined quantum wells in superlattices of GaInAs and AlInAs on InP or GaAs substrates. While QCLs offer high efficiency, the associated large levels of heat generation cause thermal conduction within the active region to strongly influence the stability and reliability, particularly for the continuous wave (CW) or high duty-cycle mode at room temperature. With layer thicknesses in the range of 2-6 nm, phonon transport can be strongly influenced by phonon scattering and, potentially, by modifications to phonon dispersion. Previous studies have examined the thermal conductivity of as-prepared QCL structures and some coupled electro-thermal-optical models based on continuum heat conduction have been proposed. In addition, there is a wealth of prior literature on phonon scattering (and even dispersion modification) for periodic nanoscale superlattice structures. However, real QCL cores contain a distribution of well (GaInAs) and barrier (AlInAs) layer thicknesses, typically ranging between 1 nm and 4 nm, with no periodicity on length scales comparable to the phonon mean free path (MFP asymp; 2 - 5 nm; stack period asymp; 50 nm). Therefore, for the better design and optimization of QCL performance, it is crucial to make progress on a comprehensive model that can account for the aperiodic behavior in QCL superlattices. The present work develops an approximate solution to the phonon Boltzmann transport equation (BTE) accounting for both the local interface scattering and the impact of boundaries of one or more interfaces displaced from the local region. A statistical method based on phonon transition at interfaces and survival rates through the material volume is employed to develop a physics-based modeling approach for aperiodic superlattices. The range of phonon transport from ballistic to continuum is studied, using the MFP and layer thicknesses are parameters. Furthermore, a comparison is made with a Matthiessen&’s rule based approach that assumes a distribution of weights assigned to proximate interfaces. The goal is to develop an effective thermal conductivity model that can be applied locally within the aperiodic structure. We compare the predictions of these simulations with out-of-plane thermal conductivity data for QCL superlattice structures obtained using time-domain thermoreflectance.

The thermal conductivity (TC) of superlattices (SLs) has attracted a great attention for the past years for their phonon properties. It has been shown that the TC of SLs decreases and reaches a minimum for a certain period thickness. Phonon coherence effects have been invoked in the literature to explain this trend but no clear evidence of the physics involved has been reported so far. In this work, we propose a mathematical definition of phonon coherence and investigate how it is affected by the period thickness. Semiconductor SLs are studied based on an equilibrium Molecular Dynamics approach. Both perfect and defected SLs are considered in this study.

A reduced thermal conductivity of thermoelectric materials is necessary to obtain an enhanced figure of merit ZT for thermoelectric generators and Peltier coolers. Thin thermoelectric films are suitable for thermoelectric sensor applications. An enhancement in ZT for Si-Ge thin films by nanostructuring offers a new temperature range for Si-based thermoelectric devices. The reduction in the thermal conductivity in superlattices is achieved by diffuse interface scattering of phonons. With a mismatch of phonon dispersion, the scattering of short-wavelength phonons is enhanced due to localized phonon states. Some theoretical work predicted a further decrease in thermal conductivity with nonperiodic superlattice structures, due to a confinement of long-wavelength phonons. The presence of lattice defects such as dislocations can also lead to lower thermal conductivities. In this study, we have investigated the thermal conductivities of Si-Ge based superlattices. Periodic and nonperiodic Sim-Gen superlattices with stacks of m Si and n Ge layers of various thicknesses were grown by molecular beam epitaxy on (111) Si substrates. The influence of periodicity was investigated. Further investigations were carried out on nanowire arrays prepared from these superlattices by catalytic etching. The structures were characterized by cross-section transmission electron microscopy. A comparison between the different approaches for the effective reduction in the thermal conductivity will be presented.

The amorphous/crystalline superlattices (a/c SLs) with large conduction band discontinuities can be used for resonant-tunnelling diodes, modulation doped field effect transistors and quantumwell infrared photodetectors [1]. They are also interesting candidates for low cost thermoelectric power devices [2]. These SLs can be made with materials which can display large lattice mismatch and/or which can have interfaces. The latter ones are essentially defect free and atomically sharp [3].
To the best of our knowledge the only investigation of the heat transfer through a/c interfaces was made by Von Alfthan et al [4]. He concludes that the thickness of amorphous regions does not affect the thermal conductivity (TC), while the thickness of crystalline regions has a more dramatic effect on the overall conductivity. We propose to extend this study with the prediction of the Kapitza resistance. We will also appraise the effect of the SL&’s parameters such as period and interfacial roughness, as well as the temperature. A recent theoretical work of Donadio and Galli on crystalline silicon nanowires with amorphous surfaces showed that the TC is not affected by the temperature and it is close to the one of amorphous materials [5]. This unusual temperature dependence is explained by the presence of a majority of non-propagating vibrational modes.
There is a lack of information about a/c silicon interfaces, concerning both SLs and nanowires. In our current study SLs of a-Si/c-Si preliminary results will be presented for the TC and Kapitza resistance of the interfaces as a function of the SLs period, the roughness of interfaces and the temperature [6]. Preliminary results show that the Si atoms that belong to the amorphous silicon regions and located close to the interfaces exhibit higher atomic energy than the inner atoms in amorphous regions. This might related with the enhancement of phonon scattering at the interfaces.
1 R.W. Fathauer, “New class of Si based superlattices: Alternating layers of crystalline Si and porous amorphous Si1minus;xGex alloys”, Appl. Phys. Lett. 61, 2350 (1992).
2 H. Ohra, R. Huang and Y. Ikuhara, “Large enhancement of the thermoelectric Seebeck coefficient for amorphous oxide semiconductor superlattices with extremely thin conductive layers”, Phys. Status Solidi (RRL) 2, 105(2008).
3 S.C. Agarwal, “Amorphous silicon-based superlattices ”, Bull. Mater. Sci. 14, 1257 (1991).
4 S. Von Alfthan, A. Juronen, and K. Kaski, Mat. Res. Soc. Symp. Proc. 703, 6.2.1 (2002).
5 D. Donadio and G. Galli, “Temperature dependence of the thermal conductivity of thin silicon nanowires” Nano Lett. 10, 847 (2010)
6 M. Talati, T. Albaret and A. Tanguy “Atomistic simulations of elastic and plastic properties in amorphous silicon”, EPL 86, 66005 (2009)

We experimentally investigate the role of size effects and boundary scattering on the thermal conductivity of silicon-germanium alloys. The thermal conductivities of a series of epitaxially grown Si_1minus;xGe_x thin films with varying thicknesses and compositions were measured with time-domain thermoreflectance. The resulting conductivities are found to be 3 to 5 times less than bulk values, and vary strongly with film thickness. By examining these measured thermal conductivities in the context of a previously established model, it is shown that long wavelength phonons known to be the dominant heat carriers in alloy films, are strongly scattered by the film boundaries, thereby inducing the observed reductions in heat transport. These results are then generalized to silicon-germanium systems of various thicknesses and compositions; we find that the thermal conductivities of Si_1minus;xGe_x superlattices are ultimately limited by finite size effects and sample size rather than periodicity or alloying. This demonstrates the strong influence of sample size in alloyed nanosystems. Therefore, if a comparison is to be made between the thermal conductivities of superlattices and alloys, the total sample thicknesses of each must be considered.

Silicon nanowires have recently been shown to be promising thermoelectrics due to their reduced thermal conductivity and improved Seebeck coefficient and electrical conductivity relative to bulk. However, they do not have conversion efficiencies comparable with the best bulk thermoelectrics, and further avenues must be explored in order to make them a viable energy harvesting approach. One method of tuning thermoelectric properties which has not been fully developed is that of elastic strain engineering, which is known to affect charge carrier effective mass and band gap as well as phonon dispersion and group velocity. Strain engineering should have enhanced efficacy in nanostructured materials, which exhibit a large range of elastic strain as compared to their bulk counterparts. Although some groups have measured the effect of strain on electrical properties of silicon nanowires, methods for accurate measurement of coupled thermomechanical properties have been elusive.
We present a novel non-contact approach for measuring thermal conductivity of a single suspended nanowire subjected to varied strain levels, which we name µ-Raman optomechanothermography. We employ a microelectromechanical (MEMS) device to apply uniaxial tensile stress to individual silicon nanowires under a confocal µ-Raman spectroscope. Raman maps across the length and width of the nanowire at several different laser intensities enable the deconvolution of the effects of stress and temperature on the Raman spectrum. Fits of the temperature profiles at the various laser intensities along the length of the nanowire combined with estimates of absorbed laser power yield measurements of thermal conductivity corrected for contact resistance. Representative results of thermal conductivity as a function of stress for Si nanowires will be shown and discussed in the context of changes to phonon group velocities and relaxation lifetimes predicted by atomistic simulation.

While the study of thermal transport in low-dimensional nanostructures has been receiving growing attention, the options to conduct experimental measurements on such nanostructures are limited. Certain approaches to measurement, such as the thermal bridge method or 3-omega; method, can be used to derive the thermal conductance of a nanowire as a whole, and scanning probe techniques can be used to conduct spatially-resolved measurements. However, measurement uncertainties associated with the contact thermal resistance between the sample and substrate (or thermal probe) remain a challenge to be addressed. Here we report a new thermal measurement technique that is capable of profiling the thermal conductance of an individual nanowire with a spatial resolution better than 20nm. In this technique, a focused electron beam is employed as a localized heating source to establish a temperature gradient along the nanowire. The heat fluxes from the two ends of the nanowire are measured using platinum resistor loops on two suspended thermally-isolated membranes. We show that, by a single scan of the electron beam along the nanowire, the local thermal conductance altered by non-uniformities in the nanowire, such as local defects, change of surface roughness and variations in diameter, can be discriminated. Moreover, this technique is capable of measuring the thermal boundary resistance across epitaxial material interfaces in the nanowire. By using this technique, the long-standing problem of ill-defined thermal contact resistance between the nanowire and the two membranes, which is a serious drawback in the conventional thermal bridge method, is avoided. This technique thus provides a powerful tool for studying the underlying physics of thermal transport in nanostructures, which will in turn improve the thermal models adopted in the design of nanodevices, and inform the fabrication of nanostructured thermoelectric materials with enhanced performance.
REFERENCES:
ZQ Wang, R Xie, CT Bui, D Liu, X Ni, B Li, JTL Thong, “Thermal transport in suspended and supported few-layer graphene”, Nano Lett. 11, 113-118 (2011) ;
CT Bui, R Xie, M Zheng, Q Zhang, CH Sow, B Li, JTL Thong, “Diameter-dependent thermal transport in individual ZnO nanowires and its correlation with surface coating and defects”, Small 8, 738-745 (2012).

Recently, we have reported that the thermal conductivity of silicon nanowire arrays roughened by metal-assisted chemical etching (MAC-etch) is strongly correlated to both the magnitude of the roughness and a broadening of the one-phonon Raman linewidth. We have hypothesized that microstructural disorder induced by the etching chemistry leads to such changes to the Raman linewidth. Here, we simplify the study of such effects by chemically roughening Si wafers instead of nanowires. We have studied the effects of various previously reported roughening procedures on the near-surface thermal properties using time-domain thermoreflectance. We find that the thermal conductance of the near-surface region is reduced substantially by MAC-etching, despite the expectation that pristine roughened surfaces should have increased conductance due to enhanced surface area. In addition, highly roughened surfaces show strong acoustic echoes with reflection coefficient indicative of a soft interface. These features are consistent with the presence of near-surface disorder and in some cases microporosity.

Joule heating in nanowires is a fundamental heat transfer problem in nanoscale science and technology. It is important in thermal management of nanoscale solid-state displays, emitters, thermionic devices and sensors, and, also in new functional applications of nanowires or nanotubes. The resistive heating and the resulting temperature distribution along the wire is a function of several parameters including electrical and thermal properties, wire diameter and circumference, and, more importantly, the boundary conditions at the ends of the wire. Heat transfer in nanowires is also sensitive to the radiation/convection through the circumference because the surface to volume ratio is inversely proportional to wire diameter, potentially creating size effect on the temperature profile. Also, one of the common techniques to determine thermal conductivity of nanowires or films is by Joule heating by applying steady or pulsed electric power. Despite the importance, there is no exact analytical solution yet for temperature distribution in Joule heated nanowires, including the radiative/convective heat transfer and non-zero heat flux boundary conditions. In this presentation, we present an analytical series solution for the temperature distribution along the length of a nanowire. The solution was derived from the modified Fick&’s second law of heat transfer including joule heating and radiation/convection terms. Using Laplace transformation, the time-dependent nonhomogeneous heat transfer equation was converted into the subsidiary equation. The equation was then solved by inverse Laplace transformation, with the solution satisfying the radiative and the flux boundary conditions. This solution can be very useful in determining the temperature distribution as affected by the nanowire parameters and radiative heat transfer conditions as well as in developing chip-based experimental methods to measure size-dependent phase transition temperatures in phase change memory materials.

Recently, diffusive phonon transport in nanostructured materials has been a subject of intense interest. In this work, we demonstrate how the limits of heat transport can be tested in three novel material systems by extending the thermal measurement platform to probe material structure and provide a direct correlation to their thermal properties.
Phonons are lattice vibrations and their scattering in solids has largely been explained like collision of particles. Since the development of nanostructures, diffusive boundary scattering from large surface-to-volume ratio materials has been studied in nanowires and superlattices. To beat this diffusive scattering limit, we designed nanowires with broadband roughness close to the dominant phonon wavelength (1-10nm) at room temperature. The decrease in thermal conductivity of intrinsic silicon by a factor of ~30 from 140 W/m-K to 5 W/m-K in this sub-diffusive regime opens up the possibility of multiple scattering stemming from coherent phonon wave effects. Transmission Electron Microscopy (TEM) based techniques including 3D tomography were then used to map out the morphology and we find that we can reduce the thermal conductivity to as low as 1 W/m-K, while preserving the single-crystalline core, which is as low as that of amorphous silicon or silica. Correlating the surface roughness and porosity to the measured thermal conductivity opens up a new paradigm to observing wave physics in thermal phonons at room temperature in nanomaterials.
Secondly, the platform developed previously was extended to be compatible with TEM, allowing us to characterize the crystal structure of measured nanowires. While phonon optics experiments in the 1970s showed a crystallographic direction dependent thermal conductivity, we performed the first 1-1 mapping of nanowire growth direction and thermal conductivity in Bismuth Nanowires. In the boundary scattering regime with diameter 100nm, a nanowire in the [-102] direction had k = 8.5 W/m-K, ~6 times higher than a nanowire in the [110] direction with k = 1.5 W/m-K.
Finally, we manufactured tapered Vanadium Oxide beams to study asymmetric phonon physics that manifested in temperature dependent thermal rectification. The interplay between electrons and phonons and the possibility of asymmetric scattering rates prompted us to look closely at the existence of Metal-Insulator interfaces that could result in thermal rectification. Between 150K and 340K, the V_nO_2n-1 phases could be either metallic or insulating with nanoscale domains. We performed high resolution Auger spectroscopy on single-crystal Vanadium Oxide beams that showed a stoichiometry variation and measured thermal rectification as high as 22%. The rectification behavior turns off (<4%) once the whole beam reaches the metallic phase, higher than 340K. Our platform thus couples materials characterization, especially TEM, with thermal property measurement to enhance understanding of thermal phonons.

Transfer printing [1] integrates dissimilar materials on large-area substrates to enable new functionalities. The interfacial thermal conductance of transfer-printed objects attains importance in applications involving heat dissipation. The first experimental investigation of transport across transfer-printed Au-Si and Au-SiO2 interfaces [2] indicate a surprisingly high interfacial thermal conductance. We investigate such transport theoretically using a combination of contact mechanics and electron-phonon transport, considering both metal-dielectric and metal-elastomeric interfaces.
Using the theory of Kogut and Etsion [3], we show that the plastic deformation of Au, coupled with capillary forces due to water bridges formed between asperities lead to significantly large fractional area coverage of ~0.20 for Au-SiO2 interface. We find the value of thermal conductance, G for Au-SiO2 interface to be ~15 MW/m2K which is of the same order of magnitude as the experimental value (~45 MW/m2K) [2]. We hypothesize that the discrepancy between theoretical and experimental data arises due to the heat conduction through water capillary bridges. Using a similar approach for Au-PDMS interface, we get fractional area coverage of ~0.14 and a thermal conductance value of ~1 MW/m2K. We discuss the implications of these results for the use of metallic interconnects in heat dissipating devices.
1. Meitl, M. A.; Zhu, Z.-T.; Kumar, V.; Lee, K. J.; Feng, X.; Huang, Y. Y.; Adesida, I.; Nuzzo, R. G.; Rogers, J. A. Nat Mater 2006, 5, (1), 33-38.
2. D. W. Oh, S. Kim, J. A. Rogers, D. G. Cahill, and S. Sinha, Advanced Materials 23 (43), 5028 (2011).
3. Kogut, L.; Etsion, I. Journal of Colloid and Interface Science 2003, 261, (2), 372-378.

Nanostructures possess unique thermal transport properties because of nanoconfinement effects. However, nanostructures are usually in contact with other nanostructures, matrix materials or substrates. For example, in various nanostructured microfibers, thin films, and bulk nanocomposites, which have been projected as structural materials for aerospace vehicles and for energy conversion applications, individual nanostructures are often in contact with other nanostructures or host materials through van der Waals (vdW) interactions. Thermal transport through these vdW interfaces could play critical role in the overall thermal transport properties of the nanostructured materials. Therefore, it is important to study thermal transport through vdW contacts between individual nanostructures. We report on experimental and theoretical studies of thermal transport through contacts between individual nanostructures, which includes (1) contact thermal resistance between individual multi-wall carbon nanotubes, and (2) thermal transport through vdW interfaces between individual boron nanoribbons.

Strained semiconductors are widely used in electronic devices due to certain advantages in their electrical and optical properties such as high carrier mobility and bandgap modifications relative to their unstrained crystal structures. Often the devices in which they are used (such as strained-Si transistors or semiconductor lasers with strained active regions) present thermal management challenges due to high heat fluxes. Understanding of heat transfer in such devices is complicated by the facts that 1) the strained layers are often quite thin relative to the phonon mean free path, 2) the “bulk” properties of the strained layers are often themselves not spatially constant if a strain gradient exists within the film, and 3) the effects of strain on the thermal boundary resistance (TBR) to an adjacent material are poorly understood. Furthermore, strain gradients usually occur over relatively long spatial scales (~100 nm) which place a large computational burden (millions of atoms) on atomistic simulations.
In this work we utilize molecular dynamics (MD) to study the thermal properties of strained Si/Ge interfaces. We first impose spatially constant strain within each semiconductor and use non-equilibrium MD (NEMD) to study how the bulk thermal conductivities and TBR vary as a function of this constant strain. We find that increasing compressive strain on both semiconductors results in a reduction in TBR. We then impose selected spatially-varying strain profiles on the structure (for example, exponential reductions in strain normal to the interface with varying relaxation lengths, which mimic relaxed epitaxial interfaces) to understand the effects of these strain profiles on “bulk” film thermal conductivity and TBR. We further study the effect of an intermixed region at the interface of varying thickness, to capture intermixing that happens during epitaxial growth or subsequent thermal annealing. The results are compared with theoretical models for thermal transport in strained semiconductors.

Phonon scattering has been well studied across material interfaces, grain boundaries, and other incoherent, disordered structures that create resistance to thermal transport. However, phonon interactions with strain fields have been must less rigorously studied. Due to the coherency in strain fields and their common proximity to incoherent phonon scattering sites such as mass impurities or incoherent boundaries, it is often difficult to isolate the specific effects of these coherent strain fields on phonon scattering and thermal resistance. To understand these strain field effects on phonon transport, we study the effects of ferroelectric and ferroelastic domain structures on the thermal transport in BiFeO3 and PbZrxTi1-xO3 thin films. These materials present unique systems to isolate the effects of domain walls and strain fields on phonon scattering phenomena. We measure the thermal conductivity of these films with time domain thermofelctance and characterize the domain structure with piezo force microscopy. We synthesize the BiFeO3 under various conditions to induce different domain variants and wall densities. An increase in the domain wall density leads to a systematic decrease in thermal conductivity of the films. From this data, we determined the Kapitza conductance across the domain walls, which is driven by the strain field induced by the domain variants. This domain wall Kapitza conductance is lower than the Kapitza conductance associated with grain boundaries in all previously measured materials, indicating the strong effects that coherent strain fields may have on phonon scattering and thermal conductance. To study this effect further, we synthesized various PbZrxTi1-xO3 films of different Ti concentrations to yield samples with different phases, and up to 12 different domain variants. We find a strong correlation between the thermal conductivity of single crystalline PbZrxTi1-xO3 films, yet the thermal transport in the PbZrxTi1-xO3 is unaffected by the phase in polycrystalline samples. Our results indicate that the domain structures and strain fields in PZT can scatter phonons more readily than incoherent grain boundaries. In general, this work demonstrates the strong effect of coherent strain fields on phonon scattering, and its comparable effects to typical incoherent phonon scattering mechanisms such as grain boundaries.

The effects of temperature-induced dynamic changes in phase and structure on the thermal properties of materials have been demonstrated in a wide range of materials. However, the effects of a solids' dynamic properties on the thermal transport across solid interfaces (thermal boundary conductance) have never been observed. Here, we show that the thermal boundary conductance between a metal film and vanadium dioxide (VO₂) changes from a phonon mediated phenomenon to an electron dominated process as VO₂ crosses over the metal-insulator-transition. VO₂ thin films were deposited on Al₂O₃ substrates using reactive bias target ion beam deposition. We evaporate thin Au:Ti or Al films on the VO₂ thin films and measure the thermal boundary conductance across the Au/Ti/VO₂ and Al/VO₂ interfaces as a function of temperature from 80 to 400K with time-domain thermoreflectance (TDTR). With particular focus on the behavior around the metal-insulator transition (MIT) at 340K, we show that the thermal boundary conductance has a large jump-discontinuity at the MIT, increasing suddenly by about 50% upon VO₂ transitioning to its metal state. The temperature trends clearly follow those of phonon- and electron-like thermal boundary conductances in the insulator and metal regimes, respectively. We utilize these results to create thermal device structures that exhibit diode (passive) and switch (active) like behavior intended for nanoscale thermal management applications.

We present a microscopic formulation of the frequency vs. wave-vector dependent phonon transmission at an interface which reveals the set of mechanisms involved in Kapitza problem. We demonstrate that the complete understanding of interfacial phonon transport relies on the knowledge of the local dynamics of the contact atoms. By illustrating our approach on semiconductors, we unveil the existence of interface modes that play an unnoticed role in transferring thermal energy.

Thermal boundary conductance between the metallic matrix and the reinforcement phase is a crucial parameter for the effective thermal conductivity of MMCs and for the exploitation of the full potential of a materials combination. Its magnitude has further a direct influence on the required particle size of the reinforcement to be effective in improving (or not too strongly reducing) the thermal conductivity of the composites. Along with examples for the influence of alloying elements on composite conductivity (in situ interface modification), the question of chemical surface modification of the particles prior to composite fabrication is adressed. Several phenomena are discussed based on model composites made by gas pressure assisted liquid metal infiltration including the systems Pb/SiC, Pb/TiB2, Al/diamond, Ag-X/diamond and Cu-X/diamond. The comparison of the Pb/SiC and the Pb/TiB2 composites is particularly interesting since it highlights the importance of the electronic contribution to the interface thermal conductance.

In most metals, heat transport is dominated by electronic excitations and the Wiedemann-Franz law is typically used to relate the electronic component of the thermal conductivity to the more easily measured electrical conductivity. In this talk, I will highlight three aspects of heat transport in nanoscale metal films and multilayers. i) We combined measurements of the through-thickness thermal conductivity of Pd/Ir multilayers by time-domain thermoreflectance and previously published studies of the through-thickness electrical conductivity of the same samples to validate the interfacial form of the Wiedemann-Franz law. The thermal conductance of Pd/Ir interfaces is asymp;14 GW m^-2 K^-1, in good agreement with the electronic diffuse mismatch model. ii) By contrast, heat transfer in a Pt/Au or Pt/Cu bilayer is strongly suppressed relative to the prediction of the Wiedemann-Franz law due to the relatively weak electron-phonon coupling in Au and Cu. By measuring the rate of heat transfer between the layers, we measured the strength of the electron-phonon coupling parameter g(T) over a wide range of temperatures, 40-300 K. The temperature dependence of g(T) is in good agreement with the predictions of the 1957 two-tempeature model of Koganov et al. iii) When the metal layer is thin and disordered, the electronic thermal conductivity is not always the dominate channel for heat conduction. We are using a new extension of TDTR measurements that enables quantitative analysis of data collected with a lateral offset between pump and probe. We are using this method with a laser spot radius as small as asymp;1 mu;m to measure the in-plane thermal conductivity of thin metal films. The sensitivity of this method is controlled by the product of the film thickness and thermal conductivity; the current sensitivity limit is on the order of 0.1 mu;W K^-1.

The thermal conductance for a series of metal - graphite interfaces has been experimentally measured with time - domain thermoreflectance (TDTR). For metals with Debye temperatures up to ~ 400 K, a linear relationship exists with the thermal conductance values. For metals with Debye temperatures in excess of ~ 400 K, the measured metal - graphite thermal conductance values remain constant near 60 MW m-2 K-1. Titanium showed slightly higher conductance than aluminum, despite the closeness of atomic mass and Debye temperature for the two metals. Surface analysis was used to identify the presence of titanium carbide at the interface in contrast to the aluminum and gold - carbon interfaces (with no detectable carbide phases). It was also observed that air - cleaved graphite surfaces in contact with metals yielded slightly higher thermal conductance than graphite surfaces cleaved in vacuo. Examination of samples with scanning electron microscopy revealed that the lack of absorbed molecules on the graphite surface resulted in differences in transducer film morphology, thereby altering the interface conductance. Classical molecular dynamic simulations of metal - carbon nanotube thermal conductance values were calculated and compared to the TDTR results. The upper limit of metal - graphite thermal conductance is attributed to the decreased coupling at higher frequencies of the lighter metals studied, and to the decreased heat capacity for higher vibrational frequency modes.

Thermal transport across solid/solid interface has been extensively studied, but heat transfer pathways other than phonon transmission and electron-phonon nonequilibrium in the metal were usually neglected. In this work, we aim to build a general and unified model including both the above transport channels and others such as electron transmission and electron-interface coupling. We find that for a metallic thin film deposited on a semiconductor substrate, the electron transmission is only important when the semiconductor is heavily doped, or in the case where considerable amount of electrons are excited over the interface potential barrier to dope the substrate. In contrast, the electron-interface channel plays an important role in the intrinsic to low-doped regime, where substrate phonons can remove heat efficiently from the interface. As for transient conditions, high initial temperature and small thickness of the metallic thin film would be beneficial for electron-interface interaction. For metal/metal interface system, an analytical solution to the interfacial thermal resistance is obtained, which shows that the relative contribution from different transport channels depends on both the local condition at the interface and the bulk properties of each side of the interface.

The one-dimensional nature of carbon nanotubes combined with their high thermal conductivity makes them an excellent candidate for thermal management, thermoelectric power generation and thermal logic devices. We have studied the thermal characteristics of Joule-heated multiwalled CNTs on a polar substrate, using an established high resolution in-situ thermal mapping technique in a TEM that relies on the solid to liquid phase transition of indium islands [1]. We have experimentally observed the remote joule heating of the substrate which serves to demonstrate coupling of hot electrons with the substrate surface polar phonons [2], supported by theoretical models. The talk will provide a quantitative explanation of the conducted experiment as it probes the mechanism of heat dissipation and its dependence on varying biases.

[1] T. Brintlinger, et al., Nano Lett. 8, 582 (2008).
[2] K. H. Baloch, et al., Nature Nano. 7, 316 (2012)

Carbon nanotubes (CNTs) are attractive for applications ranging from thermal management to nanoelectronics due to their unique thermal, mechanical, and electrical properties. The ability of CNTs to result in functional assemblies with interesting surface chemistry makes it necessary to understand thermal conductivity of doped CNTs as well. In addition, thermal conductivity of bulk CNTs is compromised due to the presence of amorphous carbon, defects, impurities, and phonon scattering in 3-D network. Here, we study the thermal properties of undoped multiwalled CNT, purified CNTs, and N-doped CNTs using Raman microscopy method. The results showed that the thermal conductivity of pristine CNT films was around 70 W/m-K and that of N-doped CNT film is around 20 W/m-K to 30 W/m-K. This fundamental study also focuses on the thermal transport behavior of undoped and doped CNT films. Finally, we demonstrate the applications of such CNTs and their functionalized assemblies as an anisotropic heat dissipation material.

Anisotropy of heat conduction in multi-walled carbon nanotubes (MWNTs) is investigated by measuring axial heat flows in a pristine MWNT and in a MWNT with defects. Since the discovery of carbon nanotubes (CNT), much effort has been devoted for the realization of thermal management devices such as thermal interface materials (TIMs) using their excellent thermal conductivity. Especially, MWNTs can be synthesized at much lower cost than single-walled carbon nanotubes (SWNTs). However, the detailed mechanism of heat conduction in MWNTs, which is very confusing because of their dependence of diameter and length, has been scarcely investigated. The measurements are conducted by using high-sensitive nano-hot-film sensor developed by electron beam lithography. The thermal conductivities are 391 W/mK for a pristine MWNT and 103 W/mK for a MWNT with defects. The in- and out-of-shell thermal conductivities of each MWNT graphite shell are determined numerically with diffusive assumption, and differences of more than four orders of magnitude are obtained. We elucidate that the large anisotropy of thermal conductivity induces the huge reduction of nanotube thermal conductance by 74% compared with that of the pristine MWNT because of the presence of outer shell defects, which comprise only 2.8% volume ratio. Namely, phonons have to first transfer into inner layers at large defects and then transfer in the axial direction, which leads to low thermal conductivity of defected MWCNTs due to the very low out-of-plane thermal conductivity. By detailed transmission electron microscope (TEM) observation, the very low out of plane thermal conductivity is due to not only weak inter-shell interactions but also the gaps induced in the shells during the synthesis process. Furthermore, the hypothesis that the huge anisotropy induces not only diameter dependence but also length dependence of thermal conductivity is demonstrated, even though there is no ballistic phonon transport.

The exceptionally high values for thermal conductivity reported for individual carbon nanotubes (CNTs) have generated considerable interest in utilization of CNTs in thermal management applications. Measurements on CNT based materials (buckypaper, CNT films and mats), however, have yielded conductivity values that are orders of magnitude lower than those of the constituent CNTs. Two major factors have been proposed as being responsible for the low conductivity of the CNT materials: The reduction of the intrinsic conductivity of individual CNTs due to inter-tube interactions and low thermal conductance at CNT-CNT interfaces that may be sensitive to the surrounding environment. To investigate the effects of local structure on the intrinsic conductivity of individual CNTs and the thermal conductance across CNT-CNT interfaces, we employ non-equilibrium molecular dynamics (MD) simulations performed for different junction properties (contact area, contact angle, etc.) and local structural environments characteristic of CNT network materials (CNT length, distance to nearest neighboring junction, etc.). The results of MD simulations suggest that (1) contrary to the widespread notion of strongly reduced conductivity of individual CNTs in bundles as compared to conductivity of isolated CNTs, the van der Waals interactions between defect-free well-aligned CNTs in a bundle have negligible effect on the intrinsic conductivity of the CNTs, (2) conductance at CNT-CNT junctions is weakly affected by neighboring junctions and only when the junction separation distance is within the range of direct van der Waals interactions, and (3) for sufficiently long parallel nanotubes the conductance through the overlap region between the neighboring CNTs is proportional to the length of the overlap. A general description of the conductance at CNT-CNT interfaces is formulated in a form suitable for implementation in a mesoscopic model for thermal transport in CNT networks.
KEYWORDS: carbon nanotubes, molecular dynamics, interfacial conductance, nanoscale heat transfer

Efficiency energy use is intertwined with many aspects of the efficient performance of many technological applications. Heat dissipation limits the performance of electronics from handheld devices to massive data centers. Carbon nanotubes (CNTs) have attracted significant attention in recent years for thermal management applications utilizing their favorable properties, such as high thermal and electronic conductivities, stemming from their unique atomic structure. So far, a considerable amount of work has been dedicated to energy (electrical and thermal) transport in carbon nanotubes, either measured experimentally [Pop, et al., Phys. Rev. Lett. 95, 155505 (2005); Kim, et al., Phys. Rev. Lett. 87, 215502 (2001); Fujii, et al., Phys. Rev. Lett. 95, 065502 (2005); Choi, et al., Nano Lett. 6, 1589 (2006)] or predicted from theory [Che, et al., Nanotechnology 11, 65 (2000); Wang, et al., Appl. Phys. Lett. 88, 111909 (2006); Lukes, et al., J. Heat Transfer 129, 705 (2007); Donadio, et al, Phys. Rev. Lett. 99, 255502 (2007); Hu, et al, J. Appl. Phys. 104, 083503 (2008)], where electric fields accelerate charge carriers or a temperature gradient drives heat flow through phonon transport. However, to date almost all of the existing investigations of thermal transport of carbon nanotubes have focused on relatively low heat fluxes, i.e. the regime where the Fourier heat conduction law is valid. As transistors are continuously further miniaturized and more heat needs to be dissipated, undesired high heat flux and local hot spot regions unavoidably occur.
Here we present results [Hu, et al., Nano Lett. 12, 3410 (2012)] from non-equilibrium molecular dynamics (NEMD) simulations on a new mechanism responsible for energy transport in a carbon nanotube at high heat fluxes, beyond Fourier conduction: to this end, a wave-dominated energy transport mechanism is identified for high heat fluxes in carbon nanotubes, originated from excited low frequency transverse acoustic waves. The results show that the low frequency wave actually overtakes (more than 60% of the total for some cases) traditional Fourier heat conduction and efficiently transports the energy at high heat fluxes. This mechanism, unlike phonon gas modeling [Wang, et al., Int. J. Heat Mass Transfer 53, 1796 (2010)] which predicts that the heat flow will be choked and temperature jumps will be observed at the tube ends when the phonon gas velocity reaches the thermal speed, is responsible for a different, energy transport scenario: as the heat flux increases, the heat flow will not be chocked. Instead, low frequency waves (not accounted for in phonon gas modeling) will be excited in carbon nanotube and through them the carbon nanotube becomes an energy conduit since the mechanical wave can subsequently transfer the energy more efficiently than the traditional Fourier conduction. Our findings reveal an important new mechanism for high heat flux energy transport in low-dimensional nanostructures.

The law of heat transfer in a solid was discovered by Joseph Fourier in 1811. Since then, Fourier&’s law of thermal conduction has been the empirical foundation of virtually all thermal conductors. Based on Fourier&’s law, high thermal conductivity (κ) is always achieved in crystalline solids exhibiting strong chemical bonds and is independent of sample geometries. Since it is unlikely to synthesize new materials stronger than covalently-bonded carbon materials, the room temperature κ ~ 3000 W/m-K found in diamond, graphene, and single-wall carbon nanotubes (SWCNTs) is generally considered as an insurmountable limit for all materials. Recently, theoretical works have suggested that low dimensional materials may disobey Fourier&’s law and exceed the current limit of κ for samples of very high aspect ratios. However, previous measurements on κ&’s of micrometer-long SWCNTs or graphene samples have yielded no conclusive results. Here we report the observation of non-Fourier heat conduction phenomenon in ultralong SWCNTs whose κ increases with lengths without signs of saturation and reaches an unprecedented high value at room temperature for millimeter-long SWCNTs. Remarkably, the κ&’s of the investigated SWCNTs display power-law divergences even with the presence of isotopic disorders, defects, impurities, or surface absorbents. The unlimited ultrahigh κ discovered in non-Fourier thermal conductors will open an unbounded domain for novel applications for phononics.

The effective thermal conductivity of materials composed of carbon nanotubes (CNTs) is investigated analytically and in mesoscopic simulations. The mesoscopic simulations of CNT materials are performed with a model that represents individual nanotubes as chains of stretchable cylindrical segments and describes van der Waals interaction between nanotubes by the mesoscopic tubular potentials. The description of the heat transfer in the model accounts for the contact heat transfer between nanotubes, the finite thermal conductivity of individual CNTs, and the thermal resistance of bending buckling kinks. The mesoscopic model of heat transfer is parameterized based on results of atomistic simulations of heat transfer performed for several representative systems composed of (10,10) CNTs. The results of mesoscopic simulations of thermal conductivity of interconnected networks of bundles in carbon nanotube (CNT) films and vertically aligned arrays (VAAs) containing tens of thousands of individual nanotubes reveal a strong effect of the finite thermal conductivity of individual nanotubes on the conductivity of the CNT materials. The physical origin of this effect is explained in a theoretical analysis of systems composed of straight randomly dispersed CNTs. An analytical equation for quantitative description of the effect of finite thermal conductivity of individual CNT on the effective conductivity of CNT materials is obtained and adopted for continuous networks of bundles characteristic of CNT films and buckypaper. Contrary to the common assumption of the dominant effect of the contact conductance, the contribution of the finite conductivity of individual nanotubes is found to control the value of conductivity of CNT films and VAAs at material densities and CNT lengths typical of real materials. The correlations between the structural characteristics of the CNT networks, such as CNT bundle size and effective pore diameter, and the conductivity of the CNT materials are discussed.

Manipulating the thermal conductivity of composites and nanomaterials is highly desirable not only for thermal insulation or conduction, but also for thermoelectric (TE) applications [1]. In naturally occurring materials, the thermal conductivity is primarily determined by atomic structure and interatomic forces. By contrast, nanomaterial composites could be tuned for either high or low thermal conductivity by manipulating the orientation, density, doping or functionalization of their nanoscale components.
In this study, we develop a suspended infrared (IR) thermometry platform combined with a computational model for rapid analysis of nanomaterial thermal properties. In particular, we use aerosol synthesized single-wall carbon nanotubes (SWCNT) to fabricate networks (CNNs) by a dry deposition technique [2]. Such CNN samples are transferred to our measurement platform, between two large Cu blocks serving both as electrical contacts and heat sinks, separated by an adjustable gap to vary the length of the suspended CNN. We also measure the thermal properties of similar samples embedded in a dielectric (AlOx) using a 3-omega method [3].
For the suspended CNN samples, we extract the in-plane thermal conductivity from the imaged temperature profile obtained by IR microscopy with the sample under Joule heating. Temperature profiles peak in the center of the film (ΔTpeak ~10 K) with insignificant heating at the Cu contacts, indicating good thermal contact resistance. We simultaneously obtain the electrical characteristics of the samples, including their electrical contact resistance (RC = 2 kOmega;-mm) through a transfer length method (TLM) on samples with varying lengths (0.7-2.3 mm). IR thermometry and 3-omega measurements reveal thermal conductivity of CNN composites ranging from 0.5-50 W/m/K, which is limited by the high thermal resistances of SWCNT junctions [4]. By comparison with scanning electron microscopy (SEM) cross-sections, we uncover how the thermal conductivity of such CNNs correlates with microstructure, alignment, bundling, density of SWCNT junctions and functionalization (e.g. by incorporating in AlOx or PEDOT:PSS polymer matrix). Our comprehensive approach highlights a path towards tuning the thermal conductivity of SWCNT-based nanocomposites by controlling the elements of such networks.
[1] C. Yu et al., ACS Nano 5, 7885-7892 (2011)
[2] A. Kaskela et al., Nano Lett. 10, 4349-4355 (2010)
[3] D. Cahill, Rev. Sci. Instrum. 61, 802-808 (1990)
[4] H. Zhong et al., Phys. Rev. B. 74, 125403 (2006)

It is of scientific and technological interest to analyze the minimal concentration of nanostructures such as carbon nanotubes (CNTs) necessary to form a percolating network. The rationale is that CNT networks have been proposed as constituents of thin film transistors for electronics and biosensors, polymer composites for electromagnetic interference shielding, etc.
However, a major issue is that of the problem in predictability of the percolation threshold. Additionally, the threshold seems to be dependent on the nanostructure geometry as well as synthesis processes and could have a strong influence on the device properties.
We show evidence of electrical and thermal conductivity percolation in polymer based
carbon nanotube (CNT) composites, which follow power law variations with respect to the CNT
concentrations in the matrix. The experimentally obtained percolation thresholds, i.e., ~ 0.074
vol % for single walled CNTs and ~ 2.0 vol % for multi-walled CNTs, were found to be aspect
ratio dependent and in accordance with those determined theoretically from excluded volume
percolation theory. A much greater enhancement, over 10 orders of magnitude, was obtained in
the electrical conductivity at the percolation threshold, while a smaller increase of ~ 100 % was
obtained in the thermal conductivity values. Such a difference is qualitatively explained on the
basis of the respective conductivity contrast between the CNT filler and the polymer matrix.
We also demonstrate and report, for the first time ever, evidence of percolation behavior in thermal conductivity, through experiments on nanotube-polymer composites. Such a behavior is explained through an understanding of the differences between in-plane and cross-plane thermal transport .

As carbon is one of the most abundant elements, it offers a novel and potentially cost effective choice towards designing next generation of nanoelectronic devices. Moreover, allotropic forms of carbon such as carbon nanotubes (CNTs) and graphene are excellent carriers of thermal and electrical energy, and more importantly, these properties can be tuned controllably in multiple ways through different external stimuli (such as dopants, defects, etc). Of particular interest to this study is the issue of interface thermal resistance (ITR), which is associated with thermal energy transfer at the interface between two materials (its inverse is termed as interface thermal conductance (ITC)). Till now, most ITC simulation studies have been limited to single-wall carbon nanotubes (SWCNTs) and few layers of graphene layers. In this study, non-equilibrium molecular dynamics (NEMD) have been performed to focus on interface heat transfer characteristics of SWCNTS, possible effects due to their chirality, multi-wall CNTs (up to 10 concentric CNTs) and multi-layer graphene nanoribbons (up to 32 multi-layers of graphene). The predicted values for ITC are in good agreement with previous literature. We observe that SWCNTs have higher conductance then flat graphene nanoribbons (double-layer), but approaches its value as diameter of the CNTs increase. In addition, no noticeable trend was observed for conductance as a function of chiral angle. Regarding, multi-layer and multi-wall studies, we find that interface conductance increases non-linearly in a monotonic manner for multi-layer CNT graphene nanoribbons and approaches inter-layer thermal conductance in bulk graphite with increase in number of layers. However, for MWCNTs, we find that the interface conductance show a non-monotonic behavior, i.e., a maximum conductance is observed at certain number of multi-walls for a specific outer diameter nanotube. We also find that the peak position (in terms of number of walls) is dependent of nanotube diameter, and increases with increase in nanotube diameter.

Carbon nanotubes (CNTs) have been considered as possible fillers in thermal interface materials (TIMs) for about a decade. The results were not conclusive owing to the high thermal resistance between CNTs and the matrix material [1]. It is clear that a drastic enhancement of thermal conductivity of CNT-polymer composites is only possible with the improved thermal coupling between CNTs and the matrix. For this reason, it is important to investigate how functionalization of CNTs changes the interface between the filler and the polymer matrix and affects the thermal conductivity of the resulting composites. For this study, a set of composite samples was prepared from two different matrices, a thermoset commercial epoxy resin, which is utilized in the automotive industry, and polydimethylsiloxane (PDMS), a silicone rubber, widely used for bioapplications. CNTs with different diameters and lengths were used as fillers. Some of the CNTs were added as grown and others were subjected to carboxylic (-COOH) surface functionalization [2]. The thermal measurements were conducted using the “laser-flash” method with pyroceram and neat polymer as reference materials for heat capacity and thermal conductivity. The typical CNT-polymer composite samples were discs of ~12 mm in diameter and ~2.5 mm thickness with the densities of ~1 g/cm³ . The results were filler and functionalization dependent. The highest thermal conductivity achieved was found for an unfunctionalized single-walled CNT (SW-CNT) filler with an average of 21% enhancement from the neat epoxy at 3-wt.% loading over 25-75 °C. This was followed by an unfunctionalized multi-walled CNT (MW-CNT) filler with 20% average enhancement from the neat epoxy at 3-wt.% loading over 25-75 °C. The carboxylic (-COOH) functionalized SW-CNT filler was found to reduce the thermal conductivity of the neat epoxy by an average of 7% at 3-wt.% loading over 25-75 °C, whereas, as listed above, the same SW-CNT filler without functionalization achieved the highest average enhancement of any of the fillers. The functionalized SW-CNT filler was found to enhance the thermal conductivity of PDMS by an average of 12% from neat PDMS at 3wt.% loading over 25-75°C. Functionalized MW-CNT filler was found to have the same effect as un-functionalized MW-CNT filler on the average thermal conductivity at 3wt.% loading in epoxy over 25-75 °C, in this case a 15% enhancement from the neat epoxy over 25-75 °C. The enhancement of MW-CNT fillers was a positive function of MW-CNT diameter at both 1wt.% and 3wt.% loading.
The work in Balandin Group was supported, in part, the Winston Chung Energy Center and UC Discovery program.
[1] A.A. Balandin, "Thermal properties of graphene and nanostructured carbon materials," Nature Materials, 10, 569 - 581 (2011). [2] A. Chiolerio et al., in Carbon Nanotubes - Polymer Nanocomposites and Materials Processing, edited by Siva Yellampalli (InTech Publishers, 2011), p. 217-218.

Thermal storage for electric vehicles (EVs) promises a means to deliver heating and cooling to the cabin without draining electric battery power to maximize driving range. However, thermal energy densities of 0.14 kWht/L and 0.12 kWht/kg for heating and cooling are needed for practical implementation into EVs. We are developing a thermal battery based on an adsorption cycle where the novelty lies in the adsorption bed with zeolite (ZT) adsorbents. To maximize the heat and mass transfer of the bed, high thermal conductivity binders to ZTs are desired. In this work, we integrated carbon nanomaterials, such as carbon nanotubes (CNTs), graphene oxides (GOs) and carbon aerogels (CA), with ZTs by the impregnation and/or hydrothermal methods to enhance the thermal conductivity while minimizing decrease in adsorption capacity. Meanwhile, we varied the density of the composites using a hydraulic press. We characterized both the thermal conductivity and adsorption capacity of the various composites. In general, the thermal conductivity was proportional to the density of composites, but the rate of vapor transport was delayed with increasing density. In addition, the thermal conductivities of CNTs/ZT composites were higher than those of the other samples tested. Moreover, we demonstrated that functionalized CNTs (f-CNTs) had higher thermal conductivity (0.55 W/mK) than that of non-functionalized CNTs (0.22 W/mk), which is attributed to the hydrophilicity of the f-CNT surface that increases the contact with ZTs. In addition, no decrease of the adsorption capacities was observed because only a small amount of f-CNTs (~0.1 wt% of f-CNT in f-CNTs/ZT composite) was added. We aim to further increase the thermal conductivity by further studying the synergetic effect between CNTs and GOs. Our results provide helpful insights and guidance for the development of high thermal conductivity binders for advanced thermal batteries.

Graphene, a prominent nano-material for future electronics, has exceptional electronic, thermal and mechanical properties. Phonon transport at graphene nano-contacts in its electronic devices is critical for the efficient thermal management of graphene based nano-electronics. Thermal transport at graphene-metal contact becomes particularly important in short channel field effect transistors and graphene-Cu hybrid-interconnects where the metal contact can turn into a crucial heat removal pathway. Therefore, a good understanding of phonon transport at the graphene-metal interface is essential for the development of graphene based nano-electronics.
Graphene forms different interfaces with different metals, e.g., a physisorption interface by charge transfer or a chemisorption interface by orbital hybridization. The interactions at physisorption interfaces is weak and dominated by the van der Waals (vdW) forces, while strong metal carbide bonding can be formed at the chemisorption interfaces. In this study, we consider Cu and Ti metals to illustrate these two different types of interactions at graphene-metal interface. We consider a single layer graphene sandwiched between two surfaces of metal to explore interfacial thermal interactions. Density functional theory (DFT) calculations and atomistic Green&’s function (AGF) approach have been considered to simulate interface phonon conductance. A supercell of graphene residing on metal substrate is used in VASP package for DFT simulations. The harmonic matrices used in the AGF calculations were constructed using the force constants obtained from the DFT calculations. The distance between graphene and metal substrate is first optimized and then the force constants are calculated by displacing atoms. Phonon dispersion relations and density of states (DOS) are obtained using lattice dynamics calculations. A distinct phonon spectra mismatch is observed between metal and graphene. For example, the phonon modes in Cu are below 10 THz while phonons in graphene are dominated by modes above 10 THz. The force constants calculated from the DFT simulations and the developed AGF based model facilitates the estimation of the phonon transmission coefficients and interfacial thermal conductance across the metal/graphene/metal interface. The phonon transmission function shows the degree of coupling between phonons of different frequencies in metal/graphene/metal system.

Perovskite MgSiO₃ is considered to be one of the major components of the Earth&’s lower mantle. As such, it has being studied extensively via atomistic simulations using classical potentials, as well as by first principles approaches. Nearly 30 different classical potentials have been developed for this important material. In this work we report a comprehensive analysis of the performance of these potentials in representing the physical properties of MgSO₃ perovskite determined from experiment and first principles simulations. In particular we analyze structural, elastic and thermal properties, including thermal expansion and thermal conductivity,computed via fast and accurate Boltzmann Transport Equation solver. The potential that represents MgSiO₃. perovskite properties the best according to our results is one due to (Alfredsson, M., Brodholt, J.P., Dobson, D.P., Oganov, A.R., Catlow, C.R.A., Parker, S.C., Price, G.D., Physics and Chemistry of Minerals 31, 671 (2005)). Using this potential, we investigate the thermal conductivity of the MgSiO3 perovskite at the conditions of the Earth lower mantle and discuss the implications for mantle dynamics. We would like to acknowledge the support from National Natural Science Foundation of China (Grant 11005070) and Shandong Natural Science Foundation (ZR2010EM030). This work was supported by the NSF Materials World Network Project under Grant No. DMR-0710523 and NSF-REU, Grant 0755256.

Thermoelectric properties of heavily phosphorus-doped SiGe nanowires were calculated from 300 to 800 K by using an improved model based on the Boltzmann transport equation with relaxation time approximation. All the electron and phonon scatterings were comprehensively discussed and utilized to develop the new model for estimating three thermoelectric properties - electrical conductivity, thermopower, and thermal conductivity - of SiGe nanowires. It has been found that non-ionized dopant impurities have relatively large influence on electron and phonon transport. Phonon scatterings by Ge clusters and phosphorus clusters suppress thermal conductivity of SiGe nanowires. The simulation results based on our new model have excellent agreement with experimental data at low to medium temperature ranges. The thermoelectric properties at high temperatures were also estimated, showing an improved thermoelectric figure-of-merit, ZT (~1.2) at 800 K. The large improvement, compared to bulk counterparts, can be attributed to a significant reduction of thermal conductivity. This value can be further increased by using an optimum carrier concentration and removing non-ionized impurities. A maximum projected ZT value of Si0.73Ge0.27 nanowire at 800 K was estimated to be ~1.6 with a carrier concentration of 1.06 × 10^20 cm^-3. This result demonstrates a strong potential to have highly efficient thermoelectric device made of SiGe nanowires.

In recent years, with the continuous development of nanostructured materials,
deviations from the standard bulk heat transport were observed.
In low dimensional nanostructures, the confinement of the phonon modes, the
presence of surfaces/interfaces as well the
interactions in the phonon gas strongly affects the heat transport mechanisms.
Therefore new tools are needed in order to describe these new effects in
an efficient and comprehensive manner.
Fractional exclusion statistics (FES) has already proved to be an important
tool in the study of thermodynamical properties of interacting boson and
fermion systems, which are regarded as an ideal FES gas.
Recently, the transition rates for an ideal FES gas were established [1],
which opens the possibility of analyzing interacting boson and fermion systems
in non-equilibrium. We make here a step further and introduce a transport
model based on FES, using Monte Carlo simulations.
The transport model based on FES is applied on quasi-one-dimensional systems,
such as core-shell structures.
The statistical parameters which define the FES gas are extracted from the
interacting phonon gas, where we take into account both electron-phonon
and phonon-phonon interactions.
From experimental point of view, the electron-phonon scattering rate
as well as the phonon decay dynamics can be directly measured using
ultrafast Raman spectroscopy.
We also investigate the propagation of interacting
phonons in inhomogeneous media, which are described in a similar fashion as
in Ref. [2]. Within our approach we are able to point out the particularities
of heat conduction in nanoscale systems with multiple interfaces.
[1] G.A. Nemnes, D. V. Anghel, J. Stat. Mech. P09011 (2010)
[2] G.A. Nemnes, D. V. Anghel,
"Fractional exclusion statistics in systems with localized states",
J. Phys.: Conf. Series (accepted, 2012)

Ge/Si heterostructures have shown great potential for application in thermoelectric energy conversion devices due to their excellent thermoelectric properties. Ge/Si heterostructures have also attracted much attention for improving the performance of optoelectronic devices such as photodiodes, semiconductor lasers, and solar cells. Control of the thermal conductivity in these structures is of crucial importance. Thermal conductivity in Ge/Si supperlattice structures has been widely studied. However, previous research mainly concentrated on the effects of period thickness on the thermal conductivity. In the present research, the effects of the crystalline state of the individual layer on the thermal conductivity in Ge/Si supperlattice structures were investigated. We utilized a new frequency-domain thermoreflectance method using completely optical techniques (i.e., the omega; method) to measure the thermal conductivity of Ge thin films on Si substrates. We prepared a trilayer sample consisting of an Au sensing film, a target Ge thin film, and a single crystal Si substrate by magnetron sputtering method. According to the one dimensional heat conduction equation of the sample system, the thermal conductivity of Ge thin films was calculated. The results show that the thermal conductivity of Ge thin films is strongly dependent on substrate temperature and sputtering power.

We analyze the heat transfer from a heat source of sub-mean free path size located on top of a cold substrate. We calculate this transfer with an implementation of the ballistic-diffusive equations. Our goal is to observe what the significant deviations to real results are by using this approximation of the Boltzmann transport equation for heat carriers such as phonons or air molecules.

We analyze the heat transfer between the hot tip of a scanning thermal microscope (SThM), an instrument based on the atomic force microscope, and a cold sample. The distance between the tip and the sample is varied down to few nanometers, in order to reach the ballistic regime in ambient conditions. We also vary the pressure in order to observe the impact of this transport regime when the whole heated volume loses ballistic heat flux. We observe the cooling of the tip due to the tip-sample heat flux and compare it to the current models of literature. In addition, we compare our results with a heuristic model based on shape of the heat flux lines, which were not taken into account in previous works. This work underlines the need to account for the ballistic transport regime in ambient air when the sizes are nanometer-scale.

In the rapidly developing fields of micro-electronics, opto-electronics, and micro-mechanics device performance is limited by heat transfer. As feature sizes decrease, temperature gradients become more challenging to measure since conventional temperature measurements such as infra-red emissivity measurements fail on a micrometer scale. Therefore, the development of new thermometry techniques with high spatial resolution is of significant importance for better device characterization and optimization. For this reason, temperature dependent micro-Raman measurements have been suggested and implemented as a thermometry technique with a spatial resolution of 1µm. However, these methods have a low thermal accuracy and are limited to specific materials.
We have developed a new method for temperature measurements with sub-micron spatial resolution based on the temperature dependent Raman shift position, which is independent of the device material and has a high thermal accuracy. Homogeneously dispersed microparticles serve as an indicator for the temperature of the underlying device. A temperature image can be obtained by analyzing the shift positions of a Raman image generated using a confocal Raman microscope with a 532 nm Laser. Since the shift position in the Raman signal is caused by the temperature dependent phonon energy in the micro particles, the Raman image can be directly converted into a temperature image. As an example, we have successfully demonstrated this new method on a micro-heater, revealing significant internal temperature gradients.

A thermal conductivity reduction of up to two orders of magnitude from bulk has been reported in silicon thin films with a periodic arrangement of unfilled pores (i.e., a porous thin film). In this work, we use finite element method calculations, lattice dynamics calculations, the Boltzmann transport equation, and a phonon-boundary scattering model to identify the mechanisms of the reduction. Porous thin films with hexagonal, square, and triangular arrangement of pores are considered. For the square lattice, we also study arrangements with a distribution of pore sizes.
We model the classical effect of material removal using finite element method calculations and find that the thermal conductivity reduction factor is the same as that predicted from an effective medium approach.
The scattering of phonons from boundaries is modeled using a Monte Carlo free path sampling approach. The phonon properties required as input are obtained from lattice dynamics calculations using force constants from DFT calculations. By considering only phonon-phonon and phonon-boundary scattering, we predict the solid-phase thermal conductivity reduction. For porosities larger than 0.30, the solid thermal conductivity of films with a hexagonal arrangement of pores is greater than that of films with square arrangement of pores, as expected based on number of nearest neighbor pores. For smaller porosities, however, the square lattice has an anomolously higher thermal conductivity. The solid thermal conductivity of films with a triangular arrangement of pores is smaller than thermal conductivity of films with other two arrangement of pores for the range of porosities considered (0.10- 0.60). For a distribution of pore sizes at constant porosity on the square lattice, we predict a decrease in the thermal conductivity with an increase in the spread of the pore size distribution. We also calculated thermal conductivity accumulation functions in order to determine an effective phonon-boundary length scale for the porous thin films. The thermal conductivity accumulation function represents contribution of different mean free path phonons towards the total thermal conductivity.

The shrinking dimensions of electronic devices demand fundamental research on the heat transport phenomena on the nanoscale. The heat transport from such structure into a substrate is usually measured in a pump-probe setup through the thermal response upon short laser pulse excitation.
Here we present ultrafast time-resolved electron diffraction in reflection geometry (tr-RHEED) as valuable tool to study fundamental mechanisms of heat transport in nanoscale hetero structures. Grazing incidence of 7-30 keV electrons ensures surface sensitivity. Analyzing different diffraction orders allows to clearly distinguish between different structures, e.g., films, clusters, or surface reconstructions. In a pump probe setup the sample is excited by an 800 nm laser pulse of 50 fs duration and subsequently probed with an ultrashort electron pulse. The transient temperature evolution is observed through the sudden drop and subsequent increase of intensity by the Debye-Waller effect. The thermal boundary conductance is then determined from the exponential recovery of the diffraction intensity.
To demonstrate the presence of finite size effects in heat transport we present experimental results on ultrathin Bi(111) films on Si(001) as well as on nanoscale Ge clusters on Si(001).
Single-crystalline Bi(111) films in a thickness range from 2.5 nm up to 120 nm were grown in-situ by molecular beam epitaxy under ultra high vacuum conditions. For thicknesses larger than 6 nm we observe a linear behaviour between cooling time and film thickness which is in a good agreement with the commonly used models for heat transfer, AMM and DMM. For thicknesses less than 6 nm, however, the cooling time shows a clear deviation between theory and experiment of more than 250%. The strong deviation for these thin Bi(111) films can be explained by a vertical confinement of the phonons inside the film due to total internal reflection.
To study the additional impact of a lateral confinement the transient temperature of self organized grown epitaxial Ge hut- and dome-clusters was determined. These nanoscale clusters exhibit typical dimensions which are much smaller than the mean free path of phonons in Ge. The hut-clusters cool within a time of 50 ps while the larger dome clusters need thrice as long with 150 ps. The measured thermal boundary conductance is thus a factor of two to three smaller than predictions from the AMM and DMM for a two-dimensional Germaniumlayer.

In order to improve the performance of the conventional heat exchange fluids many approaches have been tested. Nanofluids (NFs) are a novel class of nanotechnology-based colloidal suspensions engineered by stabilizing suspended nanoparticles (NPs) in a conventional heat transfer liquid such as water or glycol families. These new class heat transfer fluids have shown potential to enhance thermal properties of base fluids. Stable fluids containing micrometer sized particles (MFs) have been already tested to enhance the thermal properties of base liquids. Particle size plays an important role in thermal conductivity and viscosity of NFs. Literature data on the effect of particle size on thermal conductivity and viscosity of NFs and MFs are limited, therefore, there is a serious need to perform a detailed study on the influence of particle size on the thermal conductivity and viscosity of heat transfer fluids. In this work a systematic study has been performed to investigate, experimentally and theoretically, the impact of Cu NPs and MPs, as well as the composition of the base liquid in thermal and rheological properties of fluids. For this purpose, Cu NPs and Cu MPs were dispersed in ethylene glycol and diethylene glycol with different percentages of particles loading between 1 wt% and 3 wt%. Ultrasonic agitation was used for obtaining a stable suspension and the use of surfactants was avoided. The physicochemical properties of all suspensions were characterized by using various techniques including particle size analyzer, Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM) and Infrared Spectroscopy (FT-IR). The thermal conductivity and viscosity of the NP and MP suspensions were measured. Then a comparison between obtained experimental results and estimated data predicted by theoretical were performed. Our findings on the physicochemical, thermal and rheological properties of the fluids, containing NPs and MPs with different size are presented in detail.
Acknowledgements: This work is performed with the financial support from European Commission - FP7 NanoHex project.

Heat transfer plays an essential role in many fields such as transportations, power generation, air conditioning and microelectronics. Conventional fluids for heat transfer application such as water, and ethylene glycol have low thermal conductivity. One way of enhancing their thermal properties is to create mixture by adding solid particles into the commonly used fluids. Nanofluids (NFs) are novel suspensions containing nanometric metallic or oxide particles which have shown potential to enhance heat transfer properties. Because of large aspect ratio and high thermal conductivity, carbon nanotubes (CNTs) are excellent candidates for improving thermal conductivity of NFs. In this study two CNT based NFs system were investigated: using as-received CNTs as well as CNTs with brief heat treatment. A two-step method was used to fabricate stable NFs by suspending multi-walled CNTs in a varying loading from 0.025wt% to 1wt% into water as the base liquid. To stabilize the CNTs in water two different surface modifiers as Gum Arabic and Triton X-100 with different concentration were used. The influence of heat treatment of CNTs and CNTs surface - base liquid interface on the physicochemical properties of NFs were characterized by using various techniques including SEM, TEM, FTIR, XRD, DLS and Zeta potential measurements. The thermal conductivity was measured by Transient Hot Wire (THW) method and the viscosity values were evaluated by a rotary viscometer. The thermal conductivity enhancement reached up to 10% at 0.1 wt% for NFs containing heated CNTs and TX-100 as surface modifier. Also a comparison between experimental findings and theoretical predictions for both thermal conductivity and viscosity were performed. Our findings revealed that heat treatment of CNTs will result in reaching enhanced performance of NFs with higher thermal conductivity and low viscosity.
Acknowledgements: This work is performed with the financial support from European Commission - FP7 NanoHex project.

Here we present data that suggests the effective thermal conductivity of aluminum nitride (AlN) film depends on the surface roughness of the supporting substrate. Thermal conductivity is critical to Light Emitting Diodes (LED) since high temperatures decrease light output efficiency, degrade emission spectrum, and shorten LED lifetimes. Demand for high power LEDs has increased over recent years, complicating heat dissipation challenges. While thermal packaging is important, better thermal management inside the LED structure itself is also required. Here we focus on the AlN layer since it has the lowest effective thermal conductivity of all nitride films in blue/green LEDs [Z. Su, APL, 2012]. We measured AlN films grown on SiC with different surface roughness, as well as AlN films grown on sapphire and Si substrates. On each substrate, we have four thicknesses of AlN, 50nm, 100nm, 250nm and 500nm. Using the 3-omega method, a decreasing effective thermal conductivity has been observed with increasing surface roughness. However, the differing lattice mismatch between SiC/AlN and sapphire/AlN interface hasn&’t revealed an obvious effect on the AlN thermal conductivity. We believe that roughness causes atomic disorder at the AlN/SiC interface, which reduces the interface conductance. Atomic resolution Titan TEM images support this hypothesis.

Organic-inorganic heterojunctions show promise for uses in molecular electronics and thermo-electric devices due to their scalability and ease of manufacture. Fascinating physical phenomena, especially in the area of thermal transport, are witnessed in these materials due to the intimate connections between organic and inorganic components at the nano-scale. We study the thermal properties, characterized by the thermal conductance, of a self-assembled monolayer (SAM) junction through a combined experimental and computational approach. Physical characteristics of the junction are varied to quantify their effects on the thermal conductance.
SAM junctions are ordered, periodic arrays of a single layer of organic molecules packed between two inorganic substrates. They are prepared in the laboratory by first growing a monolayer on either Au or GaAs substrates and then attaching the second metal layer through a transfer printing technique. This method prevents any damage to the SAM during printing, which has been observed for alternative techniques such as sputtering and evaporation. Parameters such as molecular length, chemistry, and junction temperature are varied to study their effect on the junction thermal conductance. Frequency domain thermo-reflectance (FDTR) - a laser-based non-contact measurement scheme to probe the thermal properties of thin films, is employed to study the samples. This method relies on the temperature response of a surface to the frequency of an oscillating heat flux imposed on it.
Complementary molecular dynamics simulations are also performed on the SAM junctions to obtain further insight into the effect of physical parameters on the junction thermal conductance. The overlap of density of states between the leads and the molecules has been reported to influence the junction conductance. This is studied by looking at the behavior of the thermal conductance for dissimilar leads. Lattice dynamics calculations are employed to study the effect of molecular vibrations on the thermal coupling between the leads.

It is now well established that nanocomposites exhibit improved thermal and mechanical properties compared to pure polymers. Despite over two decades of research using experimental studies and modeling works, mechanistic underpinnings behind these enhancements still remain under debate. Moreover, very few studies have explored relation between two or more polymer properties affected by the incorporation of nanomaterials. In our current study, we characterized the properties of polymer nanocomposites using synthetic hydrogels incorporating silica nanoparticles as the model system; both these materials have been well characterized, are commercially available, and are routinely used in a wide variety of industrial and scientific applications. Specifically, we aim to investigate the relationship between viscoelastic and thermal properties of such nanocomposites. Our preliminary results suggest that hydrogel mechanical properties are significantly dependent on the particle size and concentration of the nanoparticles. We hypothesize that the observed enhancement in viscoelastic properties of hydrogels upon the addition of nanoparticles should also benefit thermal conductivity of the resulting hydrogel nanocomposites. Rotational rheometry, atomic force microscopy, and laser flash technique will be used to characterize the structure and properties of hydrogels upon the addition of silica nanoparticles. As such, the study will provide fundamental understanding on how nanoparticles behave in polymers.

Thermal energy storage based on phase change phenomena is promising for solar thermal power generation or sustainable air conditioning and heating. However, low thermal conductivity has presented a critical design challenge in terms of energy charge/discharge rate. Thermal conductivity enhancement through nanofluids has been explored to mitigate this issue, though degree of enhancement remains controversial. This debate has made conductivity enhancement the primary focal point of nanofluid research. Conversely, other thermal properties that characterize thermal storage materials, such as phase change enthalpy, are not as well-researched. For the purpose of energy storage applications, nanoparticle addition has an adverse effect on specific storage capacity. A few researchers have reported a reduction in phase change enthalpy with particle loading, well below the mass loss prediction, which has yet to be explained. Interfacial layering, which was formerly considered as a mechanism for conductivity enhancement, may instead play a role in phase change phenomena, caused by the introduction of nucleation sites. Therefore, we propose an experimental investigation into a possible correlation between particle interfacial density and observed reductions of phase change enthalpy. We have probed the thermal properties of paraffin-based, carbon nanotube nanosuspensions at various nanotube loadings and sizes. Preliminary results suggest an increasing deviation from predicted phase change enthalpy with decreasing nanotube size and increasing nanotube loading.

Carbon nanotubes (CNTs) offer superior thermal, electrical, and mechanical properties for a variety of applications. In particular, researchers have studied methods to create materials based on CNT network scaffolds in order to realize the enhanced nanoscale properties of CNTs at the macroscale. Measured values of thermal conductivity in CNT networks, however, have often been substantially lower than theoretical predictions. Recently, phonon interference was speculated as a possible reason for this reduced thermal conductivity [1].
We have used all-atom molecular dynamics (MD) simulations to investigate whether effects such as phonon interference may play a significant role in heat transfer within CNT networks. First, we used MD to measure the thermal boundary resistance (TBR) at a junction of two perpendicular CNTs, finding good agreement between our simulation results and those of other research groups. We then used non-equilibrium MD (NEMD) to simulate heat transfer in networked structures (such as a system consisting of three CNTs arranged in an “H” shape) in order to study the effect of CNT spacing on TBR, examining both normal space and frequency space to look for the presence of standing waves or other interference phenomena. Simulation results were then compared with measured data from CNT networks of various densities, including single-walled CNT aerogels with ultralow density.
[1] R. S. Prasher, X. J. Hu, Y. Chalopin, N. Mingo, K. Lofgreen, S. Volz, F. Cleri, and P. Keblinski, Phys. Rev. Lett. 102, 105901 (2009).

Multiwalled carbon and boron nitride nanotubes have shown promising thermal conduction behavior for heat transport management of nanoscale electronic devices. However, the total conductance is limited by microscopic thermal resistances, such as the contact resistance between the nanotube and the substrate it rests upon. Characterizing this contact resistance has proven difficult and the values reported in literature show a large spread. As a result, the physics of the thermal transport between nanotubes and supporting substrates is not well understood. We have developed an in-situ transmission electron microscopy technique for thermal imaging, which we refer to as electron thermal microscopy, and this new technique has proven to be a valuable method for in-situ observation and characterization of thermal transport on the nanoscale. Previous experimental device geometries have shown that the contact resistance with substrates is high, generally greater than 250 Km/W, but these studies unfortunately did not allow for the determination of specific values. Using a new device geometry, featuring etched trenches in the substrate, we are able to suspend selected portions of the nanotube to manipulate the contact area of the nanotube with its substrate. This device geometry allows us to focus on precise determination of the thermal contact resistance between the nanotube and the substrate, and these new results will be compared in context with a larger set of measurements from the literature.

The occurrence of inelastic phonon scattering events at solid-solid interfaces has been indirectly inferred from measurements and calculations of thermal boundary resistance as a function of temperature. However, no predictive model yet exists to describe the degree of elastic and inelastic scattering at a given interface, and it remains an important unknown in models of boundary resistance. We examine the degree of inelastic interfacial scattering in wave-packet simulations using molecular dynamics. This method allow the isolation of interfacial aspects that are inherently conflated in experiments: anharmonic interatomic interactions, interfacial roughness, and interdiffusion. In particular, we attempt to isolate the effect of anharmonic interactions at the interface only, which is not possible experimentally. Improved understanding of inelastic scattering will also help to advance the understanding of other important but underdeveloped aspects of boundary resistance models, such as the degree of specularity.

Here, we use broadband frequency domain thermoreflectance (BB-FDTR) to measure thermal conductivity accumulation functions of Si, GaAs, GaN, AlN, and SiC at temperatures of 80 K, 150 K, 300 K, and 400 K and show that they collapse to a universal function in the high temperature limit. The thermal conductivity of a semiconductor is a function of the material&’s specific heat, phonon group velocity, and phonon mean free path (MFP), defined as the distance a phonon travels between scattering events. While the specific heat and phonon group velocity can be predicted and measured, determination of the phonon MFP spectrum has remained a challenge. Knowledge of the phonon MFP spectrum provides important information regarding heat dissipation within semiconducting materials, particularly as device feature dimensions approach phonon MFPs, as in electronic and photonic applications.
BB-FDTR is a novel technique developed to measure the spectral contributions of phonons to bulk thermal conductivity as a function of phonon MFP, also known as the thermal conductivity accumulation function. BB-FDTR uses a heterodyne approach to measure the thermal conductivity accumulation function, allowing for continuous resolution of the phonon MFP spectrum spanning two orders of magnitude (0.3 - 8 mu;m in Si at T = 300 K). Results in Si and GaAs compare favorably to numerical predictions (Esfarjani, et al., PRB, 2011) (Luo et al., arXiv, 2012) and show that phonons with long MFPs (>1 mu;m) contribute significantly to the bulk thermal conductivity at T = 300 K.
Next, we present a method to predict the thermal conductivity accumulation function as the temperature of the material approaches its Debye temperature. Using the measured spectra at T = 400 K and assuming Umklapp scattering as the dominant scattering mechanism, a universal accumulation function was found to exist in GaAs, GaN, and Si after normalizing the phonon MFP. The existence of a universal accumulation function suggests that the phonon MFP spectrum is a universal feature of matter in the high temperature limit, and can be used to predict the thermal conductivity accumulation function for any crystalline semiconductor near its Debye temperature.

The demand to measure and understand thermal transport at the nanoscale is increasing recently with needs to predict and/or control heat conduction through nanostructures. Time-domain thermoreflectance (TDTR) is a powerful tool not only to measure thermal conductance of thin films and interfaces but also to extract mean-free-path dependent properties with the spatial resolution smaller/comparable to the mean-free-paths [1]. A nontrivial challenge now is to resolve an area below the diffraction limit [2]. For this, we have attempted to utilize plasmon resonance of gold nanoparticles in TDTR measurements. Gold nanoparticles are widely used to obtain thermal imaging with high spatial resolution by exciting an area with diameter of tens of nanometers. Gold nanoparticles dispersed in toluene solution are casted onto a sample surface by spin-coating method with various particle densities. The diameter of gold nanoparticles is tens of nanometers, which is sensitive to a wavelength of a pump beam imposing thermal impulses on the sample surface. Taking the samples with appropriate transmittance and absorbance for the pump and the probe beams, thermal response and its dependence on the particle density and size of heating area are obtained by TDTR. The usability of the method and the underlying mechanism are discussed.
Reference:
[1] A. J. Minnich, J. A. Johnson, A. J. Schmidt, K. Esfarjani, M. S. Dresselhaus, K. A. Nelson and G. Chen, Phys. Rev. Lett. 107, 095901 (2011)
[2] J. A. Johnson, A. A. Maznev, J. K. Eliason, A. Minnich, K. Collins, G. Chen, J. Cuffe, T. Kehoe, C. M. S. Torres and K. A. Nelson, Experimental Evidence of Non-Diffusive Thermal Transport in Si and GaAs, MRS Proceedings 1347, (2011)

We use molecular dynamics simulations to compute Van der Walls junction thermal conductance between singlewalled carbon nanotubes (SWCNTs) as a function of the crossing angle. While with the increasing angle, the junction conductance decreases, the conductance per unit area, i.e., interfacial thermal conductance remains constant. Also larger-diameter SWCNTs are characterized by almost the same interfacial thermal conductance. By contrast, recent experimental studies by D. Y. Li and collaborators 1 have shown that that the interfacial thermal conductance between multiwalled carbon nanotubes (MWCNTs) increases with the diameter of the nanotubes. To elucidate this behavior we studied a simplified model involving an interface between two stacks of graphene ribbons that mimics the contact between multiwalled nanotubes. Our results, in agreement with experiment, show that the interfacial thermal conductance indeed increases with a number of graphene layers, corresponding to larger diameter and larger number of walls in MWCNT. These results, combined with our observation of almost diameter independent interfacial conductance of single-walled carbon nanotubes (SWCNT), indicate that the increase of interfacial conductance of MWCNT with diameter is attributed to the stacking of multiple graphene layers.
1Prof. D. Y. Li, Vanderbilt University, private communication (2011).

We report on the Kapitza conductance and phonon transmissivity at contacts between various metals and GaN from 80 to 500 K via time-domain thermoreflectance. By comparing the vibrational spectra of metals and gallium nitride, temperature dependent data indicates that inelastic phonon-phonon scattering processes do not contribute significantly at temperatures below 300 K. The influence of roughness and adhesion are investigated by depositing Au films on GaN substrates with different RMS surface roughness and the inclusion or exclusion of a Ti wetting layer, respectively.

Knowledge of the distribution of phonon mean free paths (MFPs) is important for energy applications such as waste heat recovery using thermoelectric power generators. Recently, a thermal conductivity spectroscopy technique was introduced that is able to measure MFPs over a wide variety of materials and length scales. However, the multiple time scales associated with the transient thermoreflectance experiment previously used to perform the measurement complicates the data interpretation. Here, we introduce a single-shot asynchronous optical sampling (ASOPS) technique that can rapidly acquire data without a delay stage and removes all modulation and accumulative effects. We use the technique to measure MFPs in several semiconductors and confirm the importance of long MFP phonons to thermal transport in these materials.

Thermal conductivity, k, of alloyed materials is typically less than the conductivity of any of the components of the alloy and varies highly non-linearly with the composition. Using molecular dynamics (MD) simulation we investigate the effect of alloying in 1-dimensional layered crystals some of which have been shown to exhibit very low thermal conductivity. In particular we study a range of model materials composed of layers of graphene and tungsten selenide (WSe2). We focus our study on the relationship between thermal conductivity and the fraction of WSe2 layers. We also determine the role of long-range order by comparing thermal conductivity of ordered (superlattice-like) and random layered structures with the same composition.

Azobenzene polymer chains are potential candidates for nanoscale molecular devices due to ability to switch it conformation via optical excitation. This allows to perform mechanical work at nanoscale, and, perhaps more importantly create an electrical or thermal transport nanoscale switch.
In this work, using non-equilibrium molecular dynamics (NEMD) simulations, we model thermal transport across silicon-azobenzene covalent junction as a function of chain length and conformation. Contrary to our expectation, the thermal conductances for straight and curved chains are similar to each other. This is consistent with vibrational density of states analysis (VDOS) that shows very similar spectra for the two configurations. To gain more detail understanding of the phonon transport across the two junctions we determined phonon transmission coefficients as a function of phonon frequency for both structures.

We report on the thermal and electrical transport properties of Au-single layer graphene (SLG) contacts with various materials or molecules placed between the Au and SLG. Sheets of single layer graphene grown by CVD and transferred onto SiO₂ substrates were chemically functionalized using electron beam generated plasma, and gold contacts were patterned onto the functionalized SLG to create two-terminal devices. Measurement of the cross-plane thermal conductance across the functionalized contacts was performed using time domain thermoreflectance (TDTR). We show that functionalization with oxygen and nitrogen enhances the conductance across the Au/SLG interface, while fluorine exhibits little to no change. The influence of these adsorbates on the thermal conductance is attributed to their affect on the bond between the Au and SLG. Additionally, in-plane current-voltage (IV) measurements were performed on these devices and comparisons are made among contacts with different functional groups between the gold and SLG, as well as contacts made with a titanium wetting layer and no interfacial layer. It is shown that functionalization with oxygen and fluorine results in devices with a more non-linear, rectifying IV characteristic compared with both Au/Ti/SLG and Au on bare graphene. These results are explored in the context of the doping of graphene via metal contacts and the Schottky barrier heights at these interfaces. Furthermore, we demonstrate the potential for chemical functionalization to create both ohmic and rectifying contacts with desirable electrical characteristics. This work is supported in part by the Naval Research Laboratory base program.

With the recent development in nanotechnology, nanostructures in forms of pores, grains and layers are widely used to enhance thermoelectric performance of semiconducting materials mainly by lowering the lattice thermal conductivity. For prediction of performance and/or optimization of structures, detailed knowledge of phonon transport properties in the nanostructures is essential. While numerical simulations are useful tools to probe the detailed properties, the approach to solve the linearized phonon Boltzmann transport equations stochastically by Monte Carlo method has been demonstrated to be useful to analyze phonon transport in mesoscale and complex structures [1-3] beyond the capability of atomistic simulations. The approach has become even more powerful with the recent advances in first-principles-based calculations of mode-dependent phonon transport properties [4-6], such as group velocity and relaxation time. In this study, we have performed the Monte Carlo simulations to investigate phonon transport properties and lattice thermal conductivity in nanostructured thermoelectric materials. Nanostructures in various forms are constructed by introducing the interfaces with modeled frequency-dependent phonon transmission functions. Particular attention is paid to the influence of nanostructure length-scales on the mode-dependent lattice thermal conductivity, and its sensitivity to the characteristics of the interfacial transmission functions. Indication of the results to the design of nanostructured materials will be discussed.
This work is partially supported by the Japan Society for the Promotion of Science, PRESTO, KAKENHI 2360178. The authors acknowledge Prof. Gang Chen for insightful discussions.
Reference:
[1]S. Mazumdar, J. Heat Transer, 123 (2001) 749. [2] D. Lacroix, et al., Phys. Rev. B., 72 (2005) 064305. [3]Q. Hao, et al., J. Appl. Phys., 106 (2009) 114321. [4]D. A. Broido, et al., Appl. Phys. Lett., 91 (2007) 231922. [5] K. Esfarjani, et al., Phys. Rev. B., 84 (2011) 085204. [6] J. Shiomi., et al., Phys. Rev. B., 84 (2011) 104302.

Highly anisotropic, electrically insulating materials are sought for thermal management in the thermal management of miniaturized electronics. Materials with strong magnetic coupling, such as the copper-oxide chains in cuprates, can carry heat via spin excitations, in addition to conventional heat conduction channels of electrons and phonons. Spin waves or “magnons” in low-dimensional quantum magnets have also been suggested to support ballistic heat transport.[1] In the two-leg spin ladder Ca9La5Cu24O41, where magnon-hole scattering is suppressed by a low local hole concentration, Hess et al.[2] observed over 40:1 anisotropy in the thermal conductivity Λ near room temperature. However, the strength and nature of magnon-phonon interactions are unclear. We find that the effective phonon plus magnon Λ of Ca9La5Cu24O41, as measured by time-domain thermoreflectance (TDTR), depends strongly at low temperatures on the modulation frequency of the surface heating applied in TDTR. To explain the frequency dependence, we construct a two-temperature model with periodic surface heating of the phonon channel and linear coupling between the magnon and phonon channels. Fitting the model to our TDTR data and flash-fluorescence data from Otter et al.,[3] we extract an effective magnon-phonon coupling constant on the order of 10^15 W m^-3 K^-1 with strong temperature dependence between 100 K and 300 K.
References: [1] Zotos et al., PRB 55:11029, (1997) [2] Hess et al., PRB 64:184305 (2001) [3] Otter et al., IJHMT 55:2531 (2012)

Understanding of heat transport between a heated nanoparticle and its surroundings is a necessary first step in designing nanoscale heat sources for applications in nanoscience and nanotechnology. Au nanorods are of particular interest due to strong optical absorption, and tunability of optical absorption in the near-infrared by controlling their aspect ratio. We investigate heat transport of Au nanorods immobilized on a crystalline quartz substrate and immersed in organic fluids. Au nanorods are abruptly heated by a sub-picosecond optical pulse, and the cooling of the Au nanorods is monitored with pump-probe transient absorption. We developed a numerical model to analyze the heat flow from Au nanorods to the surrounding fluid and to the high thermal conductivity solid support. For hexane, toluene, ethanol, and methanol, the thermal conductance of the nanorod / fluid interface falls within a narrow range, 20 < G_f < 40 MW m^-2 K^-1, and G_f values increase with increasing fluid polarity. The thermal conductance of the nanorod / support interface for the sample immersed in fluid is 15 < G_s < 65 MW m^-2 K^-1, which is smaller than the one in air, G_s asymp; 140 MW m^-2 K^-1. We propose that adsorbed water from humid air is playing a role in the enhanced value of G_s in air compared to fluids.

Recently, literature has treated several cases, both theoretically [1, 2] and experimentally [3, 4], where a nm-sized layer between two materials has proven to have a significant impact on the thermal properties of interfaces. In this study, the effect of an interlayer between two materials on the heat transfer through their common interface is investigated in order to define when it becomes physically relevant. In other words, which thickness is required from an interlayer to change significantly the thermal transport between two materials? Does a surface treatment affecting one monolayer of material affect the heat transfer at an interface in the same way as 3, 10 or 20 layers of material? We try to quantify this effect by studying the Al/Ar:O plasma-treated diamond system using Time-Domain ThermoReflectance. The samples are produced by deposition of Al2O3 by atomic layer deposition on clean diamonds, followed by the deposition of a ~100 nm Al layer on top. In this system, a monolayer obtained by oxygen plasma treatment greatly improves TBC, but subsequent layers decrease substantially the TBC, apparently with a low influence on the temperature dependence of the TBC. The case of a nickel interlayer will also be discussed, in which electron coupling between the Al and the interlayer will be possible as well, in order to highlight a possible effect of electron conductivity.
[1] Z. Liang, H.-L. Tsai, International Journal of Heat and Mass Transfer, 55 (2012) 2999-3007.
[2] T.E. Beechem, S. Graham, P.E. Hopkins, P.M. Norris, Applied Physics Letters, 90 (2007) 1-3.
[3] P.E. Hopkins, P.M. Norris, R.J. Stevens, T.E. Beechem, S. Graham, Journal of Heat Transfer, 130 (2008) 1-10.
[4] C. Monachon, M. Hojeij, L. Weber, Applied Physics Letters, 98 (2011) 1.-3.

In the recent years, there has been growing interest in using graphene and carbon nanotubes composites as thermal interface materials in electronics cooling, in flexible electronics, and for use in battery electrodes. While graphene and carbon nanotubes with large thermal conductivity values are available at the scales of a micron or less, usage in industrial applications mandates their availability in larger length scales. Scaling is typically obtained by spreading a stack of these material flakes on a substrate. However, the effective thermal conductivity at the macroscale is not comparable to that of the individual nanostructures because of large thermal interface resistance between the nanostructures.
Recently, the issue of interface resistance has been overcome by growing ultrathin-graphite foams, which is a continuous network of covalently bonded ultrathin-graphite building blocks. The continuous structure of the foam significantly reduces the thermal interface resistance. Experimental values of effective thermal conductivity of these foams have recently been reported, and used to extract the thermal conductivity of the ultrathin graphite ligaments based on metal foam theories. However, the validity of the simple metal foam theories for the ultrathin graphite foams remains to be investigated.
In this work, we present a numerical method to obtain the thermal conductivity of the ultrathin graphite ligaments by calibrating the overall foam conductivity with reported experimental data. The geometry of the graphene foam is obtained by reconstructing a three-dimensional (3D) volume from a series of two-dimensional (2D) X-ray Computer Tomography (CT) scans. This geometry is then meshed and used in a finite volume solver to compute the effective thermal conductivity of the foam. Bayesian calibration is then used to obtain the ligament conductivity by calibrating the simulation data to experiment data. Image processing techniques on 2D CT scans are used to obtain additional properties including the thickness of the ultrathin graphite ligament and the surface to volume ratio.

Reduced graphene oxide (RGO) has provided a promising way to produce graphene on large scales. To restore the electron and thermal transport properties of pristine graphene, oxygen functional groups (e.g. hydroxyl, epoxide) needs to be largely removed without damaging the carbon lattice structure. However, it remains a challenging work to completely remove the oxygen functional groups adsorbed on graphene. Furthermore, the impact of oxygen functional groups on thermal conductivity of graphene is not clearly understood, and controlled oxygen functionalization may enable us to tailor thermoelectric properties of RGO. In this study, we have performed molecular dynamics simulations to compute thermal conductivity of oxygen functionlized graphene. In comparison with pristine graphene, thermal conductivities of oxygen functionalized graphene show a large decrease about 70-96 % for O:C ratio between 0.005 and 0.05. We also found that thermal conductivity of pristine graphene is diverged and scales linearly as logarithm of boundary length. When its boundary length is 2mu;m, the thermal conductivity is about 2400 W/mK, which is consistent with published experimental data. As oxygen functional groups (O:C ratio as low as 0.01) are adsorbed on graphene, thermal conductivities are converged and become independent of boundary length. We have done phonon mode analysis to explain this behavior.

Recent studies have taken advantage of electromigration in metal nanowires to create molecular scale devices and study charge transport at the nanoscale. However, their use has been somewhat limited by the large local temperature rise that is expected to occur during the electromigration process, which is essential to create the devices. Such temperature rises are believed to result in a degradation of the organic molecules through which charge transport is to be studied limiting the broad utility of the devices. Further, the electromigration process itself is not fully understood yet—for example, the origin of the bias dependent spatial location of the electromigration region remains elusive. In order to understand local heating during electromigration, we quantitatively measured the local temperature rise with nanoscale spatial resolution using a novel scanning thermal imaging technique developed by us. The obtained results give important insights into the process of electromigration, which will be presented in this talk.

We describe the design and application of a microfabricated ultra-high-resolution heat flow calorimeter to study the thermal transport properties of polymer nanofibers. The novel micro-calorimeter employed in this work is capable of measuring modulated heat currents with ~5 pW resolution. This level of performance is achieved by combining the excellent thermal isolation of a microdevice, suspended by thin and long beams (GTh ~150 nW/K), with the superb sensitivity of an integrated resistance thermometer that enables temperature measurements with 10 - 50 mu;K resolution (Sadat et al. Rev. Sci. Inst., 2012). Using this platform, we investigate the effects of diameter, length and crystallinity of polymer nano-fibers on their thermal transport properties. In this talk, we will describe the novel thermal transport properties experimentally observed in our studies.

The in-plane and out-plane thermal conductivities, of ZnO thin films produced by reactive sputtering, have been measured at room temperature. As a result of transmission electronic microscopy observation on the cross-section of the films, each film consists of two layers: an interfacial layer immediately above the substrate, with thickness of about 200 nm and composed of needle-like crystal grains; and the layer above the interfacial layer, composed of column-shaped grains, aligned along the out-plane direction. The grain diameters at the top of the films range from 35 to 100 nm, depending on the oxygen content of the sputtering gas. The measured out-plane thermal conductivity, on samples with grain diameter of 100 nm, are 2.4 Wm-1K-1 and 7.0 Wm-1K-1, for the interfacial and the above layer respectively. The in-plane thermal conductivity varies from 2.7 to 6.0 Wm-1K-1, decreasing as the grain diameter decreases. The thermal conductivity of the column-structured ZnO has been analyzed by an effective media theory method, with consideration of the thermal resistance at the grain boundaries. The result shows that the main reason of the low thermal conductivity of the ZnO thin film can be attributed to the reduction in the intrinsic thermal conductivity of the ZnO crystals, which is a function of the grain diameter varying with the oxygen content of the sputtering gas.

Hydrogen-terminated molecular nano-diamonds, also known as diamondoids, attract much attention in the field of nanoelectronics due to their outstanding properties. Diamondoids exhibit high thermodynamic stability, good mechanical strength, negative electron affinity, and short electron mean free paths. Their potential applications for nanotechnology include robust mechanical coatings, highly efficient electron cathodes, and seed crystals for diamond growth. Past studies have provided considerable information on several properties of self-assembled monolayers (SAMs) of diamondoids, including their orientational and electronic structure, dielectric properties, and electron-emission properties. However, little work has been done on characterizing thermal transport through SAMs of diamondoids.
In this work, we use picosecond time domain thermoreflectance (TDTR) to investigate the thermal properties of two thiol-functionalized diamondoids: Adamantane-1-thiol and [121]tetramantane-6-thiol, which are sandwiched between gold (Au) and aluminum (Al). In particular, we measure the thermal conductance of Al-diamondoid SAM-Au junctions. Preliminary measurements indicate that the thermal conductance is 41.3 ± 4.7 MWm-2K-1 for the SAMs of adamantane-1-thiol and 36.3 ± 2.8 MWm-2K-1 for the SAMs of [121]tetramantane-6-thiol. We also study SAMs of diamondoid-thiols on platinum (Pt) for comparison with the SAMs of diamondoid-thiols on Au. Thermal conductance data for other types of SAMs such as mercaptoethanol and dodecanethiol are also presented for comparison. We will discuss the impact of the strength of substrate-molecule bonding on phonon heat transport across the interface.

The thermal transport properties of interfaces are of utmost importance in mitigating and controlling the thermal properties of nano-systems. However, the effects of the atomic composition, disorder, and chemistry around these interfaces on thermal transport are largely unstudied, and can result in large deviations in the phonon scattering mechanisms contributing to thermal boundary conductance. In this work, we measure the thermal boundary conductance between thin aluminum films and silicon substrates that have been subjected to a varying level of proton implantation and post-irradiation surface cleaning procedures. It is found that proton bombardment of the silicon substrates leads to hydrocarbon contaminants at the interface and oxygen migration into the silicon from the native oxide layer. Due to both the changes in the carbonaceous and native oxide layers, the thermal boundary conductance between the Al films and Si substrates, as measured via time-domain thermoreflectance, is shown to span a factor of three depending on irradiation conditions and cleaning techniques. Oxygen plasma cleaning of the surface is used to remove the hydrocarbon layer resulting in a less resistive interface than an unprocessed wafer. This increase in thermal boundary conductance caused by smearing of the native oxide layer into the Si substrate, resulting in a graded interface, is confirmed by transmission electron microscopy. This graded interface acts as an effective ''vibrational bridge,'' creating a smooth vibrational transition between the Al film and Si substrate.

The thermal conductivities of 1mu;m copper-niobium multilayer films of different period thicknesses are measured by time-domain thermoreflectance over a temperature range of 80 - 296 K. The values for thermal conductivity are then used to calculate the thermal conductance between Cu/Nb interfaces where the total thermal resistance of the film is treated as the sum of the resistance of the layers and that of the interfaces. Results show that Cu/Nb interface conductance increases with the decrease in period thickness reaching a value as high as 20 GWm^-2K^-1 for a 1x1 Cu/Nb superlattice. At shorter period thicknesses ballistic electron transport dominates the thermal transport through interface resulting in high interface conductance. The results are well described with a model based on Boltzmann transport equation where we account for both diffusive and ballistic transport of electrons through the Cu/Nb interface.

Lithographically prepared gold nanowires of different lengths are
characterized with respect to heat dissipation at a solid liquid
interface. The heat dissipation of the system will increase with
stronger interfacial bonding between the solid and liquid. The
interfacial bonding of the solid/liquid interface is altered by
increasing the hydrogen bonding strength of water with the addition of
salt. The change in heat dissipation is measured by using a nanoscale
temperature sensor based on the temperature dependent photoluminescent
of Erbium (III) that is doped into a semiconductor matrix of AlGaN.

The exchange of heat from an intensely heated solid nanoparticle to the surrounding fluid is an important and challenging aspect of nanoscale heat transfer. Such systems have several important applications, particularly, in the field of medicine where significant ongoing research is in progress to use nanoparticles for hyperthermia based destruction of tumor cells. Though the concept of delivering heat via nanoscale heat sources to achieve biological response has been clearly demonstrated, an understanding of the thermal transport, the distribution of the temperature field, and associated microstructural changes and phase transformations is lacking. A striking observation made in several laser-heating experiments is that embedded metal nanoparticles heated to extreme temperatures may even melt without an associated boiling of the surrounding fluid. Also, molecular dynamics simulations show a phase stability of the liquid in spite of local supercritical temperature excursions. To gain a deeper understanding of the origin of the stability of the liquid above the critical temperature we analyze a free-energy based phase field model. The parameters of the free-energy functional in the model are dependent on temperature, providing coupling with the spherically symmetric high temperature gradient. The model shows that with increasing particle curvature, and resulting increasing temperature gradient, de-wetting occurs at increasing temperatures that can be well above the critical temperature. We discuss the liquid stability in terms of an interplay between the “local bulk” free energy decrease associated with the liquid-vapor transition and the surface tension of the liquid-vapor interface.

A family of nano-particules-doped hybrid glass based on a periodic nano-alignment, was designed for unconventional optical device materials. TEM images of the doped hybrid glass reveal a novel nano-fringe pattern. The resulting doped hybrid glass shows a low thermal conductivity and high compressibility. When the laser beam goes through a solid medium, the density wave is usually linear; because, in solid media, heat doesn&’t decay through the solid medium effectively. Interestingly, the highly compressed doped glass shows a strong ‘acoustic response&’ as strong as liquid; the acoustic response comes from the solid host was as compressive as liquid. In laser experiment, we calculated ‘the coefficient of phonon diffraction (D)&’, which is proportional to the coefficient of thermal conductivity. The number (D) was FIVE times smaller than that of normal glasses; the thermal conductivity of the doped hybrid glass is FIVE times less than that of normal glasses. Therefore, the doped hybrid glassy host serves as a ‘heat generator&’ thus, the heat gets transferred into expansion or compression wave (acoustic waves) effectively. It is a new optical property, which hitherto hasn&’t been discovered.

Graphene and hexagonal boron nitride are promising candidates for thermal management devices due to their high thermal conductivities. Prior to device production, a rigorous characterization of heat carriers, phonons in this case, is essential. Accordingly, in this study, anharmonic phonon relaxation times in graphene and its BN isomorph are calculated by utilizing molecular dynamics (MD) simulations. For the definition of atomic interactions, re-optimized Tersoff-type potentials are used in order to obtain accurate phonon frequencies and group velocities. Using the ground state phonon polarization vectors, the mode amplitudes and energies are calculated from MD. The decay in the mode energies due to Umklapp processes are related to relaxation times. This procedure is similar to solving the Boltzmann transport equation in principle but instead of analytical definitions, relaxation time in the collision/scattering term is obtained implicitly by the natural dynamics of the system. Thermal transport coefficients are calculated by employing kinetic theory with mode and wave number dependent phonon relaxation times, group velocities and heat capacities. It is shown that the smaller thermal conductivity in hexagonal boron nitride is due to both group velocities and relaxation times. The resulting thermal conductivity values are also compared with previous Green-Kubo calculations using the same force fields.

The thermal conductivity of nanocrystal arrays (NCAs) is found to be tunable with the nanocrystal diameter, and chemistry. Nanocrystals (inorganic crystalline cores 2-10 nm in size encapsulated in organic monolayers) self-assemble from colloidal suspensions into close-packed 3D NCA films. These films exhibit tunable electronic and optical properties that can meet various demands in optoelectronic and energy conversion applications. Coupled with their scalable solution-based fabrication process, they provide a cheap and versatile substitute for conventional single crystal semi-conductors and nanostructured materials.
Electronic transport in NCAs has been studied extensively. Little is known, however, about the nature of thermal transport in these complicated materials. The thermal conductivity measured for different NCAs is independent from the film thickness, and the bulk core thermal conductivity, yet is tunable from 0.1-0.3 W/m-K by increasing the nanocrystal diameter. Effective medium approximation (EMA) modified by incorporating a finite thermal conductance at the core ligand interface correctly captures the measured diameter-dependent magnitudes and trends. Changing the chemistry of the nanocrystal (i.e., different core and ligand species) enables further control for manipulating the NCA thermal conductivity. Heavier core species in NCAs decrease the thermal conductivity while shorter, inorganic ligand species exhibit the opposite effect. These observations are consistent with predictions from the modified EMA framework. Temperature dependent measurements yielded an increasing thermal conductivity trend that plateau at temperatures higher than the core species Debye temperature. This measured trend mirrors those of self-assembled monolayers (Luo & Lloyd, J Heat Transfer, 2010) and can be elucidated by considering the thermal activation and alignment of the core and ligand vibrational states.

Structures consisting of multiple nanometer-scale semiconductor thin films are ubiquitous in modern solid state devices. An example is the multiple quantum well in a light-emitting diode, built from alternating nanofilms of two differing materials such as InGaN and GaN. This material arrangement leads to useful optoelectronic properties, but device efficiency is limited due to thermal performance. Implementing thermal management strategies for these devices requires an understanding of thermal transport through nanometer-scale thin film structures. Thermal transport through such structures is complicated by the presence of material interfaces. Interfaces scatter phonons and are characterized by an interface thermal resistance. Isolated interfaces between crystalline semiconductors are well studied. Thermal transport through superlattices (infinite periodic arrangements of thin films), which exhibit significant reduction of thermal conductivity compared to bulk values of the constituent materials, is also well studied. Neither the infinite superlattice nor the isolated interface accurately represents a real multiple thin film structure, a system which has multiple interfaces, but is not infinite in extent. Our objective is to explore this intermediate regime. Since phonons are the primary carriers of thermal energy in semiconductors, we consider a Lennard-Jones multiple thin film structure using classical, non-equilibrium molecular dynamics simulations and the direct heat method. By alternating the mass of the Lennard-Jones material in adjacent thin films, we simulate mass-mismatch interfaces and calculate the overall thermal resistance of thin film structures placed between long, bulk-like leads. We vary the average temperature, mass ratio, film thickness, and number of films, as well as introduce disorder in film thickness and species mixing at the interfaces. The results are compared to the resistances of a simple thermal circuit model. We find that the mass and arrangement of the bulk-like leads affects the resistance of the thin film structure, suggesting ballistic phonon transport of superlattice-like phonons on length scales greater than the intrinsic mean free paths of bulk Lennard-Jones phonons.

Typical materials used in nanoscopic devices are amorphous and their thermal properties at temperatures of the order of 1 K and below are similar to the properties of macroscopic glassy materials. The thermal properties of macroscopic glassy materials are explained within the so called Standard Tunneling Model (STM), which assumes that in the solid exists an ensemble of dynamical defects modeled by two-level systems (TLS). The TLSs contribute to the heat capacity of the solid by absorption and emission of energy and to the heat and electrical transport by the interaction with the phonons, electrons, and other quasiparticle. Yet, the STM is suitable for the description of bulk materials, in which the TLSs interact only with simply polarized plane-waves, like phonon's displacement field, electron's wave function, etc. In a nanoscopic material, the phonon's elastic field is a complicated superposition of longitudinally and transversally polarized waves and the STM description fails.
We propose an amended model for the TLSs which can be applied to describe consistently their interaction with any kind of elastic strain field, including that of the phonons in a mesoscopic membrane [1,2]. Moreover, we have been able to describe consistently the TLSs interaction with elastic waves in crystals with defects and quasicrystals, and explain the anisotropic sound attenuation in such systems, which has been an open theoretical problem for over three decades [3,4,5].
References
[1] D. V. Anghel, T. Kuehn, Y. M. Galperin, and M. Manninen, Phys. Rev. B 75, 064202 (2007).
[2] T. Kuehn, D. V. Anghel, Y. M. Galperin, and M. Manninen, Phys. Rev. B 76, 165425 (2007).
[3] D. V. Anghel and D. V. Churochkin, EPL 83, 56004 (2008).
[4] D. V. Anghel and D. V. Churochkin, Phys. Rev. B 78, 94202 (2008).
[5] D. V. Anghel and D. V. Churochkin, submitted to Phys. Rev. B.

Aluminum-hydroxide-covered multi-walled carbon nanotubes (A-MWCNT) were fabricated
as a thermally conductive material. The thermal conductivity of A-MWCNT was estimated
based on Casimir theory. The effective thermal conductivity of A-MWCNT was estimated at
about ~26 W/mK. The thermal conductivity of A-MWCNT/epoxy-terminated polydimethylsiloxane(ETDS) composite was examined as a function of A-MWCNT loading,
and the results showed the maximum value at 1.5 wt% of A-MWCNT loading, above which
it decreased slightly. The effective medium approximation (EMA) developed by Maxwell-
Garnett (M-G) was used to analyze the thermal conducting behavior of the composite. The
experimental results showed negative deviation from the expected thermal conductivity, Ke,
beyond 1.5 wt% of A-MWCNT loading, because the composites containing A-MWCNT
were strongly affected by interfacial resistance. The interfacial resistance value calculated
from M-G approximation increased when filler loading was higher than 1.5wt% because of
the folded and partially agglomerated A-MWCNT along with insufficient interfacial
interactions

Extremely high thermal conductivity of graphene shows great potential for thermal engineering. A few theoretical studies on graphene thermal conductivity have been done with Boltzmann transport equation (BTE). The previous studies on graphene thermal conductivity consider only 2-dimensional vibration characteristics which result in ZA, ZO phonon mode in the phonon dispersion relation, but they do not consider 2-dimensional vibration transport characteristics. The present study focuses on how we can model the 2-dimensional vibration (phonon) transport characteristics as well as 2-dimensional vibration characteristics in graphene sheet.
In 2-dimensional materials, the degree of freedom of transport direction is 2 so that the thermal conductivity is expressed as k=1/2Cv2tau; by kinetic theory. In 3-dimensional material, phonon transport is modeled with spherical radiation and 4π solid angle. On the other hand, phonon transport in 2-dimensional system is planar-circular rather than spherical. The spherical 4π solid angle radiation system should be modified to 2π planar circular angle radiation system for two dimensional phonon transport. With the planar-circular phonon transport model, BTE is solved for each transport direction in planar-circular radiation system with finite volume method and 3 Umklapp scattering model for graphene dispersion relation.
We calculate the graphene thermal conductivity with and without 1.1% carbon isotope and the results are well matched with the experimental data of isotope controlled graphene thermal conductivity by Chen et al.(2012, Nature Materials) for both cases. The calculated thermal conductivity of graphene with our model does not show any divergence with increasing system size which is observed in the previous theoretical studies on graphene thermal conductivity and well converges with the thermal conductivity by the kinetic theory, which indicates our simulation model is successfully describing 2 dimensional phonon transport.

Paraffin wax is sought as an environmentally friendly thermal storage material. Although this organic and chemically-stable phase change material (PCM) is capable of storing large amounts of thermal energy at tunable temperatures due the ability to control carbon chain length, the rate at which it can transfer this energy is limited by its characteristic low thermal conductivity. Methods to enhance the effective thermal conductivity include addition of high conductivity nanoparticles or embedding the wax in porous foams. Although the introduction of high conductivity materials intends to increase the heat transfer rate, the impact on other system parameters - specifically latent heat, melting temperature, and stability - must also be considered to ensure the development of effective cyclic thermal storage systems. In this work, we present a comparative analysis of the two methods, focusing on the impact of introduction graphite nanoplatelets on the thermal conductivity, latent heat, melting temperature, and stability of paraffin was composites. In addition, the impact of porous foams on the composite thermal storage system was considered. In an effort to improve stability, the effect of dispersants, oxidation of the wax, viscosity of the wax, mixing time, and hydrocarbon chain length on the stability of paraffin- xGnP-15 graphite composites was studied. It was found that the addition of Octadecylphosphonic acid (ODPA) is an effective stabilization dispersant for xGnP. In addition, control of mixing time, viscosity, and oxidation of the wax influences stability in the molten state. Overall, it was found that a mixing time of 24 hours for xGnP-15 along with ODPA mixed in a high viscosity, oxidized microcrystalline wax results in composite PCM systems with the greatest stability determined at 80°C in the molten state. Through this combination of processing steps, increase in the stability or settling time of the molten paraffin/graphite composites was increased as measured by capacitance sedimentation and visual inspection from 11 minutes to 50 hours. Differential scanning calorimetry and Hot Disk measurements indicate that mixing time has no effect on latent heat, melting temperature or thermal conductivity while the introduction of ODPA reduces the thermal conductivity by 4%, but has limited impact on latent heat and melting temperature. Similar measurements show that oxidation reduces the latent heat, melting temperature and thermal conductivity of microcrystalline wax each by about 15%. Similar measurements will be presented for paraffin mixed with high conductivity porous materials. This work supports the eventual development of a stable, cost-effective, non-corrosive, non-toxic latent heat storage system for waste heat recovery in residential and commercial buildings.

Carbon nanotubes (CNTs) are considered to be very promising and useful material due to their exceptional thermal, electrical, optical and mechanical properties. Many studies have been performed in the past decade in an effort to explore and develop devices which could leverage the excellent properties of CNTs. A type of devices are CNT network thin film transistors (CN-TFTs) which may find applications in flexible displays, sensors, e-clothing, antennas, etc. Much of the research efforts on CN-TFTs are towards overcoming fabrication challenges to improve the performance of these devices [1,2]. However, fewer studies have focused on the thermal reliability of these devices during operation, which is an important aspect for electronics typically mounted on thermally insulating substrates.
In this work we explore the effect of the size of the device on power dissipation and thermal reliability. The high aspect ratio (length/width) of CN-TFTs has been previously utilized to obtain high ON/OFF current ratio as it helps to reduce number of metallic percolating paths in unsorted CNT networks which typically have 1:2 metal-semiconducting ratio [3,4]. We present and compare the results of smaller and larger width devices for various channel lengths with the intent of providing a guideline which can be used to optimize the device size considering both electrical performance and thermal reliability. We examine breakdown characteristics such as peak power and breakdown voltage to provide useful metrics of reliable operation of these devices. We apply both experimental and computational methods to analyze the electrical and thermal transport in CNT-TFTs. The analysis presented here will provide important insights to find solutions for enhanced performance and reliability of the device.
[1] Cao, Q. et. al., Medium-scale carbon nanotube thin-film integrated circuits on flexible plastic substrates. Nature 2008, 454, 495-500.
[2] Ha, M. et. al., Printed, sub-3v digital circuits on plastic from aqueous carbon nanotube inks. ACS Nano 2010, 4, 4388-4395.
[3] Kim, S. et. al., Fully transparent pixel circuits driven by random network carbon nanotube transistor circuitry. ACS Nano 2010, 4, 2994-2998.
[4] Pimparkar, N. et. al., Theory and practice for improved ON/OFF Ratio in carbon nanonet thin film transistors. Nano Research 2009, 2 (2). pp. 167-175.

We use non-equilibrium molecular dynamics (NEMD) to study heat transfer through structures consisting of a few layers of graphene or WSe2 sandwiched between silicon crystals. For graphene layers, we show that the transmission coefficient of individual vibrational modes depends strongly on the frequency and the number of graphene layers due to interference effects. By contrast, and in agreement with recent experiments, we find that the interfacial conductance, which represents an integral over all phonons, is essentially independent of number of layers, indicating ballistic phonon transport and smoothing out of interference effects. When one of the graphene layers is replaced by a WSe2 sheet, we observe a large temperature drop at WSe2 in contrast to the otherwise flat temperature profile of graphene layers, suggesting strong phonon scattering by WSe2. Moreover, when all graphene layers are replaced by WSe2 sheets, large temperature gradient suggests phonon transport through layers turns diffusive.

The cross-plane thermal resistances Rc of few-layer graphene (FLG) versus layer number were calculated from equilibrium molecular dynamics (EMD) simulations for both suspended and silica supported configurations. The concerned layer number ranges from 2 to 30. The resistances between specific layers (inter-plane resistance) were calculated from temperature difference fluctuations, while the averaged cross-plane resistances were derived from thermal conductivity calculated by Green-Kubo formula. No temperature dependence was observed in Rc, and it was found to decrease as layer number increases in both FLG configurations.
When the layer number of suspended FLG increases from two to four, a dramatic resistance jump from 10.10×10-9 to 3.10×10-9m2KW-1 was observed. This is due to the change in the number of available interacting layers. However, this resistance jump is much reduced in supported FLG, indicating that phonon leaking across the graphene-substrate interface is favorable to decrease cross-plane thermal resistance of FLG at low layer numbers. The decrease of Rc versus layer number in supported FLG was also confirmed by COMSOL simulation. The existence of silica substrate increased the cross-plane thermal conductivities of FLG by a factor of two, comparing to the suspended ones. But this effect is eliminated when layer number reaches seven. An ultra low cross-plane thermal conductivity of 0.067 W/mK was obtained in suspended 2-layer graphene. EMD simulations also show that graphene-silica interfacial resistance was slightly decreasing but became constant to 1.7×10-8 m2KW-1 when FLG layer number reached seven. These results provide a better insight in the heat transfer across FLG and yield useful information on the design of FLG based thermal materials.

Layer-by-layer (LBL) assembly of multilayer structures from 2-dimensional materials leads to artificially stacked van der Waals (vdW) solids for new devices and applications [1,2]. VdW solids have strong in-plane bonds and weak inter-layer vdW interactions (like natural graphite), however LBL assembly could lead to tunable and highly anisotropic heat transport properties between the in-plane and cross-plane directions [3,4].
In this work, we probe the thermal anisotropy of LBL-assembled structures from graphene layers grown by chemical vapor deposition (CVD), and explore extrinsic factors influencing heat flow in such vdW solids. Using electrical thermometry on suspended membrane platforms we find that the in-plane thermal conductivity of graphene monolayers on SiO2 varies from 100-300 W/m/K over the temperature range 80-350 K. This is an order of magnitude lower than freely suspended CVD-grown graphene films [5,6], highlighting the strong role the substrate plays in limiting in-plane thermal transport [7].
We then measure the cross-plane thermal conductance (G”) of such LBL graphene films by time domain thermoreflectance (TDTR). We find a reduction in G” with increasing layer number (n) from G” asymp; 25 to 10 MW/m^2/K for n = 1 to 10. These values are approximately a factor of two lower than the G” of exfoliated graphite samples [8]. We attribute this to a weakening of vdW coupling between layers, which may be due to trapped organic contaminants as suggested by transmission electron microscopy (TEM). Nevertheless, the intrinsic G” of such ultra-thin layers approaches the calculated ballistic cross-plane thermal conductance of bulk graphite, revealing a cross-plane phonon mean free path of ~10 nm.
In summary, this is the first study, to our knowledge, investigating effects of tunable thermal anisotropy in LBL-assembled vdW solids. Our results also highlight the important roles of extrinsic influences on heat flow in such solids, offering a path towards manipulating thermal transport in artificially stacked heterostructures.
[1] G. Gao, et al., Nano Lett. 12, 3518 (2012), [2] L. Britnell, et al., Science 24, 947 (2012) [3] D. Cahill, MRS Bulletin 37, 855-863 (2012), [4] E. Pop, et al., MRS Bulletin, DOI:10.1557/mrs.2012.203, [5] W. Cai, et al., Nano Lett. 10, 1645 (2010), [6] S. Chen, et al., Nat. Mat. 11, 203 (2012), [7] J. H. Seol, et al., Science 328, 213 (2010), [8] Y. Koh, et al., Nano Lett. 10, 4363 (2010)

Since transferred and exfoliated graphenes are generally believed to be partially suspended between asperities of the substrate while epitaxial graphene conforms to the substrate, heat transport across interfaces of epitaxial and transferred graphene could be significantly different. Particularly, if thermal conductance of graphene interfaces is limited mainly by heat transport across nanovoids in the graphene/metal interfaces, it is expected that the thermal conductance of interfaces of transferred graphene is significantly lower compared to that of epitaxial graphene.
To test this idea, we compared the thermal conductance of Al/graphene/Cu interfaces for both epitaxial and transferred graphenes. For the epitaxial graphene sample, we CVD-grew the graphene from copper foil and deposited a 100 nm thick Al on the sample. We measured the thermal conductance of the Al/graphene/Cu interface by time-domain thermoreflectance. We found that the thermal conductance of the Al/graphene/Cu is significantly lower than that of a control sample of Al/Cu without graphene. This reduction in the thermal conductance is due to a large Debye temperature mismatch between metals and graphene, and is consistent with prior measurements on interfaces of exfoliated graphene, in which heat is mainly carried by phonons.
For the transferred graphene, we first deposited a 1.4 mu;m Cu thin film on a 290 nm SiO2 on Si. We transferred CVD-grown graphene sheets onto the Cu thin film, and subsequently deposited a 100 nm thick Al film on the sample. To our surprise, we found that for transferred graphene, the thermal conductance of the Al/graphene/Cu interface is significantly enhanced compared to the control Al/Cu interface without graphene. We attributed this enhancement to heat conduction by electrons across the interfaces between metal and transferred graphene. We note that transferred graphene could be heavily n-doped by the PMMA used during the transferred process.

The recent progresses in the synthesis and isolation of atomic layered materials have enabled the fabrication of novel functional devices as well as fundamental studies of transport phenomena in two-dimensional (2D) systems. Several intriguing questions on 2D phonon transport and thermoelectric phenomena will be discussed here. The first topic is focused on the reduced lattice thermal conductivity found by experiments and molecular dynamics simulations in supported, encased, and surface-functionalized graphene. The reported phonon dispersion of supported graphene will be used to discuss whether modified phonon dispersions or group velocities also play an important role in the observed suppression compared to phonon-interface scattering. Moreover, the layer thickness dependence of the lattice thermal conductivity of supported multilayer graphene and hexagonal boron nitride (h-BN) samples will be used to clarify whether the suppressed thermal conductivity is mainly caused by local perturbation of atomic bonding near the interface, or also largely influenced by leakage of phonons across the interface, the latter of which would depend on the phonon dispersion and scattering inside the supporting material. In addition, the measured thermoelectric properties of bismuth telluride atomic layers will be analyzed to yield insight into the classical size effects on the lattice thermal conductivity and the charge mobility, as well as the effects of the surface states and energy quantization on thermoelectric transport in the topological insulator. Besides these fundamental questions, the potential applications of 2D materials for thermal management will be discussed. In particular, it will be emphasized that the basal-plane thermal conductivity of high-quality graphite presents a realistic upper limit in the thermal conductivity of graphene materials used in thermal management. Compared to thick graphite, nevertheless, the high surface to volume ratio of single- and multi-layer graphene and h-BN still makes them attractive as filler materials to enhance the thermal properties of composites. In addition to the optimum thickness of these nanofillers, a continuous ultrathin-graphite foam structure will be presented as an approach to overcoming the interface thermal resistance bottleneck found in other percolated networks of carbon nanofillers.

It is widely known that graphene and many of its derivative nanostructures have exceedingly high reported thermal conductivities (up to 4000 W/mK at 300 K). Such attractive thermal properties beg the use of these structures in practical devices; however, to implement these materials while preserving transport quality, the influence of structure on thermal conductivity should be thoroughly understood. For graphene nanostructures, having average phonon mean free paths on the order of one micron, a primary concern is how size influences the potential for heat conduction. To investigate this, we employ a novel technique to evaluate the lattice thermal conductivity from the Green-Kubo relations and equilibrium molecular dynamics in systems where phonon-boundary scattering dominates heat flow. Specifically, the thermal conductivities of graphene nanoribbons and carbon nanotubes are calculated in sizes up to 3 microns, and the relative influence of boundary scattering on thermal transport is determined to be dominant at sizes < 1 micron, after which the thermal transport largely depends on the quality of the nanostructure interface. The method is also extended to carbon nanostructures (fullerenes) where phonon confinement, as opposed to boundary scattering, dominates, and general trends related to the influence of curvature on thermal transport in these materials are discussed.

High purity bulk graphite is applicable in many capacities in the nuclear industry. While in earlier designs graphite was most often used as a moderator, its unique properties are also being exploited in order to develop high-tech fuel elements for next-generation nuclear reactors. The thermal conductivity of graphite has been found to vary as a function of how its morphology changes on the nanoscale, and the type and number of defects present. We compute thermal conductivities at the nanolevel using large scale classical molecular dynamics simulations and by employing the Green-Kubo method in a set of in silico experiments geared towards understanding the impact of defects in the thermal conductivity of graphite.

This lecture will overview our recent studies of thermal transport and dissipation in graphene, carbon nanotube, and phase-change material devices. We used infrared (IR) thermal imaging to visualize heat dissipation in functioning graphene transistors. Coupling such experiments with electro-thermal simulation has uncovered physical insights into their carrier densities, fields, temperature, and reliability during operation. We have also employed AFM-based techniques to measure the temperature with high resolution near graphene-metal contacts, and uncovered thermoelectric effects that could be engineered to partially mitigate the Joule heating generated during typical device operation. We examined high-field transport and dissipation in graphene nanoribbons (GNRs), finding that narrow GNRs benefit from (at first counter-intuitive) cooling effects due to heat spreading into their substrate and contacts. Through thermal engineering, we have achieved current densities >109 A/cm2 in GNRs, almost comparable to those of carbon nanotubes, despite a lower thermal conductivity of GNRs which appears limited by phonon-edge scattering. Combined, such studies offer a more complete picture of high-field transport and dis-sipation in carbon-based devices and interconnects under realistic operating conditions.

Recently, a novel nanostructured material - graphene nanoribbons (GNR) encapsulated inside individual single-walled carbon nanotubes (SWCNTs) has been synthesized [1]. The experimental observations and the first principal simulations suggest that the electronic structure of the GNRs inside SWCNTs remains the same as in the free-standing GNRs indicating possible applications in nanoelectronics and photonics. The material can be prepared in the form of a thin film deposited on various substrates. The thermal properties of GNR encased inside SWCNTs can vary greatly depending on various structural parameters. In this presentation we report results of the measurements of the thermal conductivity of the thin films consisting of the entangled SW-CNTs with GNRs encased inside them. The films were placed on thermally insulating glass substrates. The measurements were performed using a modified Raman optothermal technique [2]. The Raman spectrum of GNR-inside-SWCNT thin films revealed the G peak and 2D band typical for sp2-bonded carbon allotropes together with the radial breathing mode (RBM), which is a unique feature of SWCNT. The temperature coefficients of the Raman G peak and 2D band were determined by measuring Raman spectrum at the low-power excitation levels and varying the temperature of the samples externally in a cold-hot cell [2]. At the next step, the excitation power of the Raman laser was increased to induce a local heating. The local temperature rise due to laser heating was calculated from the shift in the Raman peak spectral position. The numerical simulations of heat diffusion were performed to extract the hermal conductivity value. It was found that the thermal conductivity of the thin films consisting of GNR encased inside SWCNTs is in the range of ~ 30 - 50 W/mK. This value is similar to that in the films made of conventional randomly entangled CNTs. Theoretical considerations suggest that GNRs encased inside SWCNTs can be promising fillers for the thermal interface materials [3]. Further experimental and theoretical studies are required in order to clarify the fraction of heat transported via CNTs and GNRs and the main mechanisms limiting thermal conductivity in such composite materials.
[1] A. V. Talyzin, I. V. Anoshkin, A. V. Krasheninnikov, R. M. Nieminen, A. G. Nasibulin, H. Jiang and E. I. Kauppinen Nano Lett.11, 4352 (2011)
[2] A.A. Balandin, Nature Materials, 10, 569 - 581 (2011).
[2] K. M. F. Shahil and A. A. Balandin Nano Lett. 12, 861 (2012)

Carbon nanotubes (CNT) and graphene platelets have been used as fillers for increasing the thermal conductivity of composites. Despite the record-high thermal conductivity reported for clean, suspended CNTs and graphene, the effective thermal conductivity of the nanocomposites is much lower than predictions based on effective medium theory. Among several issues such as phonon scattering at the interfaces between the nanofillers and the medium, the meager increase in the effective thermal conductivity has been attributed to the large thermal interface resistance between the nanofillers in the percolated networks.
Our recent study of continuous ultrathin-graphite foam has provided an approach to overcoming the interface thermal resistance barrier [1]. Much higher thermal conductivity was obtained for freestanding ultrathin-graphite foams than other percolated networks of carbon nanomaterials at a similar volume loading, but the thermal performance of the foam as a filler in composite materials has not been reported.
Here we report an experimental investigation of the thermal conductivity of (i) free-standing ultrathin-graphite foams, (ii) phase change materials (PCM)/ultrathin-graphite foam composites, and (iii) ultrathin-graphite foams after the PCM of the samples studied in (ii) is removed. Three different methods were established for the thermal conductivity measurements and validated against each other. The experimental results show that effective medium theory is accurate even when interface thermal resistance is not considered in the model. Comparison of the measurement results for the free-standing foams and the same foams after the PCM was removed allow us to evaluate the effects of interaction with PCM residues on phonon transport in the ultrathin-graphite ligaments. In addition, the small volume loading of the ultrathin-graphite foam needed to achieve the desired thermal conductivity has negligible effect on the phase change enthalpy of the PCM composites. We appreciate support from ARPA-E contract DE-AR0000178.

Industry continues to progress towards developing even smaller electrical devices. However, this size reduction must be met with better ways to meet energy efficiency and heat sensitivity needs. The unique thermal properties of carbon systems, such as the high thermal conductivity of single walled carbon nanotubes (SWNT) [1], potential thermal rectifying properties in carbon nanocones (CNC) [2] and asymmetric graphene ribbons (GR) [3], and the recent proposal of potential ballistic thermal transport in cup-stacked carbon nanofibers (CSNF) [4], make carbon nanostructures promising candidates for next generation thermal transport applications.
Carbon nanofibers can have a wide diversity of geometric underlying structures, and better understanding of the implications of nanostructure on transport properties is critical in building on complex integrated technologies. The conical-helix nanofiber (CHNF) is a annular structure formed by a helically wound graphene ribbon. This nanofiber's thermal properties have not been fully explored. Experiments suggest radically different thermal properties such as a two orders of magnitude decrease in thermal conductivity for conical nanofibers compared graphene [5]. Furthermore, graphene nanoribbons have been observed unraveling from these structures leading to the possibility of covalently bonded interconnects between these very different nanocarbon materials.
Using non-equilibrium molecular dynamics, we explore thermal transport properties of carbon nanofibers (CSNF and CHNF) in comparison to GR and SWNT. The structures of CSNF and CHNF are very similar except the continuity of covalent bonds in CHNF. We explore the applicability of CHNF to low conductivity applications. Simulations were performed for a wide range of lengths from 10 nm to 200 nm. The thermal conductivity of the CHNF structure shows reduced length dependence compared to other structures. In-plane conduction is shown to be dominant in CHNF. This mode of conduction leads to a twisting motion and highly variable cone angles as a result of low friction between the overlapping graphitic layers. CHNF structures also show reduced conductivity compared to other nanostructures which agrees with previous experiments [5]. The very low thermal conductivity of helical nanofibers could have possible applications in many industries including thermoelectronics.
References:
[1] M. Fujii et al., Phys. Rev. Lett. 95, 065502 (2005).
[2] N. Yang, G. Zhang and B. Li, Appl. Phys. Lett. 93, 243111 (2008).
[3] N. Yang, G. Zhang and B. Li, Appl. Phys. Lett. 95, 033107 (2009).
[4] Y. Ito, M. Inou, and K. Takahashi, J. Phys. Condens. Mat. 22, 065403, (2010).
[5] C.Yu et al., J. of Heat Trans. 128, 235 (2006).

Heat transfer through atomic and molecular junctions (AMJs) is fundamentally different from that in bulk materials. For example, theoretical studies have suggested intriguing phenomena such as divergent thermal conductivity in 1-dimensional molecular chains. However, probing thermal transport in AMJs is challenging due to the difficulties associated with creating AMJs and detecting the small heat currents (~few pW) flowing through them: such small heat currents are to be expected as the thermal conductance of AMJs are predicted to be very small (~pW/K). In this talk, we present our recent progress, which has enabled us to overcome these experimental challenges. Specifically, we will present a novel double tip-scanning thermal microscopy (DT-SThM) technique, which combines the capabilities of a picowatt resolution heat flow calorimeter with the capabilities of scanning probes that are suitable for trapping single molecules. We will present experimental results that demonstrate both the excellent heat flow resolution of these probes as well as the heat transport characteristics of point contacts and nanoscale AMJs.

Thermal conductivity of nanoscale thin films with very low thermal conductivity (< 1 W/m-K) is challenging because of the difficulty in accurate measurements of spatial variation in temperature field as well as the heat losses. In this paper, we present a new direct and steady state technique that mimics the phenomenon that a bridge with both surfaces exposed to wintry condition typically ices before the pavement.
Accordingly, the technique involves freestanding nanofabricated specimens that are anchored at the ends, while the entire chip is heated by a macroscopic heater. The first step is to deposit the specimen film on the wafer with desired thickness. The specimen pattern is then transferred to the film using photo-lithography. The photo-resist pattern is then used as the etch mask for the underlying specimen film while removing the unwanted portion using a reactive ion etching process using CF4 and O2 chemistry. This step results in the patterned specimen with the silicon substrate exposed. To remove the substrate under the specimen with minimal undercutting, highly anisotropic deep reactive ion etching using SF6 based chemistry was used, followed by a quick isotropic reactive ion etching.
Once the specimen is fabricated, the die is then mounted on a Kapton foil heater using thermally conductive adhesives. Two anchored ends of the micro-bridge specimen has the constant temperature boundary conditions. However, the specimen temperature (Ts) drops very quickly away from the anchor and remains constant for most of the length. This is due to the low thermal conductivity of the specimen. The temperature profile is characterized using an Infrascope II thermal microscope.The spatial and temperature resolutions are 2 microns and 0.1 degree C respectively.
Measurement of the spatial map of temperature field as well as the natural convective heat transfer coefficient allows us to calculate the thermal conductivity of the specimen using an energy balance modeling approach. The technique is demonstrated on thermally grown silicon oxide and low dielectric constant carbon doped oxide films. The thermal conductivity of 400nm silicon dioxide films was found to be 1.2 W/mK, which is in good agreement with the literature. Experimental results for 200 nm thin low-k oxide films demonstrate that the model yield thermal conductivity measurement with greater than 95% accuracy, which improves with reduction in thermal conductivity.

Static and dynamic hot spots limit the performance and reliability of electronic devices and integrated circuits. We show that transient thermoreflectance imaging using a CCD camera can measure temperature distribution in chips with 800ps time and submicron spatial resolution. It is possible to measure the top surface temperature on metal interconnects and, with through-the-substrate near infrared illumination, at the transistor level in flip-chip packages. Recent results in transient thermal imaging of GaN transistors, electrostatic discharge protection devices, solar cells, and light emitting diodes are presented. We show it is possible to identify non-uniform temperature rise and defects in 200 to 300 nm interconnect vias that have been stressed at high temperatures as well as heating due to percolation transport in transparent indium tin oxide nanoparticle layers. Finally, we discuss about the possibility to detect ballistic heat transport at short time scales.

When the gap size between objects is smaller than the thermal wavelength predicted by Wien's displacement law, photon tunneling can dramatically enhance radiative heat transfer beyond Planck's law of blackbody radiation. Near-field radiative heat transfer generally has a strong dependence on material properties. Here, we presented a broadband near-field thermal absorber (emitter) based on hyperbolic metamaterials, which can significantly enhance the near-field radiative heat transfer with any surface polariton resonance material. In addition, there is a lack of efficient numerical methods to calculate near-field thermal radiation for complex geometries such as metamaterials. We performed a direct numerical simulation for complex three-dimensional geometries based on chaos expansion method in order to accurately investigate the heat transfer mechanisms in metamaterials.

We demonstrated a high sensitivity temperature sensor based on organic thin film thermistor and transistor. Different from the transistor based temperature sensor where the temperature sensing is done by measuring the changes of the conductivity in the subthreshold region, our current device integrate the organic thermistor to the gate electrode of the OTFT. This also allows us to eliminate the undesired factors such as bias stress or moisture doping which would also affect the channel subthreshold conductivity. The temperature sensor shows a dynamic range of 10 bits in the temperature range from 20 degree to 70 degree, and this dynamic range is significantly larger than previously reported results. The high sensitivity of our device is achieved by interconnecting the thermistor to the gate electrode of the OTFT for the signal amplification. We will also discuss the variation of device sensitivity induced by changing the resistance states and the bias voltage level. A numerical simulation model will also be presented for optimizing the sensitivity of the current thermistor-transistor temperature sensor under different temperature range and bias conditions of the transistor and thermistor. We will also discuss the relationship between the applied bias and the resistance variation. It has been observed that increasing the bias of the transistor can compensate the decrease of the resistance variation and the highest dynamic range is observed at the optimized bias voltage. This current high-resolution temperature sensor in the current temperature range is extremely suitable for electronic skin and large area thermal sensing array application.

Thermoelectrics hold great promise for applications in energy recovery, on-chip cooling, and environmentally friendly refrigeration. However, for over half a century, progress has been hampered due to the low figure of merit, ZT, of these materials. Recently, several groups have significantly enhanced phonon scattering and increased the ZT of thermoelectric materials by nanostructuring materials either with embedded nanoparticles or surface modifications.

A first principles framework for thermal transport can help accelerate progress in this field by providing new physical insight into phonon scattering mechanisms and also identifying potential material candidates. In this talk, I will provide a brief overview of our work developing a fully predictive approach to heat transfer which links an iterative solution of the phonon Boltzmann transport equation with ab-initio harmonic and anharmonic force constants[1,2]. We can calculate these force constants using either density functional perturbation theory or a real space supercell approach. Given that many thermoelectric crystals have large unit cells which lead to computationally demanding calculations, we are also exploring phonon calculations based on order-N, localized orbitals density functional approaches.
Nanoparticle embedded in alloy thermoelectrics (NEAT) materials based on SixGe1-x or Mg2SixSn1-x alloys could offer cheap and non-toxic alternatives to current commercial options like PbTe that rely on scarce and toxic materials. I will discuss our recent investigations on thermal transport in these nanostructured thermoelectrics. Our calculated thermal conductivities for both semiconductor crystals (Si, Ge, Mg2Si, Mg2Sn) and their alloys show good agreement with experiment[1,3,4]. Using a T-matrix scattering formalism, we can capture how the size and concentration of nanoparticles affects thermal transport[3]. We have also expanded the Boltzmann transport approach to investigate the size effects on the thermal transport in diamond nanowire heat conduits[5] and Mg2SixSn1-x nanowires[4]. The phonon mean free paths in bulk materials can be used to plot the normalized cumulative thermal conductivity in order to understand how nanostructuring could limit thermal transport. As a final note, I will discuss how effective this measure is when compared to full numerical thermal conductivity calculations for nanowires.

This research has been supported in part by NSF Grants CBET-1066404, CBET-1066634, and by a European Union IRG Grant.
[1] D. A. Broido et al, Appl. Phys. Lett., 91, 231922 (2007)
[2] A. Ward et al, Phys. Rev. B, 80, 125203 (2009)
[3] A. Kundu et al, Phys. Rev. B, 84, 125426 (2011)
[4] W. Li et al, submitted to Phys. Rev. B, (2012).
[5] W. Li et al, Phys. Rev. B, 85, 195436 (2012).

With the growing capability to synthesize crystal materials with imbedded scales smaller than the phonon mean free paths, there is an increasing demand for knowledge in mode-dependent phonon transport properties. Over the several years, there has been a significant progress in this field, including the development in first principles calculations of anharmonic interatomic force constants, and it has become possible to accurately calculate lattice thermal conductivity of simple crystals [1-3]. Such approach has been recently extended to characterize more complex systems such as thermoelectric crystals [4,5]. Nanostructured thermoelectrics, where accurate knowledge in phonon-mean-free-path depenedent thermal conductivity is important for material design, is one of the applications that can benefit tremendously from these calculations. However, there are remaining challenges to make the calculations more useful for the material design, including development of methods that can deal with alloyed crystals and multiple interfaces without appreciably sacrificing the accuracy. In this talk, our recent activities using the first-principles-based multiscale phonon transport calculations will be presented. Starting from the first-principles calculations of anharmonic interatomic force constants, phonon transport properties are calculated either by lattice dynamics or molecular dynamics methods. New and old methods to calculate alloyed systems will be demonstrated and validated. Finally, the obtained phonon transport properties are input to Monte-Carlo simulations solving the Boltzmann transport of phonons with interfaces for material design. The capabilities and limits of the framework will be discussed taking the cases of various thermoelectric materials, such as half-Heusler compounds, lead chalcogenides, and magnisium silicides.
[1] D. A. Broido, M. Malorny, G. Birner, N. Mingo, and D. A. Stewart, Appl. Phys. Lett. 91, 231922 (2007).
[2] J. Garg, N. Bonini, B. Kozinsky, and N. Marzari, Phys. Rev. Lett. 106, 045901 (2011).
[3] K. Esfarjani, G. Chen, and H. T. Stokes, Phys. Rev. B 84, 185204 (2011)
[4] J. Shiomi, K. Esfarjani, and G. Chen, Phys. Rev. B 84, 104302 (2011).
[5] T. Shiga, J. Shiomi, J. Ma, O. Delaire, T. Radzynski, A. Lusakowski, K. Esfarjani, and G. Chen, Phys. Rev. B. 85, 155203 (2012).

Accurately predicting the thermal conductivity of a dielectric or semiconducting material requires the properties of phonons from the entire Brillouin zone. Accurate predictions of phonon properties for bulk systems can be made with anharmonic lattice dynamics theory using ab initio calculations. However, computational costs limit the size of unit cells in ab initio calculations to be less than 100 atoms, making it difficult to directly incorporate the effects of disorder. Alternatively, theory that treats disorder as a harmonic perturbation can be used to estimate the reduction in phonon lifetimes due to disorder scattering without the use of a large unit cell. Under this approximation, the disordered crystal is replaced with a perfect “virtual crystal” with properties equivalent to an averaging over the disorder (e.g. mass or bond strength).
In this work, the virtual crystal approximation for mass disorder is evaluated by examining two model alloy systems: Lennard-Jones argon and Stillinger-Weber silicon. In both cases the perfect crystal is alloyed with a heavier mass species up to equal concentration . These two alloyed systems have different ranges of phonon frequencies, lifetimes, and mean free paths. For Stillinger-Weber silicon, the virtual crystal approximation predicts phonon properties and thermal conductivity in good agreement with molecular dynamics-based methods. For Lennard-Jones argon, the virtual crystal approximation underpredicts the high frequency phonon lifetimes, leading to an underpredicting of its thermal conductivity.

We explore a model of heat transport between two heat reservoirs mediated by a quantum particle. The reservoirs are modeled as ensembles of harmonic modes linearly coupled to the mediator. The steady state heat current, as well as the thermal conductance are obtained for arbitrary coupling strength and will be analyzed for the cases of weak and strong coupling regimes. It is shown that the violation of the virial theorem - the imbalance between the average potential and kinetic energy of the mediator - can be considered as a measure of the coupling strength that takes into account all the relevant factors. The dependence of the thermal conductance on the coupling strength is non-monotonic and displays a maximum. Temperature dependence of the heat conductance may reach a plateau at intermediate temperatures, similar to the classical plateau at high temperatures. We will discuss the origin of Fourier&’s law in a chain of macroscopically large, but finite subsystems coupled by the quantum mediators. We will also address the origin of the anomalously large heat current between the scanning tunneling microscope tip and the substrate in deep vacuum which was found in recent experiments.

We report on the thermal conductivities of microcrystalline [6,6]-phenyl C_{61}-butyric acid methyl ester (PCBM) thin films from 135 to 387 K as measured by time domain thermoreflectance. Thermal conductivities are independent of temperature above 180 K and less than 0.030 +/- 0.003 W/m/K at room temperature. The longitudinal sound speed is determined via picosecond acoustics and is found to be 30 % lower than that in C_{60}/C_{70} fullerite compacts. Using Einstein's model of thermal conductivity, we find the Einstein characteristic frequency of microcrystalline PCBM is 2.88e12 rad/s. By comparing our data to previous reports on C_{60}/C_{70} fullerite compacts, we argue that the molecular tails on the fullerene moieties in our PCBM films are responsible for lowering both the apparent sound speeds and characteristic vibrational frequencies below those of fullerene films, thus yielding the exceptionally low observed thermal conductivities

We present experimental results from our study of energy dissipation in atomic and molecular junctions. Using custom-fabricated nanoscale-thermocouple integrated scanning tunneling probes, we have studied the energy dissipation characteristics of atomic and molecular junctions. Our studies performed in an ultra-high vacuum environment describe the novel heat dissipation characteristics of nanoscale junctions and elucidate the dependence of heat dissipation on the electron transmission characteristics of junctions. We will also describe our recent efforts into experimentally probing thermal transport characteristics in single molecule junctions.

A self-assembled monolayer (SAM) junction is a periodic monolayer of organic molecules that bridges two metallic or semiconducting contacts. A nanocrystal array (NCA) is a periodic, three-dimensional array of metallic or semiconducting nanoparticles decorated with organic molecules. The electronic structure of these low-cost organic-inorganic hybrid materials can be carefully tuned, making them attractive alternatives to semiconductors in thermoelectric, photovoltaic, and electronic applications. While the electronic properties of SAM junctions and NCAs have been extensively studied, their thermal properties have received minimal attention.
To address this knowledge gap, we use molecular dynamics simulations and lattice dynamics calculations to predict the thermal conductance of SAM junctions of the thermal conductivities of NCAs. For the SAM junction, alkanethiol molecules are placed between metal leads and we predict the junction thermal conductance. The effects of molecule length, temperature, binding group, and the mass of the metal atoms are considered. We find that the degree of vibrational overlap between the metal and molecule can be used to tune the junction thermal conductance. For the NCA, we consider both a toy system and full-atom representation and examine the effects of nanoparticle size and composition on thermal conductivity. We find that the organic-inorganic interfaces are the dominant source of thermal resistance. For both SAM junctions and NCAs, the modeling predictions are compared to experimental measurements.

The thermal conductivities of ultraoriented polymer fibers made by drawing are anisotropic and can be extremely high along the fiber direction. In this study, the thermal conductivities of nine high-modulus crystalline or liquid crystalline polymer fibers were measured along the molecular chain direction of the fiber at room temperature, including polyethylene (PE: Dyneema, Spectra900, and Spectra2000), polybenzobisoxazole (PBO: Zylon as spun and Zylon high modulus), polyhydroquinone-diimidazopyridine (PDID: M5 as spun), polybenzobisthiazole (PBT), Kevlar, and Vectra. Unlike previous experiments, a time-domain thermoreflectance (TDTR) method was used to directly measure the thermal conductivity of single fibers rather than fiber bundles or fiber reinforced plastics. Among all measured fibers, Zylon HM (high modulus) with the largest tensile modulus reported as 270 GPa, has the highest thermal conductivity of ~ 23 W/m-K, which is higher than that of stainless steel. In addition, the thermal conductivities of Zylon AS (as spun) and Dyneema were characterized within temperature ranges from 100 K to 500 K and from 100 K to 400 K, respectively. The temperature dependences of the thermal conductivities of both fibers show the characteristics of a typical crystal. Since they are good electrical insulators and thermal conductors along the chain direction, these high-modulus fibers have potential applications in electronic cooling where heat dissipation is crucial.

Cross-linking of polymers is extensively utilized processing strategy to improve and optimize mechanical, chemical and thermal properties of polymeric materials. In particular, development of cross-links provides for new covalently bonded channels for heat flow, and thus increases thermal conductivity.
In this study, to gain a quantitative understanding of the relationship between the degree of cross-linking and thermal conduction, we performed non-equilibrium molecular dynamics (MD) simulations on model amorphous polymers, including polyethylene (PE) and polystyrene (PS). We found that the thermal conductivity increases more or less linearly with a degree of crosslinking (DC). However, at low concentration of cross-links (up to 10%) in the PE case, there is no visible thermal conductivity increase. Our analysis suggests that initially in this case there is a competition between increasing thermal conductivity due to introductiuon of new channels for heat flow, and decreasing thermal conductivity due to cross-links acting scattering centers for phonons propagating along the polymer chain backbone.
In order to elucidate the underlying mechanism behind the crosslink bonds contribution to the energy transfer we analyzed energy transfer modes at the microscopic level. In particular, under steady state heat flow condition the total heat flux was decomposed into the components of the energy transfer associated with molecular translation, the energy exchange by nonbonded interaction between atoms, and the energy exchange by a covalent bond interaction through polymer chains and crosslink bonds. We found that the dominant contribution to thermal conductivity is the energy transfer by a covalent bond interaction. Also, the increase of thermal conductivity with a degree of crosslinking is dominated by the contribution of a covalent bond interaction. Based on the above consideration and results, we propose a simple physical model explaining the dependence of thermal conductivity on degree of crosslinking in polymeric materials.

Most traditional models of thermal transport emphasize phonon dispersion relations that are isotropic. This approach is exact for amorphous materials, and is also widely applied to materials with cubic crystal structures. However, various important materials have crystal structures that are highly anisotropic, such as graphite, Bi2Te3, WSe2, LiCoO2, and aligned polymers, with applications ranging from batteries to thermal barrier coatings. We are generalizing traditional analytical and numerical models to account for highly anisotropic phonon dispersion relations, and calculating the resulting changes in the heat capacity, thermal conductivity, and thermal contact conductance. The results reveal that “phonon focusing” is an important phenomenon in such materials and causes trends that may initially be counterintuitive, such as the fact that increasing the sound velocity in one direction generally degrades the thermal transport in an orthogonal direction.

Significant effort has been expended in the measurement of the thermal conductivity of thin film structures to evaluate low-dimensional effects such as phonon confinement, surface scattering, and thermal boundary interface resistance. In this context, various techniques for determination of cross-plane thin film thermal conductivity, e.g., the 3-omega method, have been developed. However, in these techniques the in-plane component of the thermal conductivity is not measured, but accounted for through an anisotropy factor. The validity of such adaptation is not clear. Alternatively, non-contact optical methods, such as thermoreflectance, could be used to directly measure the in-plane thermal transport of optically active thin films.
In this paper we report on our experiments where, by using a scanning thermoreflectance technique, we have measured thermal profiles, induced by on-chip alternating electrical currents in the range of 1kHz to 45kHz, in a multilayered silicon-on-insulator structure. Additionally, several heaters, with widths ranging from 5- 90 microns, were used as additional variables to vary heat flow conditions. Information on the thermal state of the structure, both with respect to lateral distance away from the heater and depth with respect to the layer interfaces, was then obtained. At heating frequencies below 10kHz, the profiles were fitted using a transient one-dimensional heat flow equation and the in-plane thermal conductivity of the buried oxide was determined. At higher frequencies, the thermal profiles suggest that heat trapping occurs in the buried oxide due to slow lateral heat dissipation. The experimental requirements and practicality of this method to determine the in-plane thermal conductivity of thin films will be discussed.

Non-metallic crystalline materials conduct heat by the transport of quantized atomic lattice vibrations called phonons. Thermal conductivity depends on how far phonons travel between scattering events—their mean free paths (MFPs). Due to the breadth of the phonon MFP spectrum, nanostructuring of materials and devices can reduce thermal conductivity from bulk by scattering long MFP phonons, while short MFP phonons are unaffected.
We have developed a novel approach called Broadband Frequency Domain Thermoreflectance (BB-FDTR) that uses high-frequency laser heating to generate non-Fourier heat conduction that can sort phonons based on their MFPs. BB-FDTR outputs thermal conductivity accumulation functions, which describe how thermal conductivity is summed from phonons with different MFPs. Relative to alternative approaches, BB-FDTR yields order-of-magnitude improvements in the resolution and breadth of the thermal conductivity accumulation function. In crystalline silicon we probe MFPs spanning 0.3-8.0 mu;m at a temperature of 300 K and show that 46±7% of its thermal conductivity comes from phonons with MFP > 1 mu;m. In amorphous Si, despite atomic disorder, we identify propogating phonon-like modes at 300 K. Measurements of the accumulation functions in other semiconductors show interesting commonalities in the high temperature limit and suggest that there may be a universal phonon MFP spectrum.

Knowledge of phonon mean free paths (MFPs) is critical to engineering size effects for applications like thermoelectric energy conversion, yet MFPs remain unknown in many solids. However, experimental investigations of quasiballistic heat transfer have led to a thermal conductivity spectroscopy technique that is able to measure MFPs over a wide range of length scales and materials. In this talk, I will describe the theory and practice of this technique as well as insights gained from its application. For theory, I will show that determining MFPs corresponds to solving an ill-posed inverse problem of a form very similar to deconvolution. For practice, I will describe experimental techniques we are implementing that enable considerably easier interpretation of the measurements than traditional transient thermoreflectance. Finally, I will present MFP measurements that confirm the importance of long MFP phonons to heat conduction in semiconductors, with important implications for more efficient thermoelectrics.

We investigate the heat flux generated by nanometer-scale heaters located on top of confined ridges of nano to micrometer-scale sizes. The cross-section of the device can be understood as a thermal constriction between a nanoheater and a thermal heat bath. The nanoheater is made of a doped silicon line that is electrically Joule-heated. The heat flux then spreads into the non-doped silicon ridge and dissipates into the substrate. We have fabricated devices with ridge lateral size (width) between 100nm and few microns. This allows observing the heat transfer as a function of the thermal Knudsen number, i.e. the ratio of the geometrical size to the phonon mean free path. We have two sizes in our devices: the ridge vertical height and its width. To analyze the effect of the mean free path, we follow the changes in the heat transfer as a function of the temperature in the range [10-300] K.
The results are first compared to standard analytical models calculating the thermal conductances by interpolating between the diffusive and the ballistic regimes. The thermal boundary resistance between the doped and non-doped silicon is evaluated. We are then able to estimate the validity of an advanced model developed for thermal constrictions when a nanostructure is involved.

At low temperatures, time-domain thermoreflectance (TDTR) measurements of single crystal thermal conductivities are often dramatically lower than the values measured using steady-state techniques. In some cases, this reduction can be partially attributed to the phonon mean-free-paths of the bulk crystals becoming comparable to the length scale of the TDTR induced temperature gradients. However, a comprehensive understanding of this phenomenon is still lacking. For example, the impact of interfacial phonon scattering on this phenomenon is not well understood; interfacial phonon scattering creates a complex boundary condition on the heat currents between the metal film and crystal. We report the results of low temperature TDTR thermal conductivity measurements of SrTiO₃, LaAlO₃ and MgO single crystals performed with a wide array of metal transducers. The type of interface formed between the metal transducer and bulk oxide crystal has a dramatic impact on the observed differences between bulk thermal conductivity values and the TDTR-derived values. The relationship between interfacial structure and TDTR-derived thermal conductivity is most pronounced in SrTiO₃. The ordered-epitaxial interface formed between SrRuO₃ and SrTiO₃ enables the efficient exchange of thermal energy between the metal and bulk crystal. As a result, the TDTR results in this system are consistent at all temperatures above 40K with published literature values for single crystal SrTiO₃. Introducing a small amount of disorder to this interface causes a dramatic change in thermal transport of the system. Adding a Ba₆₀Sr₄₀TiO₃ layer of two to six unit cells thick between the SrRuO₃ and SrTiO₃ results in the TDTR derived thermal conductivity of SrTiO₃ decreasing by a factor of 3 to 5 at 40K. We hypothesize that interfacial disorder preferentially scatters high frequency phonons and reduces the effective thermal conductivity in the substrate by inhibiting the exchange of thermal energy between high frequency phonons in the metal and bulk crystals.

Breakthroughs in many of today&’s advanced technologies depend on the ability to (1) efficiently dissipate enormous amounts of thermal energy (heat) from very small areas (e.g., heat fluxes beyond 2000 W/cm₂) or (2) regulate system temperatures within sometimes fractions of a degree over a broad range of operation loads/conditions (e.g., active, not passive, temperature control is imperative during operation because of irregularities in the environment and changing power loads). These requirements are especially stringent for the new generation of high power electronics, lasers, propulsion, and energy conversion systems.
This presentation will review our efforts in understanding thermal transport at solid-liquid-vapor interfaces. The main topics to be covered include: (1) microdroplet evaporation on superheated and laser heated surfaces, (2) the interfacial thermal conductance of water/metal and ice/metal interfaces, and (3) new routes for characterizing surface temperature transients by incorporating ultrafast laser diagnostics with ac magnetic fields. In regards to microdroplet evaporation, some of the key findings include: (1) on superheated surfaces, a reliable upper limit of m_LG= 35±5 mu;g/s is found for the evaporation rate, which is a maxima in m_LG- analogous to the critical heat flux observed in pool boiling - that signifies the transition in the heat transfer process from a purely microdroplet evaporation regime to a droplet/film boiling regime and (2) on a laser heated Al surface, an effective interfacial thermal conductance of G= 6.4±0.4 MW/m² is measured with the time-domain thermoreflectance (TDTR) technique. This value of is interpreted as the high-frequency (ac) interfacial heat transfer coefficient measured at the droplet/Al interface and is orders of magnitude greater than the heat transfer coefficient at the droplet/vapor interface. These results suggest that evaporative heat transfer is limited by the thermal resistance at the liquid/vapor interface. Therefore, to enhance the performance of a phase-change heat transfer process, cooling systems - including the cooling configuration and coolants themselves - need to be designed to maximize the solid-liquid-vapor contact line (i.e., triple-line) length per unit surface area.

Using molecular dynamics simulations, we demonstrate that the efficiency of heat exchange between solid and gas can be significantly enhanced by adsorbing self-assembled monolayers (SAMs) on solid surfaces. For bare metal surfaces, the thermal accommodation coefficient (TAC) strongly depends on the solid-gas interaction strength. For metal surfaces modified with organic SAMs, it is found that the TAC is greatly enhanced and becomes insensitive to the variation of solid-gas interaction strength. By calculating the average solid-gas interaction time, we find the incident gas molecules thermalize with the metal surface much more rapidly when the surface is covered by either adsorbed gas molecules or SAMs. We analyze in detail how SAMs affects the energy exchange associated with parallel and perpendicular to the surface translation velocity components as well as rotational kinetic energy. The simulation results indicate that the softer and lighter SAMs compared to the bare metal surfaces are responsible for the greatly enhanced TAC.

One particularly challenging and important aspect of nanoscale heat transfer is the problem of the exchange of heat between a solid nanoparticle and the surrounding liquid. This has several important applications, not least, in the field of medicine wherein there is significant ongoing research to use nanoparticles for hyperthermia based destruction of tumor cells. Though the concept of delivering heat via nanoscale heat sources to achieve biological response has been clearly demonstrated, an understanding of the thermal transport, the distribution of the temperature field, and associated microstructural changes and phase transformations is lacking. A striking observation made in several laser-heating experiments is that embedded metal nanoparticles heated to extreme temperatures may even melt without an associated boiling of the surrounding fluid. In this work we present the results from a series of non-equilibrium molecular dynamics simulations done on an intensely heated nanoparticle immersed in a Lennard-Jones liquid. For small nanoparticles we observe stable liquid in spite of local temperatures being above critical. We also identify a “critical” particle size above which under intense heating a phase change is observed. We discuss the origin of the stability in terms of the Gibbs free energy balance. We demonstrate that the interplay between “local bulk” and surface forces can result in liquid stability above the boiling point and even above the critical temperature.

In nanostructured materials with high densities of interfaces, interfacial thermal resistance becomes increasingly important, and it can have a limiting effect on the performance of the material in many energy related applications. However, the fundamental mechanisms that control the transfer of heat across many interfaces are not yet well understood. In this talk we will discuss our recent experimental studies of heat transfer across a series of systematically varied solid-liquid interfaces where the solid and/or liquid was modified in order to isolate the fundamental mechanisms that control heat transport between the solid and liquid. Specifically we examined how the interface conductance varies as a function of the molecular chain length of an attached monolayer and how the terminal functional group of the attached monolayer affects the conductance.
Our experimental system consists of a small flow cell that contains an optically transparent substrate coated first with a thin layer of aluminum, followed by a thin gold layer, then a self-assembled monolayer (SAM) which is in contact with a liquid. We measure the thermal conductance of the solid-liquid interface optically using time-domain thermoreflectance (TDTR). With TDTR, the thermally induced change in reflectivity of the aluminum is used to measure the thermal decay of the film on a picosecond to nanosecond time scale. By examining the thermal decay of the metal film and comparing our experimental measurements to an analytical thermal model, we can extract the interface thermal conductance, G.
In this work, we prepared a series of self-assembled monolayers on gold surfaces that were in contact with water. The strong affinity between gold and sulfur in the monolayer leads to a uniform coating of the SAM on the gold surface. In our first study, we examined a series of SAMs of varying molecular chain length including 1-Undecanethiol, 1-Dodecanethiol, and 1-Octadecanethiol. These films were hydrophobic with advancing and receding contact angles of approximately 118 and 105 degrees, respectively. We found consistent interface conductance values of G=60 MW/(m^2-K) for all of the hydrophobic SAMs, indicating that chain length was not important in the conductance. This conductance is also similar to measurements and simulations reported elsewhere in the literature on similar hydrophobic SAMs.
To study the influence of the terminal group, several functionalized surfaces were prepared with contact angles ranging from 118 to 35 degrees. Interface conductance values ranged from 60 to 190 MW/(m^2-K) from the hydrophobic to hydrophilic surfaces, respectively. These results indicate that the same surface forces responsible for wetting and adhesion play an important role in thermal transport across the interface.

By controlling the cooling rate of a graphite nanoplatlet and hexadecane nanofluid, we are able to dramatically vary the frozen nanofluid thermal and electrical conductivity, as well as the lengthscale of the nanofluid crystallization. For freezing rates between ~0.5 mu;m/s and ~100 mu;m/s, the nanofluid liquid-to-solid thermal conductivity enhancement can be varied between 68% and 121%, and the liquid-to-solid electrical conductivity enhancement can be varied between two and four orders-of-magnitude for the same loading nanofluid. The post-melting liquid thermal and electrical conductivities are unaffected by the freezing rate. We hypothesize that this controllable and reversible enhancement stems from the underlying nanofluid crystallization phenonena, which we characterized with optical microscopy of the frozen nanofluid. Solidification with rapid cooling minimizes the liquid-solid enhancement by reducing the percolation between graphite nanoplatlets and nanoplatlet clusters, while slow cooling maximizes percolation between graphite nanoplatlets and nanoplatlet clusters. A prior study attributed enhanced percolation upon freezing with internal stress generated during the phase change process (Zheng et al., Nat. Commun., 2010), and it is possible that we are controlling this internal stress by freezing rate. Trends in thermal versus electrical conductivity of frozen nanofluids will be discussed in the context of inter-nanoparticle thermal and electrical resistance.

Phase-change materials (PCM) that undergo solid-liquid phase transformations are very promising materials for future energy management applications (energy storage, solar energy storage, energy efficient buildings, temperature-adaptable greenhouses...) [1]. They have indeed the ability to absorb or release high latent heat during phase transformations. As they are not conveniently used directly due to their poor thermal conductivity, micro and nano- encapsulation have been developed. The encapsulation increases the heat transfer coefficient and heat transfer of the PCM material. It also prevents leakage in the outside environment and controls the limits excessive volume changes upon the phase change [2]. So far, mainly organic/polymer core-shell systems have been developed by various methods based on polymerisation reactions. Organics/inorganics simple core-shells have also attracted attention due to their high thermal conductivity and mechanical stability [3] nevertheless efficient and simple elaboration methods still have to be demonstrated.
In this work, we developed a straightforward and up-scalable method to coat wax beads of various sizes (from tens of nanometers to tens of micrometers range) with thermally conductive materials like zinc oxide. We are expecting to enhance and tune the heat transfer coefficient and the PCM entrapment to prevent any leakage in the outside environment.
Depositions on wax beads are made at low temperature (le;30°C) with atomic layer deposition technique under fluidized bed configurations. This technique allows the precise tuning of the conformality, the thickness and the stoechiometry of the nanoscale coatings. Deposits and micro/nano- beads characterizations have been performed by Scanning Electron Microscopy, Energy Dispersive X-Ray Spectroscopy and Secondary Ion Mass Spectrometry. The effect of the size of particles on the latent heat efficiency measured with Differential Scanning Calorimetry of the encapsulated PCM will be reported. First ageing experiments examining the PCM release from encapsulated beads will also be provided.
[1] E. Oro, A. de Garcia, A. Castell, M.M. Farid, L.F. Cabeza, Applied energy, 99, 513, 2012
[2] Zhong-Hua Chen, Fei Yu, Xing-Rong Zeng, Zheng-Guo Zhang, Applied energy, 91, 7, 2012
[3] Huanzhi Zhang, Xiaodong Wang, Dezhen Wu, Journal Of Colloid and Interface Science, 343, 246, 2010

Melting point depression is the phenomenon that describes the reduction in melting temperature commonly observed in nanomaterials. This phenomenon decouples melting temperature from chemical composition and hence provides a basis for which designer latent heat storage materials can be made. Two challenges in leveraging this phenomenon for thermal storage are the synthesis of nanoparticle ensembles with a narrow size distribution and protection against nanoparticle coalescence during melt-freeze cycling. To overcome this first challenge, we employ solution-phase chemistry to synthesize bismuth nanoparticles with ~ 5% monodispersity. To overcome this second challenge, we encapsulate the nanoparticles in a polymer matrix. This matrix protects the nanoparticles against coalescence during melt-freeze cycles and thereby stabilizes the effects of melting point depression. By varying the nanoparticle diameter from 7 to 15 nm, we tune the melting temperature of the bismuth nanoparticles from ~ 210 - 250 Celsius. In addition, by varying the nanoparticle volume fraction, we demonstrate the ability to tune thermal energy storage density in these composites.

Cooling is one of the most important challenges in industries such as transportation and microelectronics. Fluids such as water and ethylene glycol are typically used as coolant, however, their heat transfer capability is limited by their low thermal conductivity. There is therefore an urgent need for innovative and effective coolants with enhanced thermal properties. It has been demonstrated that adding small quantity of solid particles into a fluid in cooling and heating process is one of the methods to enhance the rate of heat transfer. Over the last decade, a new class of fluids called nanofluids (NFs), in which nanometric particles (NPs) are suspended in a conventional heat transfer base liquids, such as water and ethylene glycol, have been developed. These fluids have shown potential to improve heat transfer properties of the base liquids. In this study our aim is to fabricate novel NFs with high stability, low aging and effective thermal transport properties with minimum impact on viscosity which have potential applications as effective coolant in advanced thermal management systems. For this purpose several SiC NFs with different type of NPs (SiC-α and SiC-β), different surface modifiers/ additives, base liquids, and various concentration of NPs fabricated. Prepared suspensions containing SiC NPs were stable for a long time without any sedimentation. The physicochemical properties of NFs were characterized by using various techniques including dynamic light scattering (DLS), Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), X-ray diffraction (XRD) and infrared spectroscopy (FT-IR). Transient Plane Source (TPS) method was used to measure thermal conductivity of the NFs. Finally proper theoretical models were used to evaluate the obtained experimental findings of thermal conductivity and viscosity and our finding on physicochemical, transport properties and rheological behavior of the NFs are presented in detail.
Acknowledgements: This work is performed with the financial support from European Commission - FP7 NanoHex project

Most biological processes are accompanied by thermal activities. Among many of thermal measurement principles, calorimetric measurement of the heat of reaction via thermo-electric signal transducer is a promising method for complete thermodynamic characterization of biological processes. However, traditional calorimetric instruments require large sample volumes and long measurement time. The development in micro-fabrication technology including microfluidic engineering enables the fabrication of calorimeters on miniaturized silicon chip. The small length scale microfluidic chip calorimeters not only decrease sample volume of consumption and measurement time but also provide precise control of reactants without need for sample pre-treatments such as labeling and/or immobilization. Since the small reaction volume leads to the micro joule reaction heats correspond to very small measured temperature differences, power sensitivity of thermometer and thermal insulation of the device from environment are challenges for accurate and sensitive measurement. In this paper, we report high sensitive chip calorimeters with vacuum insulated microfluidic system. To improve thermometer sensing capability, we use vanadium oxide based thin film thermo-resistive sensor which has a high temperature coefficient of resistance (TCR). Thermometer was fabricated on bridge structured Parylene membrane over a vacuum cavity to improve thermal isolation. Parylene microfluidic system provides excellent thermal properties and physical strength to build a high-sensitivity calorimeter. The fabricated thin film resistor showed -1.6% of temperature coefficient of resistance. From FEM simulation, we find that the Parylene membrane bridge structure produces 3.6mu;W/K of device thermal conductance. Power sensitivity measurement circuit is composed of four equal thermistors which are combined in an interconnected Wheatstone bridge circuit. With large TCR and small device thermal conductance, we expect that the device sensitivity is possibly improved down to an order of pW level which is valid for cellular metabolism measurement. We will investigate biological heat of reaction measurement including enzymatic activity and cell metabolism.

We propose an original study of nanoscale heat transfer in biological objects by investigating the heat release during phase transitions induced by electric depolarization in neurons.... Thermal conductivity and IR-optical properties have been computed from equilibrium simulations. Quantum effects are investigated concommitantly by means of a quantum thermostat. We correlate the membrane morphology (or phase) to its thermal properties at different phases.

A general model for the number of layer dependence of the effective phonon group velocity in few-layer materials is presented. The model is applied to a few important few-layer materials and compare with corresponding lattice dynamics (LD) calculations. The phonon dispersions are computed using LD calculations with classical potentials for few-layer graphene (FLG), hexagonal boron nitride (h-BN) and Bi2Te3. Due to the unavailability of suitable classical potentials, density functional perturbation theory (DFPT) is used to compute the phonon dispersions for few-layer MoS2, WS2 and WSe2. According to the model, it is found that the strong number of layer dependence in the effective phonon group velocity of Bi2Te3 is due to the large ratio between interlayer interaction and in-plane bonding strength as well as the compact layered lattice structure. The number of layer dependence in the lattice thermal conductivity of other few-layer materials studied should be mainly attributed to the change in phonon relaxation times instead.

The reduction of the thermal conductivity in low dimensional materials has been associated with two principal effects, namely, the modification of the acoustic dispersion relation due to the spatial confinement of the phonon modes and the shortening of the phonon mean free path due to the diffuse scattering of phonons at the boundaries of the membranes. Acoustic phonon confinement has been studied experimentally and theoretically. The dispersion relation curves have been measured and phase velocities of the modes determined. A reduction of the phase and group velocities of the fundamental flexural mode by more than 1 order of magnitude compared to bulk values have been observed. The lifetime of coherent acoustic phonon modes with frequencies up to 500 GHz in these membranes has been studied using the ultrafast pump-probe technique of asynchronous optical sampling. The decay time of the first-order dilatational mode was seen to decrease significantly from sim; 4.7 ns to 5 ps with decreasing membrane thickness from sim; 194 to 8 nm. The experimental results are compared with theories considering both intrinsic phonon-phonon interactions and extrinsic surface roughness scattering including a wavelength-dependent specularity. Our combined results provide an insight into the limits of nanomechanical resonators and specially thermal transport in nanostructures. The latter will be discussed in the context of these phonon studies.

In this work, we present a simple analytical model for estimating ballistic transmission rates of guided phonons in nanowires with abrupt geometric and material discontinuities. Our model includes separate consideration of each of the four lowest order nanowire phonon modes (one extensional, one torsional, and two flexural modes) and is based upon the long wavelength behavior of these modes as analyzed using continuum elastic wave theory of prismatic beams. Our model is presented using a cascading T-parameter matrix approach that is similar to methods used in the analysis of electrical networks and may be applied to a nanowire system with any number of discontinuities and arbitrary but piecewise constant cross-section. In addition to the general cascading matrix approach, we have obtained simplified analytical expressions for the cases of the single nanowire interface (e.g. coaxial nanowire stepped junction) and symmetric double interface (e.g. nanowire constriction or nanowire with single coaxial expanded section). For these cases, we show that if the nanowire material properties are constant and the cross-section is circular or square, further simplified expressions for phonon transmission rates can be found that depend only on the ratio between each nanowire section&’s diameter (or side length) and the dimensionless wavenumber. For the test case of a cylindrical silicon nanowire system, we also compare our analytical model with mode-by-mode transmission rates calculated using the scattering boundary method. The scattering boundary method is a fully-atomistic computational model that, in contrast to our simple analytical model, accounts for mode conversion, the existence of higher order evanescent modes, crystal orientation, and atomistic granularity associated with discretely distributed particles. Despite the simplicity of our analytical model, we show good agreement between the two approaches for larger nanowire systems in the long-wavelength limit. When the dimension of the smallest geometric feature is below approximately 3 nm we begin to see significant deviation between the two models. We attribute this deviation to the inherent atomistic roughness at the nanowire boundaries as well as a softening of the phonon dispersion curves due to enhanced boundary effects in the smallest nanowires. We also observe significant discrepancy between the two approaches at higher wavenumbers. This difference is attributed to the fact that the atomistically calculated mode-shapes deviate significantly from the assumed long wavelength model. We find that this deviation is most prominent for the extensional mode but is also evident in the flexural modes. We also demonstrate that mode conversion at higher wavenumbers is also a source for deviation between the two approaches.

Heat transfer remains a crucial issue for leading micro/nanoelectronics industries targeting the new 22nm transistor generation as well as future molecular circuits. The recent energy crisis has also highlighted the need for energy sparing and scavenging through techniques such as thermoelectric conversion, which significantly depends on the improvement of thermal properties. In parallel, the development of nanofabrication processes has yielded molecular-to-micrometer scale structures with matchless thermal properties. For instance, the thermal conductivity of an isolated single wall carbon nanotube (CNT) was proven to exceed the one of diamond. However, the outstanding properties of those latter structures rarely allowed producing bulk materials with equivalent performances.
In the presented talk, we will show how unexpected nanostructure properties can be and how to improve their use in application oriented bulk materials.
In a first part, we will address nanojunctions that are wires with diameters of a few to several tenths of nanometers. Our experimental data and theoretical analysis will show that silicon junctions might exhibit effective thermal conductivities as high as diamond because of the rarefaction of scattering events inside the structure.1 This outcome has potential significant impact on the design of Nanoelectonic circuits.
In a second part, Thermal Interface Materials based on Carbon Nanotubes are proposed to improve chip cooling. The thermal properties of bulk materials including CNT pellets, spherical microarchitectures and vertically alignments will be presented.2,3
Finally, we will address several ways of improving the Thermoelectric figure of merit by using nanostructuration, as for instance grain boundaries, nanopores and superlattices.4,5
References
1 L. Jalabert, T. Sato, T. Ishida, H. Fujita, Y. Chalopin, S. Volz, Nature Nanotech., in review.
2Michael Bozlar, Delong He, Jinbo Bai, Yann Chalopin, Natalio Mingo and Sebastian Volz, Carbon Nanotube Microarchitectures for Enhanced Thermal Conduction at Ultralow Mass Fraction in Polymer Composites, Advanced Materials, 22 (14) 1654, (2010).
3R.S. Prasher, X.J. Hu, Y. Chalopin, N. Mingo, K. Lofgreen, S. Volz, F. Cleri, P. Keblinski , ‘Turning Carbon Nanotubes from Exceptional Heat Conductors into Insulators&’, Physical Review Letters, 102, 105901 (2009)
4Chandan Bera, M. Soulier, C. Navone, Guilhem, Roux, J. Simon, S. Volz, and Natalio Mingo, Thermoelectric properties of nano structured Si1-xGex, and potential for further improvement, Journal of Applied Physics, 108, 124306, (2010).
5Chandan Bera, Natalio Mingo, and Sebastian Volz, Marked Effects of Alloying on the Thermal Conductivity of Nanoporous Materials, Phys. Rev. Lett. 104, 115502 (2010)

Thermal conductivity of uranium oxide is an important design parameter for efficient and safe operation of light water reactors. Poor thermal conductivity results in a large temperature gradient that leads to preferential production of defects and enhanced fission product transport. It is important to have a fundamental understanding of thermal transport in nuclear fuel to develop enhanced performance codes that have predictive capability. This requires separate effect studies where the influence of individual microstructure features are investigated. In this presentation we discuss thermal transport in ion irradiated nuclear fuel surrogates. Depleted uranium oxide and cerium oxide were irradiated with protons and α- particles using a tandem accelerator. The change in thermal conductivity due to irradiation damage was measured using laser based modulated thermoreflectance technique. Microstructure characterization was carried out using transmission electron microscopy and atom probe tomography. The correlation between microstructure and thermal conductivity was compared to predictions of classic thermal transport models.

Our recent investigations of NaxSi136 clathrates show that as x increases, first the thermal conductivity drops due to rattling of the guest (the so-called “phonon glass” effect). But on further increase of x, the thermal conductivity increases. While part of the increase is due to electronic effects, at least some of the increase is due to stiffening of the cage structure, as discerned from analysis of heat capacity results.

I show that there is a close analogy between the quantities that describe one-dimensional (1D) quantum transport and the thermodynamic quantities of 2D quantum gases at equilibrium; for example the particle, energy, heat and entropy fluxes are analogous to the particle number, internal energy, heat capacity and entropy, respectively. Based on this, I write analytic expressions for the transport quantities and I show that the heat conductivity and entropy current are independent of statistics (i.e. Bose, Fermi, and fractional exclusion statistics of direct constant exclusion statistics parameters) at any temperature. The quanta of heat conductance is therefore the low-temperature limit of the heat conductance of one channel and is the same —as expected from the analogy above— as the low-temperature limit of heat capacity. The physical interpretation of this remarkable universality of 1D transport is given in terms of configurations of particle populations which carry the same heat fluxes [1].
I extend this analysis to the ballistic heat transport in any number of dimensions and I show that the heat conductivity is independent of statistics also in higher dimensions. Among other things, this implies also that the heat conductance of a quasi-two-dimensional strucutre is quantized in a similar way as that of a quasi-one-dimensional wire. The values of the higher dimensions quanta of heat conductance are also calculated.
References
[1] D. V. Anghel, EPL 94, 60004 (2011).

In this talk, we present our recent theoretical study on thermal rectification via evanescent waves between same material plates. A thermal rectification scheme via evanescent waves has so far been presented, where the rectification relied on the temperature dependence of electromagnetic resonances [C. R. Otey, W. T. Lau, and S. Fan, Phys. Rev. Lett. 104, 154301 (2010)]. The system consisted of different material bodies such as one half-space of isotropic 3C polytype silicon carbide (SiC-3C) and the other half-space of uniaxial 6H polytype silicon carbide (SiC-6H), separated by a vacuum gap. Here we point out that thermal rectification between the same material bodies can be achieved using a dielectric coating. Our geometry consists of one half-space of SiC having the transparent dielectric coating and the other half-space of SiC that has no coating. The coating permittivity and thickness condition is analytically derived for maximizing the rectification performance. The analysis reveals that proper choice of the coating thickness allows us to select either high permittivity materials, e.g., silicon, or low permittivity materials, e.g., barium fluoride. The fluctuational electrodynamics calculation results show thermal rectification effects and validate the derivation of the coating condition. We also present the dispersion analysis that complements the direct fluctuational electrodynamic calculations. Such dispersion analysis provides additional insights into the thermal rectification effects. The same material structure presented here extends the degrees of freedom for designs of thermal rectification devices.

GaN HEMTs have shown excellent performance for high power and high frequency applications such as satellite and radar. However, there are still concerns about lifetime and reliability, both of which are reduced by higher operating temperatures. One limiting factor for heat extraction is the defect density in the GaN, particularly near the GaN-substrate interface. Although it is known that defects reduce the thermal conductivity of a material, it has been unclear whether different types of dislocations have a different impact on thermal conductivity. In this work we demonstrate that screw dislocations have a much more detrimental impact than edge dislocations on the thermal conductivity of GaN.
The need to grow GaN on foreign substrates such as SiC arises from the limited commercial availability of bulk GaN substrates. Dislocations are formed to relieve the strain induced by lattice mismatch. While their presence can, therefore, not be avoided in typical GaN heteroepitaxy, growth conditions and substrate offcut could be used to affect the type of dislocation present in the epilayer. The potential improvement was studied by using molecular dynamics simulations to compare the impact of edge and screw dislocations on the thermal conductivity of GaN layers. The conductivity of defect free GaN was reduced by (61 ± 4)% by a screw dislocation density of 2.0 x 10^(13) cm^(-2) and by (49 ± 4)% by edge dislocations of similar density. This illustrates that the type of dislocation is important for thermal conductivity. These results help to advance previous theoretical work, where dislocations parallel to the crystal c-axis, which is the principal direction of heat flow, were assumed to make no contribution to phonon scattering. Such an assumption may be valid for low dislocation densities, such as those in bulk GaN, but can lead to considerable inaccuracies for the high densities typically found in epitaxial GaN, in particular close to the nucleation layer typically present between GaN and SiC.

GaN-based high electron mobility transistors (HEMTs) are promising for next generation radar applications due to their wide band gap, high electron velocity, and high breakdown field. However, due to the high power density in GaN HEMT devices, localized self-heating can be a critical issue. HEMT self-heating can degrade device performance and impair reliability and stability. Thus, in terms of thermal management, efficient heat removal from active semiconducting regions is a key task, which is often limited by the material quality of the GaN composites.
For the epitaxial growth of high-performance GaN/AlGaN HEMT structures, SiC is commonly used as a substrate material because SiC offers much higher thermal conductivity (~400 W/mK) than conventional Si (~142 W/mK) and sapphire (~35 W/mK). An AlN transition film is commonly used as an interlayer material in the heteroepitaxial growth of GaN on SiC substrates to minimize the lattice mismatch stress and enable the growth of a high-quality GaN buffer layer. But due to significant mechanical strain present in the AlN transition film, a high density of microstructural defects exist within the volume of the transition film and near its interface, which impedes heat transport into the substrate. Substrates containing CVD diamond can be a viable material solution due to their potentially high thermal conductivity (as much as 5 times higher than that of SiC). However, the current GaN on diamond technology often incorporates a low thermal conductivity transition layer at the interface of the GaN and the diamond, which can partly offset the benefit of using the high conductivity materials.
This presentation will describe our experimental and theoretical investigation of GaN composite substrates containing Si, SiC, and diamond. We measure the temperature-dependent thermal resistance of the transition layer between the GaN and the substrate, using picosecond time domain thermoreflectance (TDTR). We theoretically examine the relevant phonon scattering mechanisms responsible for the temperature trend of the resistance. The best available data in literature are also presented in comparison with our thermal modeling as well as our data.