Browsing by Subject "Phonon transport"

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An efficient solution procedure for simulating phonon transport in multiscale multimaterial systems
(2013-05) Loy, James Madigan; Murthy, Jayathi
Over the last two decades, advanced fabrication techniques have enabled the fabrication of materials and devices at sub-micron length scales. For heat conduction, the conventional Fourier model for predicting energy transport has been shown to yield erroneous results on such length scales. In semiconductors and dielectrics, energy transport occurs through phonons, which are quanta of lattice vibrations. When phase coherence effects can be ignored, phonon transport may be modeled using the semi-classical phonon Boltzmann transport equation (BTE). The objective of this thesis is to develop an efficient computational method to solve the BTE, both for single-material and multi-material systems, where transport across heterogeneous interfaces is expected to play a critical role. The resulting solver will find application in the design of microelectronic circuits and thermoelectric devices. The primary source of computational difficulties in solving the phonon BTE lies in the scattering term, which redistributes phonon energies in wave-vector space. In its complete form, the scattering term is non-linear, and is non-zero only when energy and momentum conservation rules are satisfied. To reduce complexity, scattering interactions are often approximated by the single mode relaxation time (SMRT) approximation, which couples different phonon groups to each other through a thermal bath at the equilibrium temperature. The most common methods for solving the BTE in the SMRT approximation employ sequential solution techniques which solve for the spatial distribution of the phonon energy of each phonon group one after another. Coupling between phonons is treated explicitly and updated after all phonon groups have been solved individually. When the domain length is small compared to the phonon mean free path, corresponding to a high Knudsen number ([mathematical equation]), this sequential procedure works well. At low Knudsen number, however, this procedure suffers long convergence times because the coupling between phonon groups is very strong for an explicit treatment of coupling to suffice. In problems of practical interest, such as silicon-based microelectronics, for example, phonon groups have a very large spread in mean free paths, resulting in a combination of high and low Knudsen number; in these problems, it is virtually impossible to obtain solutions using sequential solution techniques. In this thesis, a new computational procedure for solving the non-gray phonon BTE under the SMRT approximation is developed. This procedure, called the coupled ordinates method (COMET), is shown to achieve significant solution acceleration over the sequential solution technique for a wide range of Knudsen numbers. Its success lies in treating phonon-phonon coupling implicitly through a direct solution of all equations in wave vector space at a particular spatial location. To increase coupling in the spatial domain, this procedure is embedded as a relaxation sweep in a geometric multigrid. Due to the heavy computational load at each spatial location, COMET exhibits excellent scaling on parallel platforms using domain decomposition. On serial platforms, COMET is shown to achieve accelerations of 60 times over the sequential procedure for Kn<1.0 for gray phonon transport problems, and accelerations of 233 times for non-gray problems. COMET is then extended to include phonon transport across heterogeneous material interfaces using the diffuse mismatch model (DMM). Here, coupling between phonon groups occurs because of reflection and transmission. Efficient algorithms, based on heuristics, are developed for interface agglomeration in creating coarse multigrid levels. COMET is tested for phonon transport problems with multiple interfaces and shown to outperform the sequential technique. Finally, the utility of COMET is demonstrated by simulating phonon transport in a nanoparticle composite of silicon and germanium. A realistic geometry constructed from x-ray CT scans is employed. This composite is typical of those which are used to reduce lattice thermal conductivity in thermoelectric materials. The effective thermal conductivity of the composite is computed for two different domain sizes over a range of temperatures. It is found that for low temperatures, the thermal conductivity increases with temperature because interface scattering dominates, and is insensitive to temperature; the increase of thermal conductivity is primarily a result of the increase in phonon population with temperature consistent with Bose-Einstein statistics. At higher temperatures, Umklapp scattering begins to take over, causing a peak in thermal conductivity and a subsequent decrease with temperature. However, unlike bulk materials, the peak is shallow, consistent with the strong role of interface scattering. The interaction of phonon mean free path with the particulate length scale is examined. The results also suggest that materials with very dissimilar cutoff frequencies would yield a thermal conductivity which is closest to the lowest possible value for the given geometry.
Experimental and theoretical investigations of thermal transport in graphene
(2015-08) Sadeghi, Mir Mohammad; Shi, Li, Ph. D.; Murthy, Jayathi; Howell, John; Wang, Yaguo; Akinwande, Deji; Yao, Zhen
Graphene has been actively investigated because its unique structural, electronic, and thermal properties are desirable for a number of technological applications ranging from electronic to energy devices. The thermal transport properties of graphene can influence the device performances. Because of the high surface to volume ratio and confinement of phonons and electrons, the thermal transport properties of graphene can differ considerably from those in graphite. Developing a better understanding of thermal transport in graphene is necessary for rational design of graphene-based functional devices and materials. It is known that the thermal conductivity of single-layer graphene is considerably suppressed when it is in contact with an amorphous material compared to when it is suspended. However, the effects of substrate interaction in phonon transport in both single and multi-layer graphene still remains elusive. This work presents sensitive in-plane thermal transport measurements of few-layer and multi-layer graphene samples on amorphous silicon dioxide with the use of suspended micro-thermometer devices. It is shown that full recovery to the thermal conductivity of graphite has yet to occur even after the thickness of the supported multi-layer graphene sample is increased to 34 layers, which is considerably thicker than previously thought. This surprising finding is explained by the long intrinsic scattering mean free paths of phonons in graphite along both the basal-plane and cross-plane directions, as well as partially diffuse scattering of phonons by the graphene-amorphous support interface, which is treated by an interface scattering model developed for highly anisotropic materials. In addition, an experimental method is introduced to investigate electronic thermal transport in graphene and other layered materials through the measurement of longitudinal and transverse thermal and electrical conductivities and Seebeck coefficient under applied electric and magnetic fields. Moreover, this work includes an investigation of quantitative scanning thermal microscopy measurements of electrically biased graphene supported on a flexible polyimide substrate. Based on a triple scan technique and another zero heat flux measurement method, the temperature rise in flexible devices is found to be higher by more than one order of magnitude, and shows much more significant lateral heat spreading than graphene devices fabricated on silicon.
Four-probe measurements of anisotropic in-plane thermal conductivities of thin black phosphorus
(2016-08) Smith, Brandon Paul; Shi, Li, Ph. D.; Akinwande, Deji
Phosphorene, a two-dimensional material exfoliated from black phosphorus (BP), is a promising p-type, high-mobility semiconductor. Phosphorene and BP display intrinsic in-plane anisotropic transport properties due to its puckered honeycomb lattice with distinct armchair and zigzag crystallographic orientations. The anisotropic thermal transport properties of BP and phosphorene influence the performance and reliability of functional devices made from these materials, and remain to be better understood. Here, we report the anisotropic in-plane thermal conductivities of suspended multi-layer BP samples, which are measured by a four-probe thermal transport measurement method. The measurement device consists of four microfabricated, suspended Pd/SiNx lines that act as resistive heaters and thermometers. The BP flake is suspended across the microstructure in contact with all four lines. This four-probe thermal transport measurement is equipped with the unique ability to isolate the intrinsic thermal resistance from the contact thermal resistance, which can be a major source of error in thermal conductivity measurements of nanostructures. Four BP samples were measured with thicknesses ranging from 39.2 nm to 274 nm and a peak thermal conductivity of 142 W m-1 K-1 at 80 K for a 55.6 nm thick zigzag oriented flake. The measurement results exhibit more pronounced temperature dependence with a higher peak thermal conductivity together with a weaker thickness dependence than prior reports. The results suggest the important role of defects in thermal transport in thin BP flakes, which can degrade upon exposure to air and water.
Synthesis and characterization of compound crystals with weak phonon couplings
(2022-09-22) Lee, Hwijong; Shi, Li, Ph. D.; Zhou, Jianshi; MacDonald, Allan H; Tutuc, Emanuel; Wang, Yaguo
Recent advances in experimental and computational techniques have advanced the understanding of phonon transport and phonon couplings to charge and spin degrees of freedom. As an illustrating example, the unusual phonon band features of Boron Arsenide (BAs) result in simultaneously high lattice thermal conductivity and high intrinsic carrier mobility, which make BAs an emerging III-V semiconductor for high-performance electronics devices. Meanwhile, magnon coupling with phonons allows for the thermal generation of spin waves, which can be converted into an electrical signal for readout or vice versa via the spin Hall effect in a normal metal in contact with the magnetic material. This work seeks to advance the understanding of the coupled transport phenomena in electronic and magnetic materials with unusual phonon-mediated behaviors and to address some of the fundamental questions on the interactions among energy, charge, and spin carriers in the semiconducting BAs, semimetal θ phase tantalum nitride (θ-TaN), and the magnetic insulator yttrium ion garnet (YIG). These questions are addressed through several experimental approaches based on surface electronic state measurements, steady-state bulk thermal and electrical properties measurements, frequency-dependent spin caloritronic measurements, and electron microscopy. Scanning tunneling spectroscopy measurements of cleaved BAs surfaces show a bulk bandgap of 2.1 eV as well as surface electronic states inside the bulk bandgap. These findings are relevant to the use of BAs as an active layer in future-generation electronic devices. With a similarly large phonon energy gap as semiconducting BAs, θ-TaN is grown via a high-pressure technique for transport measurements to investigate the theoretical prediction of a high thermal conductivity of this semimetal compound with a small electron density of states near the Fermi level. The results show both the effect of grain boundary scattering on suppressing the thermal conductivity and the potential of further increasing the thermal conductivity by increasing the grain size and reducing the defect concentrations. Besides these two investigations of electronic and phononic structures and transport, lock-in measurements are used to investigate the frequency dependence of the spin Seebeck effect (SSE) and detect a spin Peltier magnetoresistance (SPMR) at a heterostructure made of a platinum (Pt) thin film on YIG. The observed frequency dependence of the second harmonic SSE and first harmonic SPMR are analyzed with a model that accounts for both interface and bulk spin Seebeck effects to understand the elusive magnon transport properties.
The thermal effect of hexagonal boron nitride supports in graphene devices
(2018-12-07) Choi, David Seiji Kar Liang; Shi, Li, Ph. D.; Ho, Paul; Akinwande, Deji; Wang, Yaguo; Tutuc, Emanuel
fundamental understanding of thermal dissipation and energy transport is necessary for designing robust electronic systems and energy conversion devices. In many of these systems, minimizing the operating temperature of the working components is required for increasing the performance, lifetime, efficiency, and reliability of the device. For example, hot spots in transistors caused by the conversion of electronic energy to thermal energy has become a bottleneck in the continued scaling of microelectronics. As the demand for compact, highly conformable and mobile electronics continues to push the limit of miniaturization, these phenomena increasingly occur at the nanoscale. At these length scales, the governing physical principles differ from classical laws based on continuum mechanics and instead require a quantum mechanical treatment. The thermal transport properties of traditional three-dimensional (3D) heat conducting materials such as the metal interconnects in nanoelectronic devices tend to degrade as the critical dimension is reduced. In contrast, the thermal properties of a new class of van der Waals-based two-dimensional (2D) materials can show different size confinement effects that can potentially be utilized for thermal management. First realized by the isolation of graphene, these materials have become attractive candidates for future-generation electronic and thermal components. Due to their atomic thinness, the properties of 2-D materials are highly sensitive to their operating environment. The studies in this dissertation therefore aim to answer critical questions surrounding the practical applicability of graphene and its dielectric isomorph hexagonal boron nitride as thermal materials in real devices. Specifically, the fundamental heat dissipation pathways of joule-heated graphene channels are inspected within the framework of silicon-based electronics as well as next-generation flexible electronic architectures. The study reveals that lateral heat spreading is essential to mitigating hot-spot formation. As a result, the inclusion of h-BN as a thermal interface material between the active graphene layer and the underlying support facilitates significant reductions in device operating temperatures due to enhanced lateral heat spreading. More than a passive thermal layer, an h-BN support increases the intrinsic thermal conductivity of graphene relative to other support materials based on an additional study in this work. An analytical solution of the phonon Boltzmann transport equation is derived to explain the observed phenomenon.
Thermal transport in individual single-wall carbon nanotubes
(2007-05) Pettes, Michael Thompson, 1978-; Shi, Li, Ph. D.
This thesis presents an experimental study of phonon transport in individual suspended single-wall carbon nanotubes (SWCNTs). A microfabricated device consisting of two adjacent suspended membranes, each with a platinum resistance heater and thermometer, was used to directly measure the thermal conductance of three individual SWCNTs. These results show the effects of Umklapp phonon-phonon scattering remain weak and the thermal conductance remains roughly proportional to the ballistic conductance throughout the temperature range of 100 to 490 K. Additionally, through the use of transmission electron microscopy analysis we have for the first time directly obtained the diameter of a nanotube for which thermal measurements were obtained and determined the thermal conductivity of this SWCNT. The thermal conductivity of this 1.6 nm diameter, 4.72 μm long nanotube increases with temperature as ~T[superscript 1.5] throughout the temperature range indicating static scattering processes dominate transport in this regime. The measured thermal conductivity is greater than 1000 W/m·K above room temperature making it one of the best thermal conductors known.
Transport and coupling of phonons, electrons, and magnons in complex materials
(2016-05) Weathers, Annie C.; Shi, Li, Ph. D.; Goodenough, John B; Li, Xiaoqin E; Markert, John T; Orbach, Raymond Lee
In nanoscale systems, in which the relevant length scales can be comparable to the mean free paths and wavelengths of the energy, charge and spin carriers, it is necessary to examine the microscopic transport of heat, spin and charge at the atomic scale and the quantization of the associated quasiparticles. The intricacies of the transport dynamics can be even more complicated in materials with atomic scale complexities, such as incommensurate crystals, magnetic materials, and quasi-one-dimensional systems. Meanwhile, the transport properties and coupling between these quasiparticles is important in determining the strength of various thermoelectric and spincaloritronic phenomena, as well as the reliability of nanoscale electronics. This work seeks to further the understanding of the complicated transport dynamics in complex structured materials at nanometer and micrometer length scales, and to address some of the fundamental questions about the interactions between energy, charge and spin carriers in the conducting polymer poly(3,4- ethylenedioxythiophene) (PEDOT), the incommensurate higher manganese silicide (HMS) thermoelectric material, and the magnetic insulator yttrium iron garnet (YIG). These questions are addressed through a number of combined experimental approaches through the use of thermal conductance and thermoelectric property measurements of suspended nanostructures, inelastic neutron scattering, Brillouin light scattering, and electron microscopy. According to in-plane thermal and thermoelectric transport measurements of PEDOT thin films, the electronic thermal conductivity of this conducting polymer is found to be significant and exceeds that predicted by the Wiedemann-Franz law for metals. Furthermore, thermoelectric transport measurements of suspended HMS nanoribbons show a reduction in the lattice thermal conductivity by approximately a factor of two compared to bulk HMS, which is qualitatively consistent with that predicted from a diffuson model for thermal conductivity derived from the phonon dispersion of HMS. Lastly, pressure dependent Brillouin light scattering spectroscopy is used to determine the influence of hydrostatic stress on the dispersions of magnons and phonons in YIG, in order to determine the magnon and phonon peak frequency shift associated with localized laser heating induced strain.
Volume averaged phonon Boltzmann Transport Equation for simulation of heat transport in composites
(2016-12) Mishra, Columbia; Shi, Li, Ph. D.; Murthy, Jayathi; Ezekoye, Ofodike A.; Bonnecaze, Roger T.; Akinwande, Deji; Wang, Yaguo
Heat transfer in nano-composites is of great importance in a variety of applications, including in thermoelectric materials, thermal interface and thermal management materials, and in metamaterials for emerging microelectronics. In the past, two distinct approaches have been taken to predict the effective thermal conductivity of composites. The first of these is the class of effective medium theories, which employs Fourier conduction as the basis for thermal conductivity prediction. These correlate composite behavior directly to volume fraction, and do not account for inclusion structure, acoustic mismatch, and sub-continuum effects important in nanocomposites. More recently, direct numerical simulations of nanoscale phonon transport in composites have been developed. Here the geometry of the inclusion or the particulate phase is represented in an idealized way, and the phonon Boltzmann Transport Equation (BTE) solved directly on this idealized geometry. This is computationally intensive, particularly if realistic particle composites are to be simulated. Here, we develop, for the first time, a volume-averaged formulation for the phonon BTE for nanocomposites, accounting for the complex particle-matrix geometry. The formulation is developed for a nanoporous domain as a first step and then a nanocomposite domain is considered. The phonon BTE is written on a representative elemental volume (REV) and integrated formally over the REV using the laws of volume averaging. Extra integral terms resulting from the averaging procedure are approximated to yield extra scattering terms due to the presence of inclusions or holes in the REV. The result is a phonon BTE written in terms of the volume-averaged phonon energy density, and involving volumetric scattering terms resulting from both bulk scattering and scattering at the interfaces of the inclusions in the REV. These volumetric scattering terms involve two types of relaxation times: a volume-averaged bulk scattering relaxation time resulting from phonon scattering in the bulk matrix material, and an interface scattering relaxation time resulting from volume-averaging scattering due to interfaces within the REV. These relaxation times are determined by calibration to direct numerical simulations (DNS) of the particle or pore-resolved geometry using the phonon BTE. The additional terms resulting from the volume-averaging are modeled as in-scattering and out-scattering terms. The scattering terms are written as a function of a scattering phase function, and the interface scattering relaxation time. The scattering phase function represents the redistribution of phonon energy upon scattering at the interface. Both interface scattering relaxation time and scattering phase function matrix are functions of the interface geometry and the phonon wave vector space. The scattering phase function in the model is evaluated in the geometric optics limit using ray tracing techniques and validated against available analytical results for spherical inclusions. The volume-averaged bulk scattering relaxation time takes in to consideration the effects of the pores on the effective thermal conductivity of the composite. It is calibrated using a Fourier limit solution of the nanoporous domain. The resulting governing equations are then solved using a finite volume discretization and the coupled ordinates method (COMET). In the gray limit, the model is applied to nanporous geometries with either cylindrical or spherical pores. It is demonstrated to predict effective thermal conductivity across a range of Knudsen numbers. It is also demonstrated to be much less computationally intensive than the DNS. This model is extended to include non-gray effects through the consideration of both polarization and dispersion effects. For non-gray transport, the bulk and interface scattering relaxation times are now wave-vector dependent. Two different models are proposed for determining the interface scattering relaxation times, one assuming a constant value of interface scattering relaxation time, and another which accounts for variation with wave vector. As before both bulk and interface relaxation times are calibrated with the DNS solution in the Fourier and ballistic limits. The scattering phase function developed for gray transport in the geometric limit is expanded to consider the appropriate energy exchanges between different phonon modes assuming elastic scattering. The non-gray volume-averaged BTE is compared to the DNS for a range of porosities at the limits of bulk average Knudsen number and for intermediate average Knudsen numbers. The model with variable interface scattering relaxation times is found to better predict the variation of effective thermal conductivity with wave vector, though both models for interface scattering are less accurate than the gray model. Further, the volume-averaged BTE is extended for two material composites. We solve the volume-averaged BTE model for particle sizes comparable to the phonon wavelength in the composite matrix. We employ analytical scattering phase functions in the Mie scattering limit for particles to include wave effects. The calibration of model relaxation time parameters is conducted similar to that in the gray volume-averaged BTE model for nanoporous materials. The composite domain is solved in the Fourier limit to calibrate the volume-averaged bulk relaxation time. This relaxation time parameter considers the material properties of both the host material and particle. For small particle sizes, calibration in the ballistic limit is conducted using a nanoporous domain. This is possible as the interface scattering relaxation time is driven primarily by the travel time of the phonons between particles, and not by the residence time inside the particle. The scattering phase function is computed considering properties of both the host material and the particle scatterers. We solve the volume-averaged BTE for the two-material composite for a silicon host matrix with spherical germanium particles. We demonstrate the gray two-material composite domain for varying porosities over a range of Knudsen numbers. The present work creates a pathway to model thermal transport in nanocomposites using volume-averaging which can be used in arbitrary geometries, accounting for both bulk scattering and boundary scattering effects across a range of transport conditions. The model accounts not only for the volume fraction of particulates and inclusions, but also their specific shape and spacing. It also accounts for sub-continuum effects. Furthermore, the volume-averaging method also allows inclusion of wave effect through the scattering phase function so that particles on the order of the phonon wavelength or smaller can be considered. The formulation is also generalizable to the limit when the particles are large compared to the wavelength; in this limit, geometric optics may be employed to compute the scattering phase function. Overall, the volume averaging approach offers a computationally inexpensive pathway to including composite microstructure and subcontinuum effects in modeling nanoporous materials and composites.