Thermodynamic Characteristics of 1D Structures

Physical Review B, 2006

To elucidate the three-way relationship among a crystal's structure, its phonon dispersion characteristics, and its thermal conductivity, an analysis is conducted on layered diatomic Lennard-Jones crystals with various mass ratios. Lattice dynamics theory and molecular dynamics simulations are used to predict the phonon dispersion curves and the thermal conductivity. The layered structure generates directionally dependent thermal conductivities lower than those predicted by density trends alone. The dispersion characteristics are quantified using a set of band diagram metrics, which are used to assess the contributions of acoustic phonons and optical phonons to the thermal conductivity. The thermal conductivity increases as the extent of the acoustic modes increases, and it decreases as the extent of the stop bands increases. The sensitivity of the thermal conductivity to the band diagram metrics is highest at low temperatures, where there is less anharmonic scattering, indicating that dispersion plays a more prominent role in thermal transport in that regime. We propose that the dispersion metrics ͑i͒ provide an indirect measure of the relative contributions of dispersion and anharmonic scattering to the thermal transport, and ͑ii͒ uncouple the standard thermal conductivity structure-property relation to that of structure-dispersion and dispersion-property relations, providing opportunities for better understanding of the underlying physical mechanisms and a potential tool for material design.

ABSTRACT

Physical Review Letters, 2000

We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1d nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of this model. PACS numbers:

2003

Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to simple mathematical models consisting of coupled oscillators on a lattice. The role of lattice dimensionality on the breakdown of the Fourier's law is discussed and some universal quantitative aspects are emphasized: the divergence of the finite-size thermal conductivity is characterized by universal laws in one and two dimensions. Equilibrium and non-equilibrium molecular dynamics methods are presented along with a critical survey of previous numerical results. Analytical results for the non-equilibrium dynamics can be obtained in the harmonic chain where the role of disorder and localization can be also understood. The traditional kinetic approach, based on the Boltzmann-Peierls equation is also briefly sketched with reference to one-dimensional chains. Simple toy models can be defined in which the conductivity is finite. Anomalous transport in integrable nonlinear systems is briefly discussed. Finally, possible future research themes are outlined.

Superlattices with thermal-insulating behaviors have been studied to design thermoelectric materials but affect heat transfer in only one main direction and often show many cracks and dislocations near their layer interfaces. Quantum-dot (QD) self-assembly is an emerging epitaxial technology to design ultradense arrays of germanium QDs in silicon for many promising electronic and photonic applications such as quantum computing, where accurate QD positioning is required. We theoretically demonstrate that high-density three-dimensional (3D) arrays of molecular-size self-assembled Ge QDs in Si can also show very low thermal conductivity in the three spatial directions. This physical property can be considered in designing new silicon-based crystalline thermoelectric devices, which are compatible with the complementary metal-oxidesemiconductor (CMOS) technologies. To obtain a computationally manageable model of these nanomaterials, we investigate their thermal-insulating behavior with atomic-scale 3D phononic crystals: A phononic-crystal period or supercell consists of diamond-cubic (DC) Si cells. At each supercell center, we substitute Si atoms by Ge atoms in a given number of DC unit cells to form a boxlike nanoparticle (i.e., QD). The nanomaterial thermal conductivity can be reduced by several orders of magnitude compared with bulk Si. A part of this reduction is due to the significant decrease in the phonon group velocities derived from the flat dispersion curves, which are computed with classical lattice dynamics. Moreover, according to the wave-particle duality at small scales, another reduction is obtained from multiple scattering of the particlelike phonons in nanoparticle clusters, which breaks their mean free paths (MFPs) in the 3D nanoparticle array. However, we use an incoherent analytical model of this particlelike scattering. This model leads to overestimations of the MFPs and thermal conductivity, which is nevertheless lower than the minimal Einstein limit of bulk Si and is reduced by a factor of at least 165 compared with bulk Si in an example nanomaterial. We expect an even larger decrease in the thermal conductivity than that predicted in this paper owing to multiple scattering, which can lead to a ZT much larger than unity. Downloaded From: http://heattransfer.asmedigitalcollection.asme.org/ on 09/16/2014 Terms of Use: http://asme.org/terms 043206-10 / Vol. 131, APRIL 2009 Transactions of the ASME Downloaded From: http://heattransfer.asmedigitalcollection.asme.org/ on 09/16/2014 Terms of Use: http://asme.org/terms

Physical review, 2020

We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find nontrivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a 'heavy-tailed' probability distribution, and with large impedance mismatch between the bath and the system satisfies Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.

Superlattices with thermal-insulating behaviors have been studied to design thermoelectric materials but affect heat transfer in only one main direction and often show many cracks and dislocations near their layer interfaces. Quantum-dot (QD) self-assembly is an emerging epitaxial technology to design ultradense arrays of germanium QDs in silicon for many promising electronic and photonic applications such as quantum computing, where accurate QD positioning is required. We theoretically demonstrate that high-density three-dimensional (3D) arrays of molecular-size self-assembled Ge QDs in Si can also show very low thermal conductivity in the three spatial directions. This physical property can be considered in designing new silicon-based crystalline thermoelectric devices, which are compatible with the complementary metal-oxidesemiconductor (CMOS) technologies. To obtain a computationally manageable model of these nanomaterials, we investigate their thermal-insulating behavior with atomic-scale 3D phononic crystals: A phononic-crystal period or supercell consists of diamond-cubic (DC) Si cells. At each supercell center, we substitute Si atoms by Ge atoms in a given number of DC unit cells to form a boxlike nanoparticle (i.e., QD). The nanomaterial thermal conductivity can be reduced by several orders of magnitude compared with bulk Si. A part of this reduction is due to the significant decrease in the phonon group velocities derived from the flat dispersion curves, which are computed with classical lattice dynamics. Moreover, according to the wave-particle duality at small scales, another reduction is obtained from multiple scattering of the particlelike phonons in nanoparticle clusters, which breaks their mean free paths (MFPs) in the 3D nanoparticle array. However, we use an incoherent analytical model of this particlelike scattering. This model leads to overestimations of the MFPs and thermal conductivity, which is nevertheless lower than the minimal Einstein limit of bulk Si and is reduced by a factor of at least 165 compared with bulk Si in an example nanomaterial. We expect an even larger decrease in the thermal conductivity than that predicted in this paper owing to multiple scattering, which can lead to a ZT much larger than unity. Downloaded From: http://heattransfer.asmedigitalcollection.asme.org/ on 09/16/2014 Terms of Use: http://asme.org/terms 043206-10 / Vol. 131, APRIL 2009 Transactions of the ASME Downloaded From: http://heattransfer.asmedigitalcollection.asme.org/ on 09/16/2014 Terms of Use: http://asme.org/terms

The various inadequacies of Callaway's phenomenological model of lattice thermal conductivity has been critically analyzed and the model is repaired in a modified form in which the systematic replacement of life time by line widths amicably resolves the various issues. The involvement of various scattering events in the heat transport, e.g., boundary scattering, impurity scattering, anharmonic phonon scattering, resonance scattering and interference scattering has been addressed in the new framework with the help of quantum dynamical many body theory. The technological importance of Ge is well known and hence it becomes significantto investigate the thermal behavior of it in details as its electrical properties are temperature dependent. Further, the CdTe also shows its vital importance in the fabrication of infrared optical windows and photo voltaic solar cells. The phonon heat conductivity of Ge and CdTe in the temperature range 3.3-298 K and 1.780-239.260 K based on the modified Callaway model have been analyzed and excellent agreements between theory and experiments are reported. The present formulation is found to be well justified and can be successfully applied for the calculations of thermal conductivity of several other crystalline solids.

Annual Review of Heat Transfer, 2016

Two-dimensional materials, such as graphene, boron nitride and transition metal dichalcogenides, have attracted increased interest due to their potential applications in electronics and optoelectronics. Thermal transport in two-dimensional materials could be quite different from three-dimensional bulk materials. This article reviews the progress on experimental measurements and theoretical modeling of phonon transport and thermal conductivity in two-dimensional materials. We focus our review on a few typical two-dimensional materials, including graphene, boron nitride, silicene, transition metal dichalcogenides, and black phosphorus. The effects of different physical factors, such as sample size, strain and defects, on thermal transport in Twodimensional materials are summarized. We also discuss the environmental effect on the thermal transport of two-dimensional materials, such as substrate and when two-dimensional materials are presented in heterostructures and intercalated with inorganic components or organic molecules.

2011

An enhanced adiabatic bond charge model has been employed to study the lattice dynamics of phononic metamaterials based on group-IV and group-III-V semiconductors. Using the full phonon spectrum and a realistic Brillouin zone summation method, we have developed theories of phonon scattering rates from interface formation and anharmonicity. Numerical results for specific-heat capacity and phonon conductivity of thin Si/Ge and GaAs/AlAs superlattices are then presented and compared with available experimental measurements. The roles of various phonon scattering mechanisms in controlling the thermal conductivity in different temperature ranges have been quantified.