Session C34: Thermal and Thermoelectric Transport - Theory and Modeling

Ultra-low thermal conductivity in silicon membranes by surface oxidation and alloying

A detailed understanding of the relation between microscopic structure and phonon propagation at the nanoscale is essential to design nanomaterials with desired phononic and thermal properties. Here we show that native oxide layers that spontaneously grow at the surfaces of ultra thin silicon membranes effectively hamper the mean free path long wavelength phonons through surface resonances that hybridize with propagating modes. This mechanism can be combined with mass scattering in SiGe alloyed membranes to hinder heat carriers over the whole spectrum of frequencies, thus resulting in extremely low thermal conductivity, up to 100 times lower than the bulk.   

Thermal Transport Properties of Transition Metal Dichalcogenide Monolayers

The characterization of thermal transport in low-dimensional transition metal dichalcogenides (TMDs) is required for their efficient implementation, either for general overheating issues or specific applications in thermoelectric devices. In this study, the lattice thermal conductivities of single-layer MoS$_{2}$, MoSe$_{2}$ WS$_{2}$, and WSe$_{2}$ are evaluated using classical molecular dynamics simulations. The interactions between atoms are defined by Stillinger-Weber type empirical potentials. In the parameterization of the potentials, a stochastic optimization algorithm, namely particle swarm optimization, is utilized. For the materials considered in this study, the final parameter sets produce quite consistent results with density functional theory in terms of lattice parameters, bond distances, elastic constants, and vibrational properties. The predicted thermal properties of all materials are in very good agreement with earlier first principles calculations.   

Phonon Optimized Potentials

Atomistic simulations can be used to predict thermal properties with atomic insight, mainly via molecular dynamics (MD) simulations where the atomic forces are calculated every time step to predict atomic motions. Accurate dynamics requires an accurate method of sampling the potential energy surface (PES). For practical atomistic studies of thermal properties across relevant length ( \textgreater 10$^{3}$ nanometers) and time scales ( \textgreater 10$^{2}$ nanoseconds), a model of the PES with the following Requirements is needed: (1) PES sampling must be fast ( \textless 0.01 second/atom). (2) PES sampling must be chemically accurate ( \textless 1 kcal/mol). (3) Requirement 2 must be transferrable to thermally relevant regions of the PES. Quantum mechanical (QM) methods such as density functional theory (DFT) satisfy Requirements 2 and 3, but fail Requirement 1. Many attempts to bypass the computational costs of QM include empirical interatomic potentials (EIPs). Many EIPs fail Requirement 2 and 3, however. We have therefore created a machine learning program that can parameterize any EIP to satisfy Requirements 2 and 3. These phonon optimized potentials reproduce phonon dispersion relations, and therefore thermal properties, quite well.   

Thermal transport of III-V semiconductor materials and superlattices based on molecular dynamics with optimized Tersoff potentials

III-V compound semiconductor materials are widely used in optoelectronics devices. III-V superlattices (SLs) make the active core of quantum cascade lasers (QCLs). Achieving room-temperature (RT), high-power, and continuous-wave (CW) operation in QCLs hinges on the understanding and engineering of thermal transport in the layers and across the interfaces. Cations in III-V ternary alloys differ a lot in mass and this effect on thermal transport is hard to capture using the scattering rates deduced from common perturbation theories. Molecular dynamics (MD) simulations can explicitly take the mass difference into consideration and are suitable for calculating the bulk thermal conductivity of III-V ternary alloys. Furthermore, the morphology and anharmonic interactions at an interface are naturally captured in MD, leading to an accurate description of interfacial transport. We adopt the Tersoff-type potentials for III-V binaries and optimize them according to acoustic phonon dispersions in order to capture thermal properties. The optimized potential is then used to directly compute the thermal boundary resistance at a heterojunction interface, as well as the thermal conductivity in the SL as a whole.   

Uncovering the Role of Surfaces in Cross-Plane Thermal Transport in Superlattices

Progress towards a deep fundamental understanding of nanoscale thermal transport shall remain elusive if the physical mechanisms behind phonon surface scattering are not completely uncovered. In semiconductor superlattices, the existence of multiple interfaces in the cross-plane direction makes the surface scattering phenomena a critical aspect of thermal transport. Heat conduction in superlattices is a vital transport phenomena which if controlled effectively can lead to significant improvements in existing technologies such as quantum cascade lasers, thermoelectrics, and electronics. In this talk, we will discuss the physical mechanisms that control the cross-plane thermal transport in Si/Ge and Si$_{\mathrm{1-x}}$Ge$_{\mathrm{x}}$/Si$_{\mathrm{1-y}}$Ge$_{\mathrm{y}}$ superlattices based on our recently developed rigorous quasi-classical treatment of phonon scattering mechanisms at rough interfaces [1,2]. The dependence of phonon surface scattering on incident phonon momentum, angle of incidence and surface properties including roughness and correlation length is established. This developed understanding will be used to fundamentally analyze the modifications in heat spectra in superlattices with the aim of moving towards a paradigm of rational design of thermal materials via the use of energy distributions among phonons with different frequencies and mean free paths. [1] Malhotra, A. and Maldovan, M. \textit{Sci Rep} \textbf{6}, 25818 (2016) [2] Malhotra, A. and Maldovan, M. \textit{J Appl Phys} \textbf{120} (2016)   

Cloaking of Thermoelectric Transport

Transformation optics techniques have proven to be a versatile approach to achieve unprecedented control of electromagnetic fields, heat currents, electric currents, and other physical phenomena. Most applications and designs thus far based on such techniques have targeted independent physical domains with specific functionalities. We present transformation optics applied to thermoelectricity by exploring the invariance of the governing and constitutive equations under coordinate transformations. We show that control of thermoelectrically coupled heat and electric currents is possible with highly anisotropic and inhomogeneous materials. Using layered structures, we design a thermoelectric cloak capable of hiding objects from thermoelectric flow. These proof of principle results constitute a significant step forward towards finding unexplored ways to control and manipulate coupled transport for thermoelectric applications.   

Phonon Scattering in Thermoelectrics: Thermal Transport, Strong Anharmonicity, and Emergent Quasiparticles

Modern neutron and x-ray spectrometers can map phonon dispersions and scattering rates throughout reciprocal space, providing unique insights into microscopic scattering mechanisms, including anharmonicity, electron-phonon coupling, or scattering by defects and nanostructures. In addition, first-principles simulations enable the rationalization of extensive experimental datasets. In particular, ab-initio molecular dynamics simulations can capture striking effects of anharmonicity near lattice instabilities. A number of high-performance thermoelectric materials are found in the vicinity of lattice instabilities, including Pb chalcogenides PbX, SnSe, Cu2Se, among others. The large phonon anharmonicity found in such compounds suppresses the lattice thermal conductivity, enhancing their thermoelectric efficiency. In this presentation, I will present results from our investigations of phonons in these materials [1-4] using neutron and x-ray scattering combined with first-principles simulations, focusing on anharmonic effects near lattice instabilities. I will show how strong anharmonicity can lead to emergent quasiparticles qualitatively different from harmonic phonons, which we probe in our measurements and simulations of the phonon self-energy. Commonalities between systems will be highlighted, including connections between strong anharmonicity and the electronic structure. [1] O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M.-H. Du, D. J. Singh, A. Podlesnyak, G. Ehlers, M. Lumsden, B. C. Sales, Nature Materials 10, 614 (2011). [2] J. Ma*, O. Delaire*, A. F. May, C. E. Carlton, M. A. McGuire, L. H. VanBebber, D. L. Abernathy, G. Ehlers, Tao Hong, A. Huq, Wei Tian, V. M. Keppens, Y. Shao-Horn, and B. C. Sales, Nature Nanotechnology 8, 445 (2013). [3] C.W. Li, O. Hellman, J. Ma, A.F. May, H.B. Cao, X. Chen, A.D. Christianson, G. Ehlers, D.J. Singh, B.C. Sales, and O. Delaire, Physical Review Letters (2014). [4] C.W. Li,* J. Hong,* A.F. May, D. Bansal, S. Chi, T. Hong, G. Ehlers and O. Delaire, Nature Physics 11, 1063 (2015). [5] D. Bansal, J. Hong, C.W. Li, A.F. May, W. Porter, M.Y. Hu, D.L. Abernathy, and O. Delaire, Phys. Rev. B 94, 054307 (2016)   

Understanding the Origins of Large Negative Thermal Expansion in Ferroelectric Perovskites from First Principles

Many of the functional properties of ABO$_{\mathrm{3}}$ perovskite oxides (for example, ferroelectricity) are strongly linked to particular phonon modes in the material. In addition, in many cases it is possible to formulate simple guidelines or `rules of thumb' that link crystal structure and chemistry to specific lattice dynamical characteristics. The thermal transport properties of perovskites are thus potentially highly tunable and dynamically controllable with external fields. We use first-principles density functional theory to reveal new details related to the origin of the large negative thermal expansion (NTE) observed for ferroelectric PbTiO$_{\mathrm{3}}$. Although the origin of NTE in this material is often ascribed to ferroelectricity (which arises from the freezing in of a soft, zone-center optical phonon), our results suggest that zone-boundary modes play a major role in driving NTE. In addition, hybridization between different electronic states has a significant effect on the lattice dynamics of PbTiO$_{\mathrm{3}}$ in general, and its NTE behavior in particular. Our work has implications for the understanding of, discovery and design of NTE in perovskites and other families of inorganic materials.   

A first-principles study of thickness dependent thermoelectric power in topological insulating thin-films: Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$, and Sb$_{2}$Te$_{3}$

Three-dimensional topological insulator Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$ and Sb$_{2}$Te$_{3}$ are good thermoelectric materials. We study the semi-classical thermoelectric properties of this topological insulating thin films with the 4-10 quintuple-layer thickness using first-principles calculations and the two-channel model combined with the Boltzmann transport equations. We observe the thickness and material dependent Seebeck coefficients of n- and p-type doped films which is associated the bulk and surface gap, surface to bulk ratio and relative position of surface states with respect to bulk states.   

First-Principles Computational Study of the Properties of the Clathrate Compounds A$_{\mathrm{8}}$Al$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$(A$=$Na,Rb,Cs)

Our recent study [1] of the properties of the Type-II binary clathrate compounds A$_{\mathrm{x}}$Si$_{\mathrm{136}}$, A$_{\mathrm{x}}$Ge$_{\mathrm{136}}$ and A$_{\mathrm{x}}$Sn$_{\mathrm{136}}$ (A$=$Na, K, Rb, Cs; 0$\le $x$\le $24) has increased the understanding of the role of the guest atoms and their composition x in determining the properties of these materials. For Na$_{\mathrm{x}}$Si$_{\mathrm{136}}$, our results have helped to explain the observed dependence of the lattice constant on x, which has a very unusual, distinct minimum at x $=$ 8. In this case, we have also found a ``Mexican-hat'' shaped effective potential curve for the Na atom motion in the large, (28-atom) Si cages. Motivated by these fascinating results for Na$_{\mathrm{x}}$Si$_{\mathrm{136}}$, we have extended our study of the effects of alkali guests on the properties of the Type-II clathrates to include their effects on the properties of the Type-II the ternary clathrate compounds A$_{\mathrm{8}}$Al$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$(A$=$Na,Rb,Cs). An earlier study of similar compounds, (Rb,Cs)$_{\mathrm{8}}$Ga$_{\mathrm{8}}$Si$_{\mathrm{128}}$, has found low frequency guest rattling modes (\textasciitilde 41-51 cm$^{\mathrm{-1}})$. Here, we report the results of a first-principles computational study of the electronic, structural and vibrational properties of the compounds A$_{\mathrm{8}}$Al$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$(A$=$Na,Rb,Cs). We contrast our results with those for (Rb,Cs)$_{\mathrm{8}}$Ga$_{\mathrm{8}}$Si$_{\mathrm{128\thinspace }}$, as well as with our recent results for the binary clathrates A$_{\mathrm{x}}$Si$_{\mathrm{136\thinspace }}$(A$=$Na,Rb,Cs). Our calculations are based on the Local Density Approximation to Density Functional Theory, as implemented by the VASP code. [1] D. Xue, C. Myles, C. Higgins; Materials 2016, \textbf{9}(8), 691.   

Electronic structure and band alignments of half-Heusler semiconductors

Half-Heuslers compounds with 18 valence electrons are promising materials for electronic and thermoelectric devices. However, data on basic parameters, such as their electronic structure, electron and hole effective masses, and the position of their valence and conduction bands with respect to those of other semiconductors are scarcely available. Here we explore a few members of this large family of compounds, TiCoSb and TiNiSn, which can be grown on conventional III-V semiconductors and could potentially be integrated in III-V-based devices. We present results of first-principles calculations of electronic structure and band alignments between these materials and with respect to conventional III-V semiconductors. Electronic structures are calculated using density functional theory within both the generalized gradient approximation and the screened hybrid functional HSE06. The results are discussed and compared to the available experimental data.   

Electronic Structures and Band Alignments of Mg$_{\mathrm{2}}$(Si,Ge,Sn) Thermoelectric Materials

Mg$_{\mathrm{2}}$Si, Mg$_{\mathrm{2}}$Ge, Mg$_{\mathrm{2}}$Sn, and their alloys are considered as eco-friendly and low cost thermoelectric materials. The low energy band structures are responsible for the electron-related thermoelectric transport, such as electrical conductivity, Seebeck coefficient, and electric part of thermal conductivity. Here, by using first principles density functional theory (DFT) calculations, we investigate the electronic structures and the band alignments of Mg$_{\mathrm{2}}$Si, Mg$_{\mathrm{2}}$Ge, Mg$_{\mathrm{2}}$Sn. In DFT, the band gaps are severely underestimated compared to the experimental results. By adopting beyond-DFT calculations such as hybrid-DFT and many-body GW calculations, we obtain the reliable band gaps. We also calculate the band alignments using various calculation schemes. Based on the calculation results, we discuss the thermoelectric properties of inhomogeneous Mg$_{\mathrm{2}}$(Si,Ge,Sn) materials.   

Electronic transport simulations in nano-crystalline materials for enhanced thermoelectric power factors

Nano-crystalline thermoelectric materials have shown the potential to provide much larger Seebeck coefficients compared to pristine materials. In this work we perform electronic transport simulations to study thermoelectric transport through 2D nano-crystalline channels. In these channels, the grain boundaries act as barriers for energy filtering, which provides large improvements to the Seebeck coefficient. On the other hand, the grain geometry, doping, and the underlying electrostatic potential can be engineered in such a way as to compensate for the reduction of the electrical conductivity that the barriers on the grain boundaries cause. Thus, optimal designs can be achieved, in which the power factor is improved compared to pristine materials. We discuss in addition the influence that the variation in the local thermal conductivity of the grains compared to that of the grain boundaries has on providing further improvements to the Seebeck coefficient, as well as the influence of parameter variations on degrading the power factor.