Session A43: Focus Session: Physics of Thermoelectric Materials and Phenomena I

Searching for new Thermoelectric Materials from Theory

Thermoelectric (TE) materials is a type of energy materials that can be applied to directly convert waste heat into electricity. Research on advanced TE materials has been a world-wide focus in recent years. By employing density functional \textit{ab initio} methods, we are trying to find new compounds with promising TE performance. In this talk, the following topics will be mainly covered. 1) General discussion on the directions of searching for new TE compounds with good performance; 2) Filling fraction limits (FFLs) for filler impurities in CoSb$_{3}$. By combining \textit{ab initio} calculations and thermodynamic consideration, we explained the FFLs, revealed the underlined physical mechanism behind FFLs, and found a simple rule for selecting new filler atoms. A few new filled skutterudites with ultra high filling fractions of impurities were predicted theoretically and synthesized experimentally, and they do show promising thermoelectric performance. 3) Rare-earth-related Half-Heusler compounds are used as model systems to discuss the effect of localized electronic states on thermoelectric performance. By that, we will partially discuss the possibility of going beyond narrow-gap materials for thermoelectrics.   

Atomic Ordering and Gap Formation in Ag-Sb Based Ternary Chalcogenides

Ag-Sb based ternary chalcogenides are important in optical phase change and thermoelectric applications. Although discovered almost 50 years ago and thought to be semiconductors, a fundamental understanding of their electronic structures had been lacking. We report \textit{ab initio} electronic structure studies using density functional theory (DFT) to explain their observed atomic structures, the physics of gap formation and their low-energy properties. Total energy calculations yield theoretical atomic structures which are consistent with experiment. Ag/Sb ordering is found to have a huge impact on the electronic structure near the Fermi energy. It gives pseudogap structure in some ordered structures, and either a pseudogap or a gap in others. For the lowest energy structures, as one goes from Te to Se to S, the (indirect) band gap goes from being negative to positive. Transport properties of AgSbTe$_{2}$ can be understood in terms of a small intrinsic band gap and extremely shallow impurity states. The calculated negative band gap in this compound can be ascribed to the defficiency of DFT.   

First-principles Studies of ErAs and ErAs/GaAs Heterostructures

We present a computational investigation of the materials properties of rare-earth pnictides. ErAs, a semimetal with rock-salt structure, has been demonstrated to grow epitaxially on GaAs substrates with a continuous As sublattice and low strain. Such structures have the potential to provide high-quality thermoelectric materials. Using plane-wave based density-functional methods we have performed a detailed investigation of the effects of $f$ electrons on the electronic and atomic structure, using both norm- conserving pseudopotentials and the projector-augmented-wave method. Our preliminary results indicate that it is possible to obtain an adequate description of the band structure without having to include the $f$ electrons as valence electrons. The resulting reduction in computational complexity allows us to perform explicit simulations of heterostructures. We have also calculated deformation potential constants, to be used in detailed comparisons with experiments where strain affects the band structure.   

Electronic and vibrational properties of the Na$_{16}$Rb$_{8}$Si$_{136}$ and K$_{16}$Rb$_{8}$Si$_{136}$ clathrates

We have studied the electronic and vibrational properties of the Na$_{16}$Rb$_{8}$Si$_{136}$ and K$_{16}$Rb$_{8}$Si$_{136}$ clathrates, using the local density approximation. In qualitative agreement with the rigid-band model, the electronic band structures display no major modifications due to inclusion of the alkali metal guests. However, the electronic densities of states show two sharply peaked structures and a dip near the Fermi level. This feature may help to qualitatively explain the temperature dependent Knight shift observed for the NMR active nuclei in Na$_{16}$Rb$_{8}$Si$_{136}$. Phonon dispersion curves show low frequency, localized ``grattler'' h modes for both clathrates. These modes may efficiently scatter the heat carrying host acoustic phonons, potentially suppressing the lattice thermal conductivity. Based on the harmonic oscillator model and on our calculated rattler frequencies, we predict the isotropic mean square displacement amplitude (U$_{iso})$ of the various guests in these clathrates. Our predicted values of U$_{iso}$ for Na and Rb in Na$_{16}$Rb$_{8}$Si$_{136}$ are found to be in good agreement with experiment.   

Theoretical study of lattice thermal conductivity in Si clathrate materials

Recent experiments have shown that Si and Ge clathrate crystals are promising candidates as high ZT thermoelectric materials because of their glass-like low thermal conductivity. Based on a detailed \textit{ab initio} calculation of equilibrium statistical properties, we conclude that the distinct structural differences in the diamond-structured Si (d-Si) and the type-II Si clathrate (Si$_{136})$ only lead to some minor differences in the equilibrium thermal properties in the two tetrahedrally bonded Si phases. In this talk, we will present our recent calculations of non-equilibrium thermal transport properties of d-Si and Si$_{136}$ crystals, based on the statistical linear response theory. The key step of our calculation of lattice thermal conductivity ($\kappa )$ is to evaluate the fluctuation-correlation relation of bulk heat currents at equilibrium conditions. In the current study, we have adopted the molecular dynamics (MD) simulation techniques, using large atomic supercell models and the Tersoff potential. Our results suggest that the cage-like open framework of clathrate crystals will lead to a factor of 5-8 reduction in thermal conductivity. The MD simulation results are also discussed in the context of the simple kinetic transport model. The ``anomalous'' oscillation feature in the correlation functions of clathrate materials is explained.   

Lattice Thermal Conductivity of Superlattices from an Adiabatic Bond Charge Model

The adiabatic bond charge model (ABCM) has successfully rendered phonon dispersions of a host of bulk semiconductors [1,2] and has also been used to calculate the phonon dispersions in quantum well superlattices [3]. We have developed an ABCM for superlattices and combined it with a symmetry-based representation of the anharmonic interatomic forces to calculate the lattice thermal conductivity of short-period superlattices, using an iterative solution to the Boltzmann-Peierls equation [4]. We compare our ABCM results with those obtained from some commonly used models for the interatomic forces in semiconductors to assess the importance of accurate descriptions of the phonon dispersions in thermal conductivity calculations. [1] W. Weber, Physical Review B 15, 4789 (1977). [2] K. C. Rustagi and W. Weber, Solid State Communications 18, 673 (1976). [3] S. K. Yip and Y. C. Chang, Physical Review B 30 7037 (1984). [4] D. A. Broido, A. Ward, and N. Mingo, Physical Review B 72, 014308 (2005).   

First principles Theory of the Lattice Thermal Conductivity of Si and Ge

The room temperature lattice thermal conductivity of high quality crystalline semiconductors is limited by the scattering between phonons arising from the anharmonicity of the interatomic potential. We have calculated the lattice thermal conductivity of isotopically enriched silicon and germanium, combining a first principles approach to extract the harmonic and anharmonic interatomic force constants [1] with an iterative solution of the full Boltzmann-Peierls equation for phonon transport [2]. Our calculated lattice thermal conductivities for Si and Ge, obtained with no adjustable parameters, show very good agreement with measured values [3,4] and are a marked improvement to results obtained previously using empirical interatomic potentials [2]. [1] G. Deinzer, G. Birner, and D. Strauch, Physical Review B 67, 144304 (2003). [2] D. A. Broido, A. Ward, and N. Mingo, Physical Review B 72, 014308 (2005). [3] M. Asen-Palmer, et al, Physical Review B 56, 9431-9447 (1997). [4] T. Ruf, et al, Solid State Communications 115, 243-247 (2000).   

Three-Phonon Phase Space as an Indicator of the Lattice Thermal Conductivity in Semiconductors

The room temperature lattice thermal conductivity of many semiconductors is limited primarily by three-phonon scattering processes arising from the anharmonicity of the interatomic potential. We employ an adiabatic bond charge model [1,2] for the phonon dispersions to calculate the phase space for three-phonon scattering events of several group IV and III-V semiconductors. We find that the amount of phase space available for this scattering in materials varies inversely with their measured thermal conductivities. Anomalous behavior occurs in III-V materials having large mass differences between cation and anion, which we explain in terms of the severely restricted three-phonon phase space arising from the large gap between acoustic and optic phonon branches. \newline \newline [1] W. Weber, Physical Review B 15, 4789 (1977). \newline [2] K. C. Rustagi and W. Weber, Solid State Communications 18, 673 (1976).   

Monte Carlo Simulation of Thermal Conductivity in Randomly Distributed Nanowire Composites

In this paper, we investigated the thermal conductivity of composites made of two types of randomly stacked nanowires with high contrast ratio of bulk thermal conductivity. Thermal conductivity predictions based on solving the phonon Boltzmann transport equation by using the Monte Carlo method are presented for different contrast ratios of thermal conductivity, sizes of nanowires and the volumetric fractions in the composites. For composites made of nanowires with high contrast ratio thermal conductivity, the thermal conductivity of the nanocomposites increase dramatically when the volumetric fraction of high thermal conductivity nanowire is higher than the geometry percolation threshold, although existing correlations in percolation theory do not fit the results due to the phonon interface scattering. On the other hand, when the the size of nanowires is small and the volumetric fraction of high thermal conductivity nanowire is less than percolation threshold, the thermal conductivity of the nanocomposites decreases with increasing the volumetric fraction of the high thermal conductivity nanowires. The results of this study may help the development of nanoscale thermoelectric materials in which the figure of merit is optimized by choosing appropriate nanowire size, property contrast and composition. RY acknowledges the funding support for this work by DoD/AFOSR MURI grant FA9550-06-1-0326. The simulation was conducted on a 24-node cluster supported by Intel Corporation and managed by Prof. Gang Chen and Mr. Lu Hu at MIT.   

Optimized thermal conductivities of Silicon Germanium nanowires

The measure of the thermoelectric efficiency of a material is given by its ``Figure of merit'' (Z), which is inversely proportional to its thermal conductivity, and directly proportional to its electrical conductivity. Alloys of Si and Ge are promising thermoelectric materials, since they can be engineered so as to have a low thermal conductivity relative to their electrical conductivity. We present molecular dynamics simulations of the thermal conductivities of Si$_{x}$Ge$_{1-x}$ nanowires, and an optimization strategy to obtain maximal values of ZT for these systems. We found that Si-Ge alloy nanowires have a significantly lower thermal conductivity than pure Si or Ge nanowires of the same diameter. Furthermore the alloy ordering is found to significantly effect thermal conductivities, and hence is a key parameter to control and vary in order to optimize thermal conductivities and eventually Z values. Towards this end optimal orderings of Si and Ge for low thermal conductivities have been predicted. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.   

First Principles Studies of Thermoelectric Figure of Merit of Si and SiGe Nanowires

We present predictions of the thermoelectric figure of merit (ZT) of Si$_{x}$Ge$_{1-x}$ nanowires based on Density Functional Theory calculations and cluster expansion optimizations. The electrical conductivity, $\sigma $, and Seebeck coefficient, S, were obtained using the Boltzmann transport equation in the relaxation time approximation, and first principles, electronic structure calculations. The thermal conductivity was computed using classical molecular dynamics runs. A range of SiGe nanowires with different Ge concentrations and Ge distributions were investigated. We found that the transport coefficients $\sigma $, S, and thus ZT strongly depend on the wire growth direction, surface structure, and Ge concentration, and Ge distribution. These parameters were varied to obtain a nanostructure with an optimal, high figure of merit above 2 or 3, depending on the electronic doping.   

Calculation of figure of merit for Bi$_2$Te$_3$ nanostructures

Bi$_2$Te$_3$-based materials comprise one class of promising candidates for novel thermoelectric devices, for which low/high thermal/electrical conductivity are desired. We shall present calculations highlighting the effects of reduced dimensionality on the thermoelectric figure of merit ZT for such materials, with particular emphasis on Bi$_2$Te$_3$ / Sb$_2$Te$_3$ superlattices. The calculation consists of two components, a tight-binding electronic calculation for the electrical conductivity and electronic contribution to the thermal conductivity and a Green-Kubo molecular dynamics approach for the lattice contribution to the thermal conductivity.   

Non-equilibrium thermoelectric transport in thin film heterostructures

The Monte Carlo technique is used to calculate thermoelectric transport properties across thin-film heterostructures. We study the size and position dependence of the Seebeck coefficient across a thin film InGaAsP barrier layer sandwiched between two InGaAs contact layers. With decreasing size, the effective Seebeck coefficient is increased. The transition between pure ballistic thermionic transport and fully diffusive thermoelectric transport is described. We characterized the non-equilibrium length of the device and deduce the power dissipated to the lattice.