## First-Principles Studies of Phonons and Electrons in Bulk Thermoelectrics

- Author(s): Xia, Yi
- Advisor(s): Ozolins, Vidvuds
- et al.

## Abstract

Thermoelectric materials, which enable direct conversion between thermal and electrical energy, provide an alternative for power generation and refrigeration. The key parameter that defines the efficiency of thermoelectric materials is the ‘dimensionless figure of merit’ ZT, which is composed of the Seebeck coefficient, electrical conductivity and total thermal conductivity respectively. Ideally, to achieve high ZT both the Seebeck coefficient and electrical conductivity should be large, while total thermal conductivity must be minimized. In this thesis, first-principles calculations of the Seebeck coefficient, lattice thermal conductivity and electrical conductivity are performed to study mechanisms and factors that gives rise to high ZT.

One effective way to enhance ZT is through direct reduction of lattice thermal conductivity. We perform calculation and analysis of lattice thermal conductivity for thermoelectric materials by solving the Boltzmann transport equation iteratively in the framework of perturbation theory. The second- and third-order interatomic force constants are extracted using the recently developed CSLD (compressive sensing lattice dynamics) method. Afterwards, we evaluate opportunities to achieve further reduction of lattice thermal conductivity. Our first study of ternary zinc-blende-based mineral compounds famatinite (Cu3SbS4) and permingeatite (Cu3SbSe4) shows that optical modes in these two compounds contribute a sizable portion of the total lattice thermal conductivity and thus cannot be neglected. Due to the fact that phonon modes with mean free paths larger than 10 nm carry about 80% of the heat, nanostructuring, which reduces the mean free path, is a promising way to reduce the lattice thermal conductivity by reducing the characteristic length. In addition, our simple alloying model including mass disorder reproduces experimental findings that forming solid solutions rapidly decreases the lattice thermal conductivity. An alternative way to reduce lattice thermal conductivity is to introduce guest atoms in host cage structures. Our study of type-I Si clathrates containing guest atoms Na and Ba shows that Na tends to form incoherent localized phonon mode while Ba coherently couples with the host cages. The low lattice thermal conductivities of Na- and Ba-filled Si clathrates should be attributed to the dramatic reductions in both phonon lifetime and group velocity. Analysis of phonon scattering process reveals that localized modes can be effectively emitted and absorbed, thus dramatically enhancing overall scattering rates.

Another widely adopted approach to achieve high ZT is through maintaining a high power factor. To accurately determine the Seebeck coefficient and electrical conductivity, we estimate carrier lifetime due to electron-phonon interaction under relaxation time approximation using the electron-phonon Wannier interpolation technique. Our study of noble metals Cu and Ag shows that their positive Seebeck coefficients can be mostly attributed to the negative energy dependence of carrier lifetime. In contrast to the previous study of positive Seebeck in Li, which is due to the deviation of electronic behavior from that in free electron model, it is the nontrivial energy dependence of electron-phonon interaction vertex that leads to the positive Seebeck coefficient. Intermetallic compound B20-type CoSi has drawn considerable attention due to its exceptionally high power factor and large Seebeck coefficient. Our study shows that the large negative Seebeck coefficient of the pristine CoSi is mostly due to the strong energy dependence of carrier lifetime, which together with the high electrical conductivity leads to the high power factor. For heat transport, both electron-phonon and phonon-phonon interactions contribute significantly to phonon scattering at temperatures lower than 200 K. While at temperatures higher than 300 K, phonon-phonon interaction dominates over electron-phonon interaction. Based on the optimized power factor with properly adjusted carrier concentration, we predict that the maximum ZTs at 300 and 600 K are about 0.11 and 0.25 respectively without further reducing the total thermal conductivity.

Known good thermoelectric materials often are comprised of elements that are in low abundance, toxic and require careful doping and complex synthesis procedures. High performance thermoelectricity has been reported in earth-abundant compounds based on natural mineral tetrahedrite (Cu12Sb4S13). Our first-principles electronic structure calculations of Cu12Sb4S13 show that Cu atoms are all in the monovalent state, creating two free hole states per formula unit of the pristine compound. Optimal thermoelectric performance can be achieved via electron doping. Substituting transition metals on Cu 12d sites does the job. Detailed analysis shows that Zn and Fe substitutions tend to fill the empty hole states, while Ni substitution introduces an additional hole to the valence band by forming ferromagnetic configuration. Experimentally observed extremely low lattice thermal conductivity can be attributed to the out-of-plane vibrations of the three-fold Cu ions. This is further verified by the large Gruneisen parameter calculated.