Session B34: Thermoelectrics - Sn-Se and Modeling

Structure and Properties of Sn$_{\mathrm{2}}$Se$_{\mathrm{3}}$, a mixed valent tin selenium compound.

Sn$_{\mathrm{2}}$Se$_{\mathrm{3}}$ is a possibly expected phase based on analogy with Sn$_{\mathrm{2}}$S$_{\mathrm{3}}$ but it has never been reported. It is of interest due to reported phase change memories using this composition using transitions between an amorphous phase and an unknown crystalline phase. We identify the crystal structure Sn$_{\mathrm{2}}$Se$_{\mathrm{3}}$ and report its properties at ambient pressure based on the ab initio evolutionary methodology for crystal structure prediction implemented in the Calypso code. We find a structure based on Sn-Se ribbons with clear Sn(II)and Sn(IV)sites similar to the structure of Sn$_{\mathrm{2}}$S$_{\mathrm{3}}$. Compared with the known phase SnSe (\textit{Pnma}) $+$SnSe$_{\mathrm{2}}$ (\textit{P-3m1}), the energy is only 2.3meV/atom higher. The electronic structure of this phase shows mixed valent tins Sn$^{\mathrm{2+}}$ and Sn$^{\mathrm{4+}}$ in this compound. A small band gap of 0.023 eV is obtained from the band structure consistent with the small resistance reported by Kyung-Min Chung \textit{et al}.   

The electrical and thermoelectric properties of isoelectronic doping in SnSe : a first principles study*

SnSe has been well-known as an excellent thermoelectric material with the highest ZT up to 2.6 at high temperature . Recently, there has been much attention on the thermoelectric properties of SnSe-based materials. In this work, we present a first-principles study on the electrical and thermoelectric properties of SnSe by isoelectronic doping; substitutions of C, Si, and Ge for the Sn site and S and Te for the Se site, with 3.125 and 6.250{\%} concentration. Among those dopants, C gives a big modification of band structure with the band gap reduced by the defect levels in the band gap, whereas changes in band structure by other dopants are negligible. It is suggested that the C doped SnSe can improve the Seebeck coefficient near room temperature and enhance the power factor at high temperature, because of the electrical conductivity enhanced by the localized defect state of the C doped SnSe. * This work is supported by grants from the Priority Research Centers Program (Grant No. NRF-2009-0093818) and the Basic Science Research Program (Grant No. NRF-2015R1A2A2A01003621) through NRF funded by the MOE and MSIP of Korea.   

First-principles study on the high thermoelectric efficiency originating from ``pudding-mold'' bands in n- and p-type SnSe

The performance of thermoelectric conversion is evaluated by the dimensionless figure of merit \textit{ZT}$=(\sigma S^{2}/\kappa )T,$ where $\sigma $, $S$, $\kappa $, and $T$ are the electrical conductivity, thermopower, thermal conductivity, and temperature, respectively. Recently, it has been experimentally found that SnSe exhibits a high \textit{ZT}$=$2.6 at 923 K [1]. Its high \textit{ZT} is mainly due to the ultralow thermal conductivity. Some theoretical studies have shown that the ultralow thermal conductivity originates from strong anharmonicity of the phonons, and suggested that \textit{ZT} could be further increased by doping electrons or holes[2,3]. In the present study, we analyze the thermoelectric properties of the carrier-doped SnSe to reveal the origin of its even higher performance. Using the first-principles calculation and adopting the Boltzmann equation, we obtain the electrical conductivity and the thermopower. We find that the pudding-mold-shaped band structure [4] enhances its thermoelectric performance not only in the hole-doped [2] but also in the electron-doped regime, where the Bloch states at the Fermi level originate from Se $p_{x}$ in the former, and Sn $p_{y}$ in the latter. [1] L.-D. Zhao \textit{et al}., Nature \textbf{508}, 373 (2014). [2] K. Kutorasinski \textit{et al}., Phys. Rev. B \textbf{91}, 205201 (2015). [3] R. Guo \textit{et al}., Phys. Rev. B \textbf{92}, 115202 (2015). [4] K. Kuroki and R. Arita, J. Phys. Soc. Jpn. \textbf{76}, 083707 (2007).   

Electron and Phonon Transport in SnSe 2D Nanoplatelets

Bulk single crystalline SnSe is a new promising thermoelectric material with a remarkably low thermal conductivity($\kappa )$ at above phase transition temperature (973K). Although the origin of the intrinsically low $\kappa $ of SnSe was previously attributed to strong anharmonicity in the chemical bonds, our recent work revealed that low density is another cause of the low $\kappa $ of the reported SnSe single crystals (Nature 539 (7627), E1-E2). Two-dimensional (2D) SnSe single crystalline nanoplatelets (NPs) provide an excellent platform to probe the true anharmonic effects in SnSe, which still remain elusive. A comprehensive array of tools such as EDX, EBSD and micro-Raman spectroscopy were used for characterizing 2D SnSe NPs grown using chemical vapor deposition. SnSe NPs with A1g, B3g, A2g and A3g vibrational modes identified by Raman spectroscopy grow along [100] direction. High-temperature thermopower and electrical conductivity will be presented.   

The achievement of high ZT in n-type SnSe single crystal

SnSe is a two dimensional (2D) layered semiconductor with strong Sn-Se bonding along $b-c$ plane and weaker bonding along $a$ axis direction, resulting in a strong anisotropic transport properties. Recently, Zhao \textit{et al}. reported that high thermoelectric power factor and low thermal conductivity at high temperature make SnSe as a very good p-type thermoelectric material; ZT values along $b$ and $c $axes are up to 2.6 and 2.3 at 923 K, respectively. They attributed the remarkably high ZT value along the $b$ axis to the intrinsically low lattice thermal conductivity in SnSe. More recently, two first-principles calculations predicted good thermoelectric performances in both n- and p-type SnSe's and better n-type thermoelectric properties than p-type SnSe and J. Yang \textit{et al.} predicted ZT\textasciitilde 3.1 in n- type SnSe. Here, we report that n-type SnSe single crystals were successfully synthesized by substituting Bi at Sn sites. In addition, it was found that the carrier concentration increases with Bi content, which has a great influence on the thermoelectric properties of n-type SnSe single crystals. Indeed, we achieved the maximum \textit{ZT} value of 2.2 along b axis at 733 K in the most highly doped n-type SnSe with a carrier density of -2.1$\times$ 10$^{19}$ cm$^{-3\, }$at 773 K.   

Optimization of p-type SnSe thermoelectric performance by controlling vacancies.

SnSe is a p-type layered semiconductor with orthorhombic structure, whose ZT of 2.6. So far, several doping studies have been done for this material to optimize carrier concentrations 10$^{\mathrm{19}}$-10$^{\mathrm{20}}$ cm$^{\mathrm{-3}}$ where the maximum ZT usually occurs. Recently, we have investigated intrinsic defects in SnSe using STM, resulting in that the Sn vacancy moves the Fermi energy inside dispersive valence band and produces extra holes, leading to the p-type characteristics of SnSe. Here we report that Sn vacancies of SnSe have been successfully controlled by changing cooling rate during the growth. The hole concentration is found to linearly increase with cooling rate, confirmed by Hall measurement and STM images. Room temperature hole concentrations were 0.53, 0.94, 2.00, 2.70, and 6.40$\times$ 10$^{\mathrm{17}}$ for samples with the cooling rate of 0.5, 1.0, 2.0, 3.0, and 5.0 $^{\mathrm{o}}$C/h, respectively. The electrical conductivity decreased while Seebeck coefficient increased with cooling rate. The optimal cooling rate to achieve the highest ZT as well as the thermoelectric properties will be discussed.   

How hybrid exchange affects thermoelectric transport properties of Cu2Se, III-V semiconductors, and half Heuslers: Accurate grid sampling enabled with a corrected k.p scheme.

Accurate first-principle predictions of electronic transport (i.e. conductivity, Seebeck, etc.) is challenging to obtain. It demands both a good account of scattering and band structure. For Boltzmann transport calculations, the Brillouin zone needs to be sampled very densely, limiting the applicability of brute-force calculations with sophisticated methods such GW and hybrid functional calculations in density functional theory (DFT). Here we study the importance of the band structure by comparing results of hybrid and standard functionals. To make this comparison possible, we make use of a recently developed corrected k.p-based interpolation scheme that enables rapid convergence of the grid sampling [arxiv.org/abs/1607.01429]. The method is also applicable to properties such as density of states and dielectric functions. Beyond improving the band-gap issue, we show how using a hybrid functional based band structure can significantly impact the thermoelectric properties of direct band gap materials and materials with conduction and valence states with strong d-electron character. Further demonstrating the utility of the method, we present results a computational screening of the thermoelectric properties of a range of half Heusler compounds.   

Harnessing Intervalley Scattering for High zT Thermoelectrics

Convergence of multiple valleys in the band edges improves the charge transport properties necessary for enhancing thermoelectric performance. Typically, these valleys are considered equivalent and intervalley scattering is neglected. Using the Boltzmann approach, we calculate the transport coefficients within the transport distribution function (TDF) formalism\footnote{G.D. Mahan and J.O. Sofo, PNAS 93, 7436 (1996)} for a multivalley band structure. We consider scattering between two valleys with very different effective masses that are offset in the reciprocal space. The resultant TDF is highly assymmetric about the Fermi level, which enhances thermoelectric performance. Guided by this model, we have performed a high-throughput computational search to identify band structures of known materials (calculated with density functional theory) that show similar characteristics - sharp increase in the density of states within a few $k_BT$ of the band edge. More detailed and higher accuracy calculations have been performed on the identified candidates. We therefore demonstrate that intervalley scattering, which is usually ignored in thermoelectrics, can be harnessed as an energy-filtering method to enhance thermoelectric performance.   

Thermoelectric Materials and Novel Thermoelectric Phenomena

Striking the balance between thermal and charge transport is a main goal when searching for optimized thermoelectric materials. This difficult task can be achieved by controlling detailed features in the band structure as well as increase the phonon scattering mechanisms. We will discuss methodologies developed in the AFLOW consortium (www.aflow.org) to improve the quality and the speed of the theoretical predictions through a set of examples. Specifically novel rattling mechanism in oxy-chalcogenides, electronic bands convergence due to Ca- and Ga-doping in SnTe, and novel thermoelectric minerals.   

Electron and Phonon Properties of Type II Sn Clathrates via First Principles Methods.

Clathrates are cage-like materials where high carrier mobility can coexist with low thermal conductivity. Much of the work to date has focused on the role of the guest atoms inside type I clathrate framework. The rattling of the guest atoms inside the clathrate voids is an effective way to reduce the lattice thermal conductivity leading to enhancing the figure of merit of a thermoelectric material. The focus of our investigation are type II Sn clathrates, which have been explored to a lesser extent as compared to Si or Ge materials. We present results from density functional theory simulations for calculated lattice structure, electronic structure and phonon dynamics properties. Our comprehensive investigation shows that the type of guest atoms and cage substitution via Ga atoms strongly affect the energy band structure coupled with anharmonicity effects originating from the guest atoms. Unusual effects arising from weak van der Waals interactions and important signatures in the Gruneisen parameters have also been identified. Our study expands upon the fundamental understanding of clathrate materials as new pathways for property modifications are presented.   

First-principles Study of Electronic and Thermal Transport Properties of Pb$_{1-x}$M$_x$Te (M=Mg, Ca, Sr, Ba)

PbTe is an excellent thermoelectric material because of high power factor and low lattice thermal conductivity. Recent studies by Kanatzidis et al. showed significant enhancement in the ZT of PbTe doped with Na, Mg and Sr. However, fundamental understanding of the contribution of various mechanisms to the enhancement of ZT is far from satisfactory. In this talk, we will discuss first principles density functional theory (DFT) investigations of the electronic and lattice aspects of thermal transport in doped PbTe. Electronically, we studied the effects of alloying elements (Mg, Ca, Sr and Ba) on electronic band structures and transport coefficients of PbTe. We investigated the difference between direct and Wannier interpolations, and effects of exchange-correlation functional and spin orbit coupling, in terms of band velocities and electrical conductivity. Carrier lifetimes of pristine PbTe due to electron-phonon interaction will also be reported. We also calculated lattice thermal conductivity (KL) of pristine MTe. Comparison between single mode relaxation time approximation and iterative solution of Boltzmann transport equation is made. Extracted 2nd- and 3rd-order force constants were further utilized to illustrate the mechanism of phonon softening in KL reduction.   

Ab-initio study of electron transport in lead telluride

Nanostructuring has recently witnessed great success in improving material's thermoelectric efficiency. One key aspect of this method lies in the fact that mean free paths of phonons are typically larger than those of electrons, and therefore nanostructures with certain grain sizes can reduce the thermal conductivity while preserving the good electrical property. Despite recent computational and experimental progress on identifying the phonon mean free path spectrum, the quantitative electron mean free path spectrum has been mostly unknown, especially considering practical thermoelectric materials having complex structures. In this work, we perform a fully first-principles method to study the electron transport in a prototypical thermoelectric material - PbTe, which has shown to exhibit good thermoelectric performance and strong spin-orbital coupling. Such first-principles method enables us to study the electron transport mode by mode, providing detailed scattering mechanisms and mean free path spectrum. Specifically, we find that despite of the large dielectric constant of PbTe, the polar scattering is comparable with acoustic deformation potential scattering, with the electrical transport properties agreeing well with experiments. This work is supported by DOE EFRC (Grant No. DE-SC0001299).