Session L17: Focus Session: Thermoelectrics - Electronic Structure and Transport

Potassium is a resonant level in Bi$_{1-x}$Sb$_{x}$ alloys

Bi$_{1-x}$Sb$_{x}$ alloys are the most promising thermoelectric materials for cryogenic Peltier cooling. Resonant impurity levels are known to increase the thermoelectric power and figure of merit of semiconductors and known examples are Tl:PbTe [1] and Sn:Bi$_{2}$Te$_{3}$ [2]. Here we add K:Bi$_{1-x}$Sb$_{x}$ to that list. Band structure calculations show that substitutional potassium in bismuth can form sharp density of states peaks, suggesting the presence of a resonant level. Single crystal samples were synthesized by a modified horizontal Bridgeman-Hor method. Cryogenic thermoelectric transport data will be presented as a function of K and Sb concentrations. At certain concentrations, the addition of potassium has a large effect on the thermopower, and increases the figure of merit to reach zT = 0.7 at 100K with zT $>$ 0.5 at all temperatures from 50K up to room temperature, numbers are valid along the trigonal axis of single crystals. [1] J. P. Heremans {\&} al. Energy Environ. Sci. DOI:10.1039/C1EE02612G; Science \textbf{321}, 554 (2008); [2] C.M. Jaworski {\&} al., Phys. Rev. B \textbf{80}, 233201, (2009)   

Fermi level pinning in Ti doped PbTe

The doping of PbTe attracts much interest due to the possible improvement of the thermoelectric properties by forming resonant levels. Here we report on doping of PbTe with Ti by molecular beam epitaxy, and back up the results with band structure calculations that show that Ti is a resonant level in the conduction band of PbTe. Ti is found to be a donor, leading to electron concentrations up to 1x10$^{19}$cm$^{-3}$, above which it pins the Fermi level at about 52 meV above the conduction band edge, and further increase of Ti shows no effect. At higher Ti contents the concentration of free electrons starts to rise again. However, Ti doping does not enhance the thermopower above that of similarly-doped PbTe, suggesting that the electrons on Ti are localized. We propose a model for Fermi level pinning due to different ionization states of the donor impurity which is similar to a chemical buffer. Further electronic structure calculations for Ti:PbTe confirm existence of the quasi-localized Ti states in the conduction band of PbTe and predict a local magnetic moment on Ti atom of 1.8 Bohr magnetons.   

Enhancement of Thermoelectric Figure-of-Merit by Resonant States of Aluminum Doping in Lead Selenide

By adding aluminium (Al) into lead selenide (PbSe), we successfully prepared n-type PbSe thermoelectric materials with a figure-of-merit (\textit{ZT}) of 1.3 at 850 K. Such high \textit{ZT} is achieved by a combination of high Seebeck coefficient caused by very possibly the resonant states in the conduction band created by Al dopant and low thermal conductivity from nanosized phonon scattering centers.   

Thermoelectric properties of indium-doped PbSe

P-type [1,2] and n-type [3] PbSe have recently exhibited good thermoelectric properties without using the relatively uncommon element Tellurium. Here we report thermal conductivity, galvanomagnetic and thermomagnetic properties of bulk samples of n-type PbSe doped with indium at varying concentrations within the solid solution solubility range. A figure of merit zT value well in excess of 1 has been achieved. Resonant level effect and changes in the dimensionless figure of merit will be discussed although data indicate that the thermoelectric properties do not lie above the Pisarenko relation. \\[4pt] [1] D.J. Parker et al, Phys. Rev. B 82, 035204 (2010) \\[0pt] [2] H. Wang et al, Adv. Mater. 23 1366-1370 (2011) \\[0pt] [3] J. Androulakis et al, Phys. Rev. B 83, 195209 (2011)   

Study on thermoelectric properties of n-type PbSe doped with B, Ga, and In

We report here systematic study of the thermoelectric properties of n-type PbSe with B, Ga, and In doping. The comparison of the electrical resistivity, Seebeck coefficient, and thermal conductivity is conducted. Room temperature Hall measurements show the effective increase of carrier concentration by both Ga and In doping to $\sim $10$^{20}$ cm$^{-3}$. The high power factor $\sim $ 2.4$\times $10$^{-3}$Wm$^{-1}$K$^{-2}$ is obtained when B is doped, however, it is decreased with increasing temperature, which is inversed with the other dopants. No resonant state is found in all these three materials. A figure of merit, ZT $>$1.2 at 873 K is achieved in 0.5{\%} In doped PbSe.   

Electronic structure of ferroelectrically distorted PbTe

PbTe is one of the most promising thermoelectric materials. The electronic transport properties of the p-doped system are generally explained based on the nearly degenerate pockets near $L$ and along $\Sigma$ at high temperatures, where the energy at the $L$ point decreases with increasing temperature and approaches the $\Sigma$ point maxima. Recently, Bozin et al. showed that structure of PbTe is ferroelectrically distorted at high temperatures.\footnote{E. S. Bozin, C. D. Malliakas, P. Souvatzis, T. Proffen, N. A. Spaldin, M. G. Kanatzidis, and S. J. L. Billinge, Science 330, 1660 (2011).} Following this experiment, a lattice dynamics study using first-principle molecular dynamics simulations have shown an increase of the band gap with increased temperature as seen experimentally.\footnote{Y. Zhang, X. Ke, P. R. C. Kent, J. Yang, and C. Chen, Prys. Rev. Lett. 107, 175503 (2011).} Motivated from these studies, we have performed electronic structure calculations to investigate the effect of structural distortion and expansion on the band structure. We observe that the ordering of energy levels changes dramatically with distortion. In addition to these results we will also discuss how this can affect the electronic transport properties at high temperatures.   

Potential thermoelectric performance from optimization of hole-doped Bi$_{2}$Se$_{3}$

We present an analysis of the potential thermoelectric performance of hole-doped Bi$_2$Se$_3$, which is commonly considered to show inferior room temperature performance when compared to Bi$_2$Te$_3$. We find that if the lattice thermal conductivity can be reduced by nanostructuring techniques (as have been applied to Bi$_2$Te$_3$) the material may show optimized {\it ZT} values of unity or more in the 300 - 500 K temperature range and thus be suitable for cooling and moderate temperature waste heat recovery and thermoelectric solar cell applications. Central to this conclusion are the larger band gap and the relatively heavier valence bands of Bi$_2$Se$_3$.   

Electronic and Thermoelectric properties of RuIn$_{3-x}A_{x}$ ($A$=Sn, Zn) from first principles

Recently, substitution derivatives of the intermetallic compound RuIn$_{3-x}A_{x}$ ($A$ = Sn, Zn) have been shown to exhibit relatively high Seebeck coefficients. Substitution by Sn results in n-type behavior while p-type is the norm for substitution of In by Zn. We discuss in detail the electronic structure of the parent compound and the substitution derivatives obtained from density functional theory (DFT) based calculations using the Full Potential Local Orbital (FPLO) code. The substitution effects have been studied using three different approximations: the simple virtual crystal approximation (VCA), the ordered supercell approach and the disordered coherent potential approximation (CPA). Both Sn and Zn prefer different site symmetry positions in the unit cell. While the parent compound RuIn$_{3}$ is a semiconductor, the substitution derivatives are not. For small doping concentrations, we observe a rather rigid-band-like behavior due to the parabolic nature of the bands forming the valence band maximum and the conduction band minimum. Transport properties calculated using the semi-classical Boltzmann transport equations (BoltzTraP) based on the constant scattering approximation are consistent with the experiments.   

Electronic structure and thermopower of Cu$_3$SbSe$_4$

Cu$_3$SbSe$_4$ (Se4), a ternary derivative of the II-VI zincblende semiconductors, is a narrow band gap semiconductor (band gap $\sim$0.1 -- 0.4 eV) and a promising thermoelectric. Recently, Skoug et al. [1] have measured transport properties of pure and doped Se4 (Ge and Sn substituting for Sb). They find that p-doping by 2\% Sn results in optimized value of ZT=0.72 at 630 K. To understand the electronic structure and transport properties of Se4 we have carried out ab initio density functional electronic structure calculations. LDA/GGA/GGA+U approximations do not show that Se4 is a standard semiconductor. They give a resonance-like peak near the top of the valence band of width $\sim$0.5 eV. The Fermi energy for the undoped system lies below the peak, making it a pseudo-gap system, in disagreement with experiment. Non-local exchange with relaxation of Sb-Se bonds lead to the opening of a gap (0.26 eV), its origin being intimately related to the valency of Sb. Transport calculations show that Se4 is an excellent p-type thermoelectric, in agreement with experiment. \\[4pt] [1] Skoug et al., Sci. Adv. Mater., 3, 602 (2011).   

Thermoelectric Properties of CoSb3-xSnx

We substitute Sn for Sb in CoSb3. Band structure calculations predict that Sn should be a resonant level with and energy near the top of the heavy (Co-3d) valence band. This is confirmed experimentally. Indeed, heavily Sn-doped samples show a low-temperature anomaly in their thermopower consistent with this prediction. The hole concentration, however, is too high for this materials to have a high thermopower and figure of merit.   

Is the high frequency thermopower useful for predicting properties of strongly correlated materials?

Shastry has proposed that the high-frequency thermopower can be used for meaningful predictions of the dc thermopower in many strongly correlated materials. If true, this will make it much easier to screen strongly correlated materials for useful thermoelectric properties because it is much easier to calculate the high-frequency limit. By solving this problem exactly for the Falicov-Kimball model using dynamical mean-field theory, we find that this approach often does not work. We also compare with usual approximations for the thermopower, we find that the Heikes formula gives a good description of the high frequency thermopower while the Kelvin formula is equivalent at high temperature. Unfortunately, the only accurate way to find the dc thermopower is with the conventional Kubo formula.   

Electrical and thermal transport properties of the substituted defect manganese silicides Mn$_{1-x-y}$Cr$_{x}$Ru$_{y}$Si$_{\delta \sim 1.74}$

Crystallizing in the TiSi$_{2}$ structure with considerable amount of random vacancies at the Si site, defect manganese silicides MnSi$_{\delta }(\delta \quad \sim $ 1.72-1.74) are unusual in many respects. One of them is their structural stability which is determined by the electron concentration. In addition, MnSi$_{\delta }$ is known for unusually low thermal conductivity $\sim $ 3 - 3.5 W/m K at 300 K. We have substituted MnSi$_{\delta }$ with Cr and Ru simultaneously and studied the electrical and thermal transport properties of the resulting alloys. Both resistivity and Seebeck coefficient are less sensitive to substitutions and maintain robust values as high as that of MnSi$\sim _{1.74}$. Hall measurements indicate that the carrier concentration remains high around 10$^{21}$/cm$^{3}$ and more or less same for all compositions. Thermal conductivity is decreased further and interestingly increases with T reaching values $\sim $ 2.5 W/m K at 300 K. These results will be presented and discussed.   

Transport in Old and New Thermoelectric Materials

There is increasing interest in thermoelectric materials motivated in part by recent progress and in part by the potential of these materials in various energy technologies. Thermoelectric performance is a multiply contra-indicated property of matter. For example, it requires (1) high thermopower and high electrical conductivity, (2) high electrical conductivity and low thermal conductivity and (3) low thermal conductivity and high melting point. The key is finding an optimal balance. In this talk, I discuss some of the issues involved in the context of recent results. These include the surprising doping dependence of the thermopower in PbTe and PbSe, and the interplay between acoustic and optical phonons in PbTe. The potential of some new materials is discussed. This work was done in collaboration with David Parker, Olivier Delaire and Mao-Hua Du.