Zachary M. Gibbs

Characterization of Lorenz number with Seebeck coefficient measurement

In analyzing zT improvements due to lattice thermal conductivity (κ_L ) reduction, electrical conductivity (σ) and total thermal conductivity (κ_(Total)) are often used to estimate the electronic component of the thermal conductivity (κ_E) and in turn κ_L from κ_L = ∼ κ_(Total) − LσT. The Wiedemann-Franz law, κ_E = LσT, where L is Lorenz number, is widely used to estimate κ_E from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10^(−8) WΩK^(−2) (degenerate limit). However, significant deviations from the degenerate limit (approximately 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10^(−8) WΩK^(−2) for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: L=1.5+exp[−_(|S|)_(116)] (where L is in 10^(−8) WΩK^(−2) and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si_(0.8) Ge _(0.2) where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity.

Thinking Like a Chemist: Intuition in Thermoelectric Materials

The coupled transport properties required to create an efficient thermoelectric material necessitates a thorough understanding of the relationship between the chemistry and physics in a solid. We approach thermoelectric material design using the chemical intuition provided by molecular orbital diagrams, tight binding theory, and a classic understanding of bond strength. Concepts such as electronegativity, band width, orbital overlap, bond energy, and bond length are used to explain trends in electronic properties such as the magnitude and temperature dependence of band gap, carrier effective mass, and band degeneracy and convergence. The lattice thermal conductivity is discussed in relation to the crystal structure and bond strength, with emphasis on the importance of bond length. We provide an overview of how symmetry and bonding strength affect electron and phonon transport in solids, and how altering these properties may be used in strategies to improve thermoelectric performance.

Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb3 skutterudites.

Filled skutterudites R(x)Co4Sb12 are excellent n-type thermoelectric materials owing to their high electronic mobility and high effective mass, combined with low thermal conductivity associated with the addition of filler atoms into the void site. The favourable electronic band structure in n-type CoSb3 is typically attributed to threefold degeneracy at the conduction band minimum accompanied by linear band behaviour at higher carrier concentrations, which is thought to be related to the increase in effective mass as the doping level increases. Using combined experimental and computational studies, we show instead that a secondary conduction band with 12 conducting carrier pockets (which converges with the primary band at high temperatures) is responsible for the extraordinary thermoelectric performance of n-type CoSb3 skutterudites. A theoretical explanation is also provided as to why the linear (or Kane-type) band feature is not beneficial for thermoelectrics.

Tuning bands of PbSe for better thermoelectric efficiency

Improving the thermoelectric performance of PbSe over its previously reported maximum zT can be achieved by engineering its electronic band structure. We demonstrate here, using optical absorption spectra, first principles calculations, and temperature dependent transport measurements, that alloying PbSe with SrSe leads to a dramatic change of the band structure that increases the thermoelectric figure of merit, zT. The temperature where the two valence bands converge decreases with Sr addition. The zT value, when the carrier density is optimized, increases with Sr addition in Pb1−xSrxSe and when x = 0.08 a maximum zT of 1.5 at 900 K is achieved. The net benefit in zT comes from the band structure tuning even though in other thermoelectric solid solutions it is the thermal conductivity reduction from disorder that leads to net zT improvement.

Influence of a Nano Phase Segregation on the ThermoelectricProperties of the p-Type Doped Stannite CompoundCu_(2+x)Zn_(1−x)GeSe_4

Engineering nanostructure in bulk thermoelectric materials has recently been established as an effective approach to scatter phonons, reducing the phonon mean free path, without simultaneously decreasing the electron mean free path for an improvement of the performance of thermoelectric materials. Herein the synthesis, phase stability, and thermoelectric properties of the solid solutions Cu(2+x)Zn(1-x)GeSe(4) (x = 0-0.1) are reported. The substitution of Zn(2+) with Cu(+) introduces holes as charge carriers in the system and results in an enhancement of the thermoelectric efficiency. Nano-sized impurities formed via phase segregation at higher dopant contents have been identified and are located at the grain boundaries of the material. The impurities lead to enhanced phonon scattering, a significant reduction in lattice thermal conductivity, and therefore an increase in the thermoelectric figure of merit in these materials. This study also reveals the existence of an insulator-to-metal transition at 450 K.

Optical band gap and the Burstein?Moss effect in iodine doped PbTe using diffuse reflectance infrared Fourier transform spectroscopy

Optical absorption edge measurements are performed on I doped PbTe using diffuse reflectance infrared Fourier transform spectroscopy. The Burstein-Moss shift, an increase in the absorption edge (optical band gap) with increasing doping level, is explored. The optical gap increases on the order of 0.1eV for doping levels ranging from 3◊10 18 to 2◊10 20 cm 3 , relevant doping levels for good thermoelectric materials. Chemical potential is estimated from transport measurements—specifically, Hall effect and Seebeck coefficient—using a single band Kane model. In heavily doped semiconductors, it is well-known that the band gap shrinks with increasing doping level. This effect, known as band gap renormalization, is fit here using an n 1/3 scaling law which reflects an electron-electron exchange interaction. The renormalization effect in these samples is shown to be more than 0.1eV, on the same order of magnitude as the band gap itself. Existing models do not explain such large relative changes in band gap and are not entirely self-consistent. An improved theory for the renormalization in narrow gap semiconductors is required.

Temperature dependent band gap in PbX (X=S, Se, Te)

PbTe is an important thermoelectric material for power generation applications due its high conversion efficiency and reliability. Its extraordinary thermoelectric performance is attributed to band convergence of the light L and heavy Σ bands. However, the temperature at which these bands converge is disputed. In this letter, we provide direct experimental evidence combined with ab initio calculations that confirm an increasing optical gap up to 673 K and predict a band convergence temperature of 700 K, much higher than previous measurements showing saturation and band convergence at 450 K.

Band gap estimation from temperature dependent Seebeck measurement—Deviations from the 2e|S|maxTmax relation

In characterizing thermoelectric materials, electrical and thermal transport measurements are often used to estimate electronic band structure properties such as the effective mass and band gap. The Goldsmid-Sharp band gap, Eg  = 2e|S|_(max)T_(max), is a tool widely employed to estimate the band gap from temperature dependent Seebeck coefficient measurements. However, significant deviations of more than a factor of two are now known to occur. We find that this is when either the majority-to-minority weighted mobility ratio (A) becomes very different from 1.0 or as the band gap (Eg) becomes significantly smaller than 10 kBT. For narrow gaps (Eg  ≲ 6 kBT), the Maxwell-Boltzmann statistics applied by Goldsmid-Sharp break down and Fermi-Dirac statistics are required. We generate a chart that can be used to quickly estimate the expected correction to the Goldsmid-Sharp band gap depending on A and S_(max); however, additional errors can occur for S < 150 μV/K due to degenerate behavior.

Thermoelectric properties of Sn-doped p-type Cu3SbSe4: a compound with large effective mass and small band gap

Cu_3SbSe_4-based compounds composed of earth-abundant elements have been found to exhibit good thermoelectric performance at medium temperatures. High zT values were achieved in previous studies, but further insight into the transport mechanism as well as some key material parameters is still needed. In this work, we studied the electrical and thermal transport properties of Sn-doped Cu_3SbSe_4 between 300 K and 673 K. It was found that the single parabolic band model explains the electrical transport very well. Experimentally, we determined the band gap to be around 0.29 eV. The density-of-state effective mass was found to be about 1.5 me for the doped samples. The transport properties suggested degeneracy splitting near the valence band maximum that was not captured by previous band structure calculations. The maximum zT ~0.70 was obtained at 673 K, and the optimized carrier density was ~1.8 × 10^20 cm^(−3), and the potential for further improvement of zT via material engineering is briefly discussed.

Computational and experimental investigation of TmAgTe2 and XYZ2 compounds, a new group of thermoelectric materials identified by first- principles high-throughput screening†

A new group of thermoelectric materials, trigonal and tetragonal XYZ2 (X, Y: rare earth or transition metals, Z: group VI elements), the prototype of which is TmAgTe2, is identified by means of high-throughput computational screening and experiment. Based on density functional theory calculations, this group of materials is predicted to attain high zT (i.e. B1.8 for p-type trigonal TmAgTe2 at 600 K). Among approximately 500 chemical variants of XYZ2 explored, many candidates with good stability and favorable electronic band structures (with high band degeneracy leading to high power factor) are presented. Trigonal TmAgTe2 has been synthesized and exhibits an extremely low measured thermal conductivity of 0.2–0.3 W m � 1 K � 1 for T 4 600 K. The zT value achieved thus far for p-type trigonal TmAgTe2 is approximately 0.35, and is limited by a low hole concentration (B10 17 cm � 3 at room temperature). Defect calculations indicate that TmAg antisite defects are very likely to form and act as hole killers. Further defect engineering to reduce such XY antisites is deemed important to optimize the zT value of the p-type TmAgTe2.