Single Parabolic Band Model Research Articles

Thermoelectric properties of GeSe

The recently reported superior thermoelectric performance of SnSe, motivates the current work on the thermoelectric properties of polycrystalline GeSe, an analog compound with the same crystal structure. Due to the extremely low carrier concentration in intrinsic GeSe, various dopants are utilized to substitute either Ge or Se for increasing the carrier concentration and therefore for optimizing the thermoelectric power factor. It is shown that Ag-substitution on Ge site is the most effective, which enables a hole concentration up to ∼1018 cm−3. A further isovalent substitution by Pb and Sn leads to an effective reduction in the lattice thermal conductivity. A peak figure of merit, zT of ∼0.2 at 700 K can be achieved in Ag0.01Ge0.79Sn0.2Se, a composition with the highest carrier concentration. The transport properties can be well described by a single parabolic band model with a dominant carrier scattering by acoustic phonons at high temperatures (>500 K). This further enables a prediction on the maximal zT of ∼0.6 at 700 K and the corresponding carrier concentration of ∼5 × 1019 cm−3.

Thermoelectric performance of Li doped, p-type Mg2(Ge,Sn) and comparison with Mg2(Si,Sn)

Solid solutions with chemical formula Mg2(Si,Ge,Sn) are promising thermoelectric materials with very good properties for the n-type material but significantly worse for the p-type. For power generation applications good n- and p-type materials are required and it has been shown recently that Li doping can enhance the carrier concentration and improve the thermoelectric properties for p-type Mg2Si1-xSnx. We have investigated the potential of p-type Mg2(Ge,Sn) by optimizing Mg2Ge0.4Sn0.6 using Li as dopant. We were able to achieve high carrier concentrations (1.4 × 1020 cm−3) and relatively high hole mobilities resulting in high power factors of 1.7 × 10−3 W m−1 K−2 at 700 K, the highest value reported so far for this class of material. Exchanging Ge by Si allows for a systematic comparison of Mg2(Ge,Sn) with Mg2(Si,Sn) and shows that Si containing samples exhibit a lower power factor but also a lower thermal conductivity resulting in comparable thermoelectric figure-of-merit. The data is furthermore analyzed in the framework of a single parabolic band model to gain insight on the effect of composition on band structure.

Distinct Impact of Alkali-Ion Doping on Electrical Transport Properties of Thermoelectric p-Type Polycrystalline SnSe.

Recent findings about ultrahigh thermoelectric performance in SnSe single crystals have stimulated related research on this simple binary compound, which is focused mostly on its polycrystalline counterparts, and particularly on electrical property enhancement by effective doping. This work systematically investigated the thermoelectric properties of polycrystalline SnSe doped with three alkali metals (Li, Na, and K). It is found that Na has the best doping efficiency, leading to an increase in hole concentration from 3.2 × 10(17) to 4.4 × 10(19) cm(-3) at room temperature, accompanied by a drop in Seebeck coefficient from 480 to 142 μV/K. An equivalent single parabolic band model was found adequate to capture the variation tendency of Seebeck coefficient with doping levels within a wide range. A mixed scattering of carriers by acoustic phonons and grain boundaries is suitable for numerically understanding the temperature-dependence of carrier mobility. A maximum ZT of ∼0.8 was achieved in 1% Na- or K-doped SnSe at 800 K. Possible strategies to improve the mobility and ZT of polycrystals were also proposed.

Thermoelectric properties and extremely low lattice thermal conductivity in p-type Bismuth Tellurides by Pb-doping and PbTe precipitation

We investigated the thermoelectric properties of Pb-doped compounds (Bi0.2 Sb0.8−x Pbx)2 Te3 and pseudo-binary PbTe composites of [(Bi0.2 Sb0.8)2 Te3]1−2x(PbTe)2x (x = 0.0, 0.01, 0.02, 0.05, and 0.10). The Pb-doping and PbTe-precipitation enhanced their metallic properties, as confirmed by the increase in electrical conductivity and carrier density, and the decrease in Seebeck coefficient and Hall mobility. We obtained the exceptionally low lattice thermal conductivity of 0.2 W m−1 K−1 from the single parabolic band model, which can be justified by the good fitting with the Pisarenko plot. Because of the high electrical conductivity at room temperature and high Seebeck coefficient at high temperature, with the decrease in thermal conductivity with increasing temperature, the thermoelectric figure-of-merits ZT were enhanced in the mild temperature range, which can be advantageous in energy harvesting technologies.

Increasing Seebeck Coefficients and Thermoelectric Performance of Sn/Sb/Te and Ge/Sb/Te Materials by Cd Doping

Ge and Sn in (GeTe)nSb2Te3 (GST) and (SnTe)nSb2Te3 compounds, respectively, are partially substituted by Cd. These layered compounds (n = 1) consist of NaCl‐type slabs that are separated by van der Waals gaps. Resonant X‐ray diffraction yields different Cd‐atom distributions in Cd0.2Ge0.8Sb2Te4 and Cd0.2Sn0.8Sb2Te4, which indicate how van der Waals gaps in metastable cubic GeTe‐rich or SnTe‐rich compounds (n ≥ 7) are surrounded. The latter exhibit promising thermoelectric properties with figures of merit ZT ≈ 0.8 at 450 °C. Alloying with Sb2Te3 increases the ZT value of SnTe by a factor of up to two because of an increased Seebeck coefficient and a reduced thermal conductivity; the hole concentration is significantly reduced. A further improvement in ZT by ≈20% is possible by Cd‐doping, most likely due to a more covalent bonding character, yielding a ZT of ≈1.1 at 450 °C for Cd1.2Sn10.8Sb2Te15. In order to understand the electronic transport properties of these p‐type semiconductors, the single parabolic band model is applied. By contrast, Cd doping in GST materials reduces the Hall mobility and therefore decreases the power factor compared to undoped GST materials.

Tuning Electrical Properties through Control of TiSe2 Thickness in (BiSe)1+δ(TiSe2)n Compounds

A series of (BiSe)1+δ(TiSe2)n compounds where n was varied from two to four were synthesized and electrically characterized to explore the extent of charge transfer from the BiSe layer to the TiSe2 layers. These kinetically stable heterostructures were prepared using the modulated elemental reactants (MER) method, in which thin amorphous elemental layers are deposited in an order that mimics the nanostructure of the desired product. X-ray diffraction (XRD), X-ray area diffraction, and scanning transmission electron microscopy (STEM) data show that the precursors formed the desired products. Specular diffraction scans contain only 00l reflections, indicating that the compounds are crystallographically aligned with the c-axis perpendicular to the substrate. The c-axis lattice parameter increases by 0.604(3) nm with each additional TiSe2 layer. In-plane diffraction scans contain reflections that can be indexed as the (hk0) of the BiSe and TiSe2 constituents. Area diffraction scans are also consistent with the samples containing only BiSe and TiSe2 constituents. Rietveld refinement of the 00l XRD data was used to determine the positions of atomic planes along the c-axis. STEM data supports the structures suggested by the diffraction data and associated refinements but also shows that antiphase boundaries occur approximately 1/3 of the time in the BiSe layers. All samples showed metallic behavior for the temperature-dependent electrical resistivity between 20 K and room temperature. Electrical measurements indicated that charge is transferred from the BiSe layer to the TiSe2 layer. The measured Hall coefficients were all negative indicating that electrons are the majority carrier and are systematically decreased as n was increased. Assuming a single parabolic band model, carrier concentration decreased when the number of TiSe2 layers is increased, suggesting that the amount of charge donated by the BiSe layer to the TiSe2 layers is constant. Seebeck coefficients were negative for all of the (BiSe)1+δ(TiSe2)n compounds studied, indicating that electrons are the majority carrier, and decreased as n increased. The effective mass of the carriers was calculated to be 5–6 me for the series of compounds.

Effect of Sn-Substitution on Thermoelectric Properties of Copper-Based Sulfide, Famatinite Cu3SbS4

Copper-based sulfide is an attractive material for Earth-abundant thermoelectrics. In this study, we demonstrate the effect of Sn-substitution on the electrical and thermal transport properties of fematinite Cu3SbS4 from 300 to 573 K. The carrier concentration is controlled in the range from 4 \times 10^18 to 8 \times 10^20 cm^-3 by Sn-substitution. The density-of-states effective mass is found to be ~3.0 me, assuming the single parabolic band model. The direct-type optical band gap is ~0.9 eV, which is consistent with the density functional theory calculation. The dimensionless figure of merit reaches 0.1 for Sn-doped samples at 573 K.

Thermoelectric transport mechanism of Mg2Si0.4Sn0.6-yBiy prepared by low-temperature microwave reaction

According to Debye relaxation, the polarization of electric dipole can be accomplished in 10-10 s under the action of an alternating electromagnetic filed with a frequency of 2.45 GHz, so it is feasible to obtain nano powder by carrying out solid reaction in microwave at low temperature in a short time. In this work, the syntheses of Mg2Si0.4Sn0.6-yBiy (0 ≤ y ≤ 0.03) solid solution thermoelectric materials are successfully achieved by microwave-assisted solid state reaction at low temperature with MgH2 serving as one reactant instead of Mg, and their transportation mechanisms are studied based on the SPB (single parabolic band) model as well. The results indicate that the volatilization and oxidation of Mg can be suppressed effectively in this process. Fine stoichiometric product can be achieved with nano-lamellar structure with an interlayer spacing of about 100 nm by carrying out the reaction between MgH2 and Si, Sn in microwave at 400℃ in 15 min. The introduction of Bi dopant can increase carrier concentration and lattice distortion. With the cooperation between the nano lamellar structure and lattice distortion, the phone is scattered so effectively that the sample owns a lowest thermal conductivity, κmin of 1.36 W·m-1·K-1 at 550 K based on the fact that the phonon scattering is dominant in the heat transfer process. The calculated results show that the theoretical κmin is 0.93 W·m-1·K-1, which is lower than 1.36 W·m-1·K-1. Therefore, by further adjusting the process parameters and increasing the effective doping rate of Bi and the density of the lattice defects, it is expected to obtain lower thermal conductivity. The band convergence is also verified by increasing the density-of-state effective mass. The apparent increase in m* is due to a gradual increase in carrier concentration with increasing temperature. Despite the agreement between the data and the model, the irregular behavior between m* and temperature is a very strong indication and the electric transmission performance of the sample is likely to be influenced by the structure of the multi band structure. Owing possibly to the low reaction temperature, there are Bi precipitates at the grain boundary. In addition to the phonon scattering and the alloy scattering, the Bi segregation and the scattering of carrier by nano-lamellar structure make the carrier mobility of the sample slightly lower. The lower effective doping rate and complex band structure make the carrier concentration and density-of-state effective mass low coupled with the low carrier mobility, which leads to low material factor β with a ZT of 0.66 at 600 K consequently.

Thermoelectric transport and microstructure of optimized Mg2Si0.8Sn0.2

We have optimized the thermoelectric material Mg2Si0.8Sn0.2 and analyzed the electronic transport employing a single parabolic band model.

Thermoelectric Properties and Microstructure Studies of Spinodally Decomposed PbTe<SUB>0.38</SUB>S<SUB>0.62</SUB> Alloy

PbTe is a premiere mid-range temperature thermoelectric material and recent studies have proven nanostructing as an effective approach to reduce thermal conductivity of alloys. Whereas, little attention has been given to long-term thermal stability of secondary phases and microstructural evolution. Interestingly, replacing Te with S in PbTe provides an opportunity to form nanostructures in the bulk material through spinodal decomposition, which appears in binary phase diagrams of the PbTe–PbS system. Herein, the critical composition of PbTe_(0.38)S_(0.62) alloy is fabricated to n-type by chlorine doping. Thermoelectric transport properties of the alloy are investigated in the 300–850 K temperature range and the maximum zT achieved at 800 K is 0.75 with a predicted zT ∼ 0.85 at 750 K from single parabolic band model. The microstructure of the sintered samples was studied by FEG-SEM for both the as sintered and post transport properties measurement. The experimental results are compared with estimates from the parallel and series models for heterogeneous composites of single phase PbTe and PbS. The Seebeck coefficient is in agreement with the models predictions, but the resistivity is higher and the thermal conductivity is much lower than predicted values. We propose that this is attributed to the phonon and electron scattering on solute atoms in solid solutions and at interfaces.

Improved thermoelectric performance of (Zr0.3Hf0.7)NiSn half-Heusler compounds by Ta substitution

The thermoelectric performance of Ta substituted (ZrHf)NiSn-based half-Heusler compounds is studied. Here, Ta is used on the Hf site for controlling the charge carrier concentration in contrast to the widely used Sb substitution on the Sn site. The influence of the Ta content on the thermoelectric and transport properties of (Zr0.3Hf0.7-xTax)NiSn (x = 0, 0.01, 0.05) is investigated by means of Seebeck coefficient, electrical resistivity, thermal conductivity, and Hall coefficient measurements. The results are analyzed in context of the single parabolic band model. Ta substitution increases the charge carrier concentration and suppresses the influence of impurity band, which is present in the pristine (Zr0.3Hf0.7)NiSn. Moreover, Ta substitution decouples and simultaneously increases the density-of-states effective mass (m*) and the charge carrier mobility (μ), leading to a larger weighted mobility μ·(m*)3/2. The lattice thermal conductivity is slightly suppressed due to increased point defect scattering. As a result, a Figure of Merit of 0.85 is achieved for (Zr0.3Hf0.65Ta0.05)NiSn compound at 870 K, ca. 180% improvement over the unsubstituted sample.

Enhanced thermoelectric performance in Cd doped CuInTe2 compounds

CuIn1−xCdxTe2 materials (x = 0, 0.02, 0.05, and 0.1) are prepared using melting-annealing method and the highly densified bulk samples are obtained through Spark Plasma Sintering. The X-ray diffraction data confirm that nearly pure chalcopyrite structures are obtained in all the samples. Due to the substitution of Cd at In sites, the carrier concentration is greatly increased, leading to much enhanced electrical conductivity and power factor. The single parabolic band model is used to describe the electrical transport properties of CuInTe2 and the low temperature Hall mobility is also modeled. By combing theoretical model and experiment data, the optimum carrier concentration in CuInTe2 is proposed to explain the greatly enhanced power factors in the Cd doped CuInTe2. In addition, the thermal conductivity is reduced by extra phonon scattering due to the atomic mass and radius fluctuations between Cd and In atoms. The maximum zTs are observed in CuIn0.98Cd0.02Te2 and CuIn0.9Cd0.1Te2 samples, which are improved by over 100% at room temperature and around 20% at 600 K.

Thermoelectric study of crossroads material MnTe via sulfur doping

Here, we report thermoelectric study of crossroads material MnTe via iso-electronic doping S on the Te-site. MnTe1-xSx samples with nominal S content of x = 0.00, 0.05, and 0.10 were prepared using a melt-quench method followed by pulverization and spark plasma sintering. The X-ray powder diffraction, scanning electron microscopy, and ZAF-corrected compositional analysis confirmed that S uniformly substitutes Te up to slightly over 2%. A higher content of S in the starting materials led to the formation of secondary phases. The thermoelectric properties of MnTe1-xSx samples were characterized by means of Seebeck coefficient, electrical conductivity, and thermal conductivity measurements from 300 K to 773 K. Furthermore, Hall coefficient measurements and a single parabolic band model were used to help gain insights on the effects of S-doping on the scattering mechanism and the carrier effective mass. As expected, S doping not only introduced hole charge carriers but also created short-range defects that effectively scatter heat-carrying phonons at elevated temperatures. On the other hand, we found that S doping degraded the effective mass. As a result, the ZT of MnTe0.9S0.1 was substantially enhanced over the pristine sample near 400 K, while the improvement of ZT became marginal at elevated temperatures. A ZT ∼ 0.65 at 773 K was obtained in all three samples.

Glass-like lattice thermal conductivity and high thermoelectric efficiency in Yb9Mn4.2Sb9

Motivated by excellent thermoelectric performance in the well-known Yb-based Zintl compounds Yb_(14)MnSb_(11) and YbZn_(2−x)Mn_xSb_2, this study investigates the thermoelectric properties of Yb_9Mn_(4.2)Sb_9. Unlike most transition metal containing Zintl phases, Yb_9Mn_(4.2)Sb)9 contains a partially occupied Mn site and thus does not have a valence-precise stoichiometry. Samples were synthesized by direct ball milling of the elements, followed by hot pressing. Consistent with previous reports, X-ray diffraction and wavelength dispersive spectroscopy confirmed a narrow composition range near Yb_9Mn_(4.2)Sb_9. High temperature measurements of the electronic properties of Yb_9Mn_(4.2)Sb_9 indicate that it is a degenerate p-type semiconductor with a band gap sufficiently large for high temperature thermoelectric applications. Hall measurements reveal that Yb_9Mn_(4.2)Sb_9 has a high extrinsic carrier concentration (~10^(20) h^+ cm^(−3)), which is due to the deviation from the theoretical “Zintl composition” of Yb_9Mn_(4.5)Sb_9. The measured carrier concentration coincides with the optimum concentration predicted using a single parabolic band model. Measurements of the thermal diffusivity and heat capacity reveal an extremely low, temperature-independent lattice thermal conductivity in this compound (κ_L < 0.4 W mK^(−1)), which is due to both the large unit cell size (44 atoms per primitive cell) and substantial disorder on the Mn site. This favorable combination of optimized electronic properties and low lattice thermal conductivity leads to a promising figure of merit at high temperature (zT = 0.7 at 950 K).

Advanced thermoelectrics governed by a single parabolic band: Mg2Si0.3Sn0.7, a canonical example

The well-known single parabolic band (SPB) model has been useful in providing insights into the understanding of transport properties of numerous thermoelectric materials. However, the conduction and valence bands of real semiconductors are rarely truly parabolic which limits the predictive power of the SPB model. The coincidence of the band edges of two parabolic bands, a situation arising in Mg2Si1-xSnx solid solutions when x∼ 0.7, naturally makes the SPB approximation applicable to evaluate all transport parameters. We demonstrate this in the case of Bi-doped Mg2Si0.3Sn0.7 where the minima of the two conduction bands at the X-point of the Brillouin zone coincide. The combination of a large density-of-states effective mass m* ∼ 2.6 me arising from the enhanced valley degeneracy Nv, high mobility μd due to low deformation potential Ed (8.77-9.43 eV), and ultra-low alloy scattering parameter Ea (0.32-0.39 eV) leads to an outstanding power factor, PFmax∝ (m*)(3/2)μd, of up to 4.7 mW m(-1) K(-2) at around 600 K. The specification and improved understanding of scattering parameters using the SPB model are important and instructive for further optimization of the thermoelectric performance of n-type Mg2Si0.3Sn0.7.

INFLUENCE OF THE CHEMICAL POTENTIAL ON THE CARRIER EFFECTIVE MASS IN THE THERMOELECTRIC SOLID SOLUTION Cu2Zn1-xFexGeSe4

In this paper, we describe the synthesis and characterization of the solid solution Cu 2 Zn 1-x Fe x GeSe 4. Electronic transport data have been analyzed using a single parabolic band model and have been compared to Cu 2+x Zn 1-x GeSe 4. The effective mass of these undoped, intrinsically hole conducting materials increases linearly with increasing carrier concentration, showing a non-parabolic transport behavior within the valence band.

Thermoelectric Properties and Electronic Structure of the Zintl‐Phase Sr3AlSb3

The Zintl-phase Sr3 AlSb3 , which contains relatively earth-abundant and nontoxic elements, has many of the features that are necessary for good thermoelectric performance. The structure of Sr3 AlSb3 is characterized by isolated anionic units formed from pairs of edge-sharing tetrahedra. Its structure is distinct from previously studied chain-forming structures, Ca3 AlSb3 and Sr3 GaSb3 , both of which are known to be good thermoelectric materials. DFT predicts a relatively large band gap in Sr3 AlSb3 (Eg ≈1 eV) and a heavier band mass than that found in other chain-forming A3 MSb3 phases (A=Sr, Ca; M=Al, Ga). High-temperature transport measurements reveal both high resistivity and high Seebeck coefficients in Sr3 AlSb3 , which is consistent with the large calculated band gap. The thermal conductivity of Sr3 AlSb3 is found to be extremely low (≈ 0.55 W mK(-1) at 1000 K) due to the large, complex unit cell (56 atoms per primitive cell). Although the figure of merit (zT) has not been optimized in the current study, a single parabolic band model suggests that, when successfully doped, zT≈ 0.3 may be obtained at 600 K; this makes Sr3 AlSb3 promising for waste-heat recovery applications. Doping with Zn(2+) on the Al(3+) site has been attempted, but does not lead to the expected increase in carrier concentration.

Doping for higher thermoelectric properties in p-type BiCuSeO oxyselenide

The low power factor (PF) of BiCuSeO oxyselenide inhibits further improvement on thermoelectric figure of merit in the moderate temperature range. In this Letter, we show that the electron transport properties of doped BiCuSeO oxyselenide can be accurately described in acoustic phonon scattering assumption within the framework of single parabolic band model. It is further found that the doping elements alter the electron transport properties by tuning the effective mass and deformation potential. Based on these understandings, we argue that the higher power factor can be achieved by choosing the doping element based on reducing deformation potential coefficient and decreasing effective mass.

Improved thermoelectric properties in Zn-doped Ca5Ga2Sb6

Zintl compounds with the chemical formula Ca5M2Sb6 have attracted attention as candidates for use in thermoelectric applications due to their low thermal conductivity and promising high temperature performance (i.e., zT = 0.6 at 1000 K in Ca5Al2−xNaxSb6). We have shown previously that, relative to Ca5Al2Sb6, both Ca5Ga2Sb6 and Ca5In2Sb6 have reduced phonon velocities and improved carrier mobility, suggesting that improved zT can be achieved in these materials. Here we further investigate Ca5Ga2Sb6, which is an intrinsic semiconductor with a small concentration of p-type carriers. By substituting Zn2+ on the Ga3+ site, we show that it is possible to increase and control the carrier concentration in Ca5Ga2−xZnxSb6 and thus optimize its thermoelectric behavior. A single parabolic band model was used to estimate an effective mass of m* = 1.6me, which is slightly lower than Al-based compounds. Though the reduced m* leads to a lower Seebeck coefficient, it also leads to a much higher electronic mobility. The high mobility leads to increased thermoelectric figure of merit (zT) at low and intermediate temperatures relative to Zn-doped Ca5Al2Sb6. However, due to the decreased band gap in Ca5Ga2Sb6 relative to Ca5Al2Sb6, the maximum zT in optimally doped Ca5Ga2Sb6 is reduced (peak zT ∼ 0.35 at T = 775 K).

Influence of preparation conditions on thermoelectric properties of Ba8Ga16Si30 clathrate by combining arc melting and spark plasma sintering methods

We have investigated the thermoelectric properties of clathrate samples with a nominal Ba8Ga16Si30 composition, prepared by combining arc melting and spark plasma sintering methods under different conditions. The carrier concentration of the samples greatly decreases from the order of 1021 cm−3 to 1020 cm−3 due to an increase in Ga content by changing the arc melting conditions. Consequently, the Seebeck coefficient increases and the thermal conductivity decreases while the electrical conductivity decreases. The effective mass, carrier mobility and lattice thermal conductivity are determined from an analysis using a single parabolic band model with alloy disorder and phonon scattering mechanisms. The thermoelectric figure of merit ZT significantly increases up to about 0.55 (900 K) for a carrier concentration of about 6×1020 cm−3 (RT). The simulation predicts that ZT can reach 0.8 (900 K) at the optimum carrier concentration (about 2×1020 cm−3) in the Ba8Ga16Si30 system.