Band and Phonon Engineering for Thermoelectric Enhancements of Rhombohedral GeTe.

GeTe Thermoelectrics

GeTe experiences phase transition between cubic and rhombohedral through distortion along the [111] direction. Cubic GeTe shares the similarity of a two-valence-band structure (high-energy L and low-energy Σ bands) with other cubic IV-VI semiconductors such as PbTe, SnTe, and PbSe, and all show a high thermoelectric performance due to a high band degeneracy. Very recently, the two valence bands were found to switch in energy in rhombohedral GeTe and to be split due to symmetry-breaking of the crystal structure. This enables the overall band degeneracy to be manipulated either by the control of symmetry-induced degeneracy or by the design of energy-aligned orbital degeneracy. Here, we show Sb-doping for optimizing carrier concentration and manipulating the degree of rhombohedral lattice distortion to maximize the band degeneracy and then electronic performance. In addition, Sb-doping significantly promotes the solubility of PbTe, enhancing the scattering of phonons by Ge/Pb substitutional defects for minimizing the lattice thermal conductivity. This successfully realizes a superior thermoelectric figure of merit, zT of >2 in both rhombohedral and cubic GeTe, demonstrating these alloys as top candidates for thermoelectric applications at T < 800 K. This work further sheds light on the importance of crystal structure symmetry manipulation for advancing thermoelectrics.

After constructing a stress and strain model, the valence bands of in-plane biaxial tensile strained Si is calculated by k · p method. In the paper we calculate the accurate anisotropy valance bands and the splitting energy between light and heavy hole bands. The results show that the valance bands are highly distorted, and the anisotropy is more obvious. To obtain the density of states (DOS) effective mass, which is a very important parameter for device modeling, a DOS effective mass model of biaxial tensile strained Si is constructed based on the valance band calculation. This model can be directly used in the device model of metal—oxide semiconductor field effect transistor (MOSFET). It also a provides valuable reference for biaxial tensile strained silicon MOSFET design.

SnTe is deemed a promising mid-temperature thermoelectric material for low toxicity, low cost, and decent performance. Sole doping/alloying on Sn sites was reported to result in either modified band alignment or reduced lattice thermal conductivity, thus contributing to an enhanced overall thermoelectric figure of merit. However, this strategy alone is always unable to take full use of the material's advantage, especially considering that it simultaneously pushes the hole concentration off the optimal range. In this work, we adopted a two-step approach to optimize the thermoelectric performance of SnTe in order to overcome the limitation. First, Mn was alloyed into Sn sites to increase the density of state effective mass of SnTe by regulating the valence bands; the Fermi level was further regulated by iodine doping, guided by a refined two-band model. Additionally, the lattice thermal conductivity was also suppressed by the microstructure optimizing via Mn doping and additional phonon scattering at ITe mass/strain fluctuation. As a result, a high ZT of 1.4 at 873 K was achieved for Sn0.91Mn0.09Te0.99I0.01. This study provides a way to refine the single doping stratagem used in other thermoelectric materials.

<p indent="0mm">Under the background of a worsening energy crisis, there is an increasing global demand for efficient and environmentally friendly energy conversion methods. Thermoelectric materials, which are capable of bidirectional conversion between thermal energy and electrical energy, show significant potential for applications in waste heat utilization and solid-state refrigeration technology. Thermoelectric materials offer innovative solutions to the current energy shortage. SnTe and PbTe share the same crystal structure and similar two-valence-band structure, but SnTe does not contain the toxic element Pb, has attracted great attention and research interest. Despite exhibiting relatively high thermoelectric performance in the medium to high-temperature range, enhancing the thermoelectric performance of SnTe near room temperature poses a challenge primarily due to its excessively high carrier concentration and low Seebeck coefficient. As the advancement of thermoelectric cooling technology continues, the performance of materials at room temperature becomes increasingly crucial. Previous studies have demonstrated that alloying with Sb₂Te₃ introduces a significant number of cation vacancies and dislocation defects, effectively reducing the lattice thermal conductivity of SnTe. This process also enables the modulation of the band structure, thereby increasing the effective mass, which has been demonstrated as a successful strategy for enhancing thermoelectric performance across a broad temperature range. Relevant research indicates that Sb₂Te₃(SnTe)₆ exhibits superior room temperature thermoelectric performance and average thermoelectric performance compared to other alloyed samples. Therefore based on the Sb₂Te₃ alloying approach, this study incorporates Cd doping at the Sn site to synergistically regulate the carrier concentration, density of states effective mass, and lattice thermal conductivity of Sb₂Te₃(SnTe)₆. Thermoelectric materials, Sb₂Te₃(Sn_{1−<italic>x</italic>}Cd<italic>_x</italic>Te)₆ (<italic>x</italic>=0–0.08) were synthesized by vacuum melting and spark plasma sintering (SPS). The vacuum melting reactions were heated from room temperature to <sc>1423 K</sc> over 16 hours, maintained at this temperature for 24 hours, then slowly cooled to <sc>873 K</sc> over 6 hours, and finally cooled down to room temperature. The compounds were fully characterized by a range of techniques, including X-ray diffraction, energy dispersive spectrometer, and Hall coefficient test system, etc. The X-ray diffraction and energy dispersive spectrometer results demonstrate that Cd was successfully incorporated into Sb₂Te₃(SnTe)₆. The Hall coefficient test indicates that the substitution of Cd results in an obvious decrease in the carrier concentration. The Pisarenko curves calculated based on the single parabolic band model demonstrate that the effective mass increases with an increase in Cd content. The experimental results show that the effective mass of Sb₂Te₃(SnTe)₆ and the carrier concentration are co-optimized by doping Cd at the Sn position, and the thermoelectric transport performance of the material is significantly improved over the whole temperature range. In conclusion, this study incorporates Cd doping at the Sn site to synergistically regulate the carrier concentration, density of states effective mass, and lattice thermal conductivity of Sb₂Te₃(SnTe)₆. As a result, the <italic>ZT</italic> value of Sb₂Te₃- (Sn_0.96Cd_0.04Te)₆ reached 0.26 at <sc>300 K,</sc> with an average <italic>ZT</italic> value of 0.79 in the temperature range of <sc>323–773 K.</sc> The results indicate that SnTe-Sb₂Te₃ compounds exhibit significant potential for utilization in thermoelectric power generation and cooling applications.

Using first principles calculations, we study the conduction band alignment, effective mass, and Fermi surface complexity factor of n-type Mg3Sb2 – xBix (x = 0, 1, and 2) from the full ab initio band structure. We find that with an increase in the Bi content, the K and M band minima move away from the conduction band minimum CB1 while the singly-degenerate Г band minimum shifts rapidly downward and approaches the conduction band minimum. However, the favorable sixfold degenerate CB1 band minimum keeps dominating the conduction band minimum and there is no band crossing between the Г and CB1 band minima. In addition, we show that the connection of the CB1 carrier pockets with the energy level close to the band minimum M can strongly enhance the carrier pocket anisotropy and Fermi surface complexity factor, which is likely the electronic origin for the local maximum in the theoretical power factor. Our calculations also show that the density of states effective mass, Seebeck coefficient, and Fermi surface complexity factor decrease with an increase in the Bi content, which is unfavorable to the electrical transport. In contrast, reducing the conductivity effective mass with an increase in the Bi content is beneficial to the electrical transport by improving carrier mobility and weighted mobility as long as the detrimental bipolar effect is insignificant. As a result, in comparison with n-type Mg3Sb2, n-type Mg3SbBi shows higher power factors and a much lower optimal carrier concentration for the theoretical power factor at 300 K, which can be easily achieved by the experiment.

Interlayer surface defects and thermoelectric properties in layered films of n-Bi2Te2.7Se0.15S0.15 topological insulators L. N. Lukyanova*, O. A. Usov, M. P. Volkov, V. A. Rusakov Ioffe Institute Russian academy of science, 194021 St.Petersburg, Russia *E-mail: lidia.lukyanova@mail.ioffe.ru Abstract In layered films of n-Bi2Te2.7Se0.15S0.15 topological insulators optimized for temperatures below room temperature, the morphology of the (0001) interlayer surface and thermoelectric properties were studied. On the profiles of the (0001) surface, we identified neutral impurity defects arising from the substitution of Se and S atoms for Te atoms and donor antisite defects of tellurium at bismuth sites, which affect the thermoelectric properties. The average value of thermoelectric figure of merit in n-Bi2Te2.7Se0.15S0.15 films increases to &lt;Z&gt; ≈ 3.0•10-3 K-1 in the range 80 – 215 K, while in bulk solid solution &lt;Z&gt; ≈ 2.0•10-3 K-1. An increase in the thermoelectric figure of merit in films is associated with an increase in the energy dependence of the relaxation time due to an increase in the effective scattering parameter reff. It is shown that in films the Seebeck coefficient, the density of states effective mass m/m0, and the material parameter proportional to the power factor increase, while the lattice κL and electronic thermal conductivity κe decrease, which determines the increase in thermoelectric figure of merit.

Full-shell d-orbitals of interstitial Ni and anomalous electrical transport in Ni-based half-Heusler thermoelectric semiconductors

Modeling of enhancement factor of hole mobility for strained silicon under low stress intensity

This paper aims at elucidating the origin of the high thermoelectric power factor of p-type (AgxSbTex/2+1.5)15(GeTe)85 (TAGS) thermoelectric materials with 0.4 ⩽ x ⩽ 1.2. All samples exhibit good thermoelectric figures of merit (zT) which reach 1.5 at 700 K for x = 0.6. Thermoelectric and thermomagnetic transport properties (electrical resistivity, Seebeck, Hall and transverse Nernst–Ettinghausen coefficients) are measured and used to calculate the scattering factor, the Fermi energy, the density-of-states (DOS) effective mass and hole mean free path (mfp). The DOS effective mass is very high due to the large band mass of the primary valence band and the high degeneracy of pockets in the Fermi surface from the second valence band. The highly degenerate Fermi surface increased the total DOS without decreasing mobility, which is more desirable than the high DOS that comes from a single carrier pocket. The high-temperature hole mfp approaches the Ioffe–Regel limit for band-type conduction, which validates our discussion based on band transport and is also important for TAGS alloys having high zT with heavy bands. The present results show that multiple degenerate Fermi surface pockets provide an effective way of substantially increasing the power factor of thermoelectric materials with low thermal conductivity.

A ternary phosphide Ag6Ge10P12 containing no toxic elements has attracted much attention as an eco-friendly thermoelectric material. This study reveals the relationship between the density of states effective mass mDOS∗ and carrier concentration n for achieving higher thermoelectric performance in Ag6Ge10P12. The Seebeck coefficient S of Ag6Ge10−xGaxP12 (0.0 ≤ x ≤ 0.25) with various carrier concentrations is unexpectedly improved by increasing n. Scrutinizing electrical transport properties, including the S and electrical conductivity σ, and electronic structure indicated that the improved S is owing to the enhanced mDOS∗, which originated from tuning the Fermi level in a valence band with multi-valley and pudding-mold bands. The power factor S2σ is enhanced by both improved S and σ. The total thermal conductivity κtot monotonically decreases with increasing x because of the decrease in the lattice thermal conductivity κL. Combining the improved S2σ and reduced κtot, the maximum ZT value of Ag6Ge9.875Ga0.125P12 at 390 K reaches ∼0.33 with the optimal carrier concentration n ∼7.0 × 1020 cm−3. The present results demonstrate a guideline for enhancing the thermoelectric performance of Ag6Ge10P12 by breaking the trade-off relationship between the S and σ through n. Moreover, Young's modulus E and nanoindentation hardness H of Ag6Ge10-xGaxP12 are greater than 125 GPa and 9 GPa, respectively, comparable to those of thermoelectric Si–Ge alloy. These findings and insights in the present study will serve as a basis for enhancing the thermoelectric performance and fabricating the thermoelectric module for eco-friendly phosphide Ag6Ge10P12.

Solving the Schrödinger equation with strain Hamiltonian and combining with KP theory, we obtained the conductivity effective mass and density of states effective mass of strained Si1-xGex(001) in this paper. On the basis of conductivity effective mass and density of states effective mass, considered of Fermi golden rule and Boltzman collision term approximation theory, scattering rate model was established in strained Si1-xGex(001). Based on the conductivity effective mass and scattering rate models we discussed the dependence of electron mobility on stress and doping concentration in strained Si1-xGex(001), it shows that electron mobility decrease with the increasing of stress and doping concentration. This result can provide valuable references to the research of electron mobility of strained Si1-xGexmaterials and the design of devices.

Temperature dependence of intrinsic carrier concentration and density of states effective mass of heavy holes in InSb

Lead-free SnTe-based materials are expected to replace PbTe and have gained much attention from the thermoelectric community. In this work, a maximum ZT of ∼1.31 at 873 K is attained in SnTe via promoting a high quality factor resulting from Mn alloying and BiBr3 doping. The results show that Mn alloying in SnTe converges the L band and the ∑ band in valence bands to supply enhanced valley degeneracy and the density of states effective mass, giving rise to a high power factor of ∼21.67 μW cm-1 K-2 at 723 K in Sn0.93Mn0.1Te. In addition, the subsequent BiBr3 doping can sharpen the top of the valence band to coordinate the contradiction between the band effective mass and the carrier mobility, thus enhancing the carrier mobility while maintaining a relatively large density of states effective mass. Consequently, a maximum power factor of 23.85 μW cm-1 K-2 at 873 K is achieved in Sn0.93Mn0.1Te-0.8 atom % BiBr3. In addition to band sharpening, BiBr3 doping can also effectively suppress the bipolar effect at elevated temperatures and reduce the lattice thermal conductivity by strengthening the point defect phonon scattering. Benefitting from doping BiBr3 in Sn0.93Mn0.1Te optimizes the carrier mobility and suppresses the lattice thermal conductivity, resulting in a dramatically enhanced quality factor. Accordingly, an average ZT of ∼0.62 in the temperature range of 300-873 K is obtained in Sn0.93Mn0.1Te-0.8 atom % BiBr3, ∼250% increase compared with that in Sn1.03Te.

The authors have investigated the bonding in cubic and rhombohedral GeTe by studying the charge density of each individual valence band, using the Baldereschi method. The calculated charge densities can be interpreted in terms of atomic orbitals. The orbitals that participate in the bonding are s Ge, p Te and p Ge. In cubic GeTe there are p orbitals along the three orthogonal axes forming polar sigma -bonds between the Ge and Te atoms. There is a pronounced admixture of s Ge states with p states in the second and the last valence band. This admixture is responsible for the rise of the last valence band, which makes the GeTe a narrow-gap semiconductor. For rhombohedral GeTe the bonding can be described in terms of one p orbital along the (111) direction and the three p orbitals orthogonal to the (111) direction. These orbitals interact and form an admixture of polar sigma - and pi -bonds. The bonding charge is greater for rhombohedral GeTe, resulting in an increase of the bonding and a lowering of the electronic energy of rhombohedral GeTe with respect to that of cubic GeTe. By calculation they find the dipole moment of the rhombohedral phase to be 1.4 D along the (111) direction.