Degeneracy Of Conduction Band Research Articles

NaBeAs and NaBeSb: Novel Ternary Pnictides with Enhanced Thermoelectric Performance

Thermoelectrics is a clean energy technology that converts thermal energy into electrical energy and provides an environmentally friendly and viable route to produce electricity. In this work, we thoroughly explore the thermoelectric performance of two novel ternary pnictide compounds, NaBeAs and NaBeSb, using full ab initio calculations and solving linear Boltzmann transport equations. We predict that both compounds exhibit excellent dynamical and thermal stability. The combined effect of low phonon group velocity and weak bonding interaction results in intrinsic low lattice thermal conductivities of 1.41 and 0.59 W/mK for NaBeAs and NaBeSb, respectively, in the z-axis direction at 600 K. The electronic structure exhibits high conduction band degeneracy, which results in favorable electrical transport characteristics. The unique combination of very low lattice thermal conductivity and good electrical transport properties leads to excellent n-type thermoelectric properties. Furthermore, in n-type doping, the figures of merit reach 1.82 and 4.26 for NaBeAs and NaBeSb at 600 K. Our findings show that both compounds are promising n-type thermoelectric materials at medium temperatures.

The Importance of Mg–Sb Interactions in Achieving High Conduction Band Degeneracy in Mg3Sb2 for High n-Type Thermoelectric Performance

In recent years, Mg3Sb2 has attracted much attention due to its excellent performance as an n-type thermoelectric material. The high performance of n-type Mg3Sb2 is largely due to the high valley degeneracy (NV) of the electron transport edge, which is the result of the conduction band minimum (CBM) being located at a low-symmetry, six-fold degenerate point (inside the ΓALM plane) in the first Brillouin zone. Furthermore, Bi alloying on the Sb site is well-known to improve electron mobility, and hence, performance. In previous works, this low-symmetry CBM has been attributed to interactions between the tetrahderally and octahedrally coordinated Mg-sites. However, these Mg–Mg interactions cannot explain changes in the shape of the CBM upon Bi alloying, while Mg–Sb (and Mg–Bi) interactions could explain them. Prior studies have neglected to fully consider the importance of the Sb orbitals in the existence of the low-symmetry CBM because at the CBM, there is very little contribution from the Sb orbitals. In this work, we use first-principles density functional theory and tight-binding calculations to show that the low-symmetry CBM is due to Mg-s–Sb-p interactions that are weakest at or near the CBM. Controlling the cation-s–anion-p interactions through anion- or cation-site alloying can be used as an engineering strategy to optimize thermoelectric performance.

Large improvement in thermoelectric performance of pressure-tuned Mg3Sb2.

The Mg3Sb2-based Zintl compound is a promising candidate for a high-performance thermoelectric material with the advantage of the component elements being low cost, non-toxic and earth-abundant. Here, we investigate the influence of pressure on the electronic structure and p-type and n-type thermoelectric transport properties of Mg3Sb2 by using density functional theory and Boltzmann transport theory. The energy gaps first increase and then decrease with the increasing of pressure, and a peak value of the valley degeneracy of conduction band occurs at 4 GPa. Based on the calculated band structures, the zT (figure of merit) values of p-type Mg3Sb2 under pressure are significantly enhanced, which predominantly originates from the boosted PF (power factor) contributed by the increased carrier's relaxation time. When the carrier concentration reaches 1 × 1020 cm−3, the PF of p-type Mg3Sb2 at 4 GPa is increased by 35% relative to that of the compound at 0 GPa, thus leading to a considerably improved zT of ∼0.62 at 725 K. Under the same conditions, due to the increased density of states effective mass, the n-type Mg3Sb2 exhibits a highest PF of ∼19 μW cm−1 K−2 and a peak zT of 1.7. Therefore, pressure tuning is an effective method to improve the p-type and n-type thermoelectric transport performance of Mg3Sb2-based Zintl compounds. This work on Mg3Sb2 under pressure may provide a new mechanism for the experimenters towards the enhancement of the thermoelectric performance of materials.

Band degeneracy enhanced thermoelectric performance in layered oxyselenides by first-principles calculations

Band degeneracy is effective in optimizing the power factors of thermoelectric (TE) materials by enhancing the Seebeck coefficients. In this study, we demonstrate this effect in model systems of layered oxyselenide family by the density functional theory (DFT) combined with semi-classical Boltzmann transport theory. TE transport performance of layered LaCuOSe and BiCuOSe are fully compared. The results show that due to the larger electrical conductivities caused by longer electron relaxation times, the n-type systems show better TE performance than p-type systems for both LaCuOSe and BiCuOSe. Besides, the conduction band degeneracy of LaCuOSe leads to a larger Seebeck coefficient and a higher optimal carrier concentration than n-type BiCuOSe, and thus a higher power factor. The optimal figure of merit (ZT) value of 1.46 for n-type LaCuOSe is 22% larger than that of 1.2 for n-type BiCuOSe. This study highlights the potential of wide band gap material LaCuOSe for highly efficient TE applications, and demonstrates that inducing band degeneracy by cations substitution is an effective way to enhance the TE performance of layered oxyselenides.

N-Bi2-xSbxTe3: A Promising Alternative to Mainstream Thermoelectric Material n-Bi2Te3-xSex near Room Temperature.

For decades, the V2VI3 compounds, specifically p-type Bi2-xSbxTe3 and n-type Bi2Te3-xSex, have remained the cornerstone of commercial thermoelectric solid-state cooling and power generation near room temperature. However, a long-standing problem in V2VI3 thermoelectrics is that n-type Bi2Te3-xSex is inferior in performance to p-type Bi2-xSbxTe3 near room temperature, restricting the device efficiency. In this work, we developed high-performance n-type Bi2-xSbxTe3, a composition long thought to only make good p-type thermoelectrics, to replace the mainstream n-type Bi2Te3-xSex. The success arises from the synergy of the following mechanisms: (i) the donorlike effect, which produces excessive conduction electrons in Bi2Te3, is compensated by the antisite defects regulated by Sb alloying; (ii) the conduction band degeneracy increases from 2 for Bi2Te3 and Bi2Te3-xSex to 6 for Bi2-xSbxTe3, favoring high Seebeck coefficients; and (iii) the larger mass fluctuation yet smaller electronegativity difference and smaller atomic radius difference between Bi and Sb effectively suppresses the lattice thermal conductivity and retains decent carrier mobility. A state-of-the-art zT of 1.0 near room temperature was attained in hot deformed Bi1.5Sb0.5Te3, which is higher than those for most known n-type thermoelectric materials, including commercial Bi2Te3-xSex ingots and the popular Mg3Sb2. Technically, building both the n-leg and p-leg of a thermoelectric module using similar chemical compositions has key advantages in the mechanical strength and the durability of devices. These results attested to the promise of n-type Bi2-xSbxTe3 as a replacement of the mainstream n-type Bi2Te3-xSex near room temperature.

High Thermoelectric Power Factor Realization in Si-Rich SiGe/Si Superlattices by Super-Controlled Interfaces

A Si-based superlattice is one of the promising thermoelectric films for realizing a stand-alone single-chip power supply. Unlike a p-type superlattice (SL) achieving a higher power factor due to strain-induced high hole mobility, in the n-type SL, the strain can degrade the power factor due to lifting conduction band degeneracy. Here, we propose epitaxial Si-rich SiGe/Si SLs with ultrathin Ge segregation interface layers. The ultrathin interface layers are designed to be sufficiently strained, not to give strainto the above Si layers. Therein, a drastic thermal conductivity reduction occurs by larger phonon scattering at the interfaces with the large atomic size difference between Si layers and Ge segregation layers, while unstrained Si layers preserve a high conduction band degeneracy leading to a high Seebeck coefficient. As a result, the n-type Si0.7Ge0.3/Si SL with controlled interfaces achieves a higher power factor of ∼25 μW cm-1 K-2 in the in-plane direction at room temperature, which is superior to ever reported SiGe-based films: SiGe-based SLs and SiGe films. The Si0.7Ge0.3/Si SL with controlled interfaces also exhibits a low thermal conductivity of ∼2.5 W m-1 K-1 in the cross-plane direction, which is ∼5 times lower than the reported value in a conventional Si0.7Ge0.3/Si SL. These results demonstrate that strain and atomic differences controlled by ultrathin layers can bring a breakthrough for realizing high-performance light-element-based thermoelectric films.

Enhanced thermoelectric performance of Mg2Si1−xSnx codoped with Bi and Cr

Magnesium silicides are favorable thermoelectric materials considering resource abundance and cost. Chromium (Cr) doping in magnesium silicides has not yet been explored. Using first-principles calculations, we have studied the stability of ${\mathrm{Mg}}_{2}\mathrm{Si}$ with chromium (1.85, 3.7, 5.55, and 6.25% Cr) and tin (12.5 and 50% Sn). Three ${\mathrm{Mg}}_{2}\mathrm{Si}$ compounds doped with Sn, (Sn + Bi), and (Sn + Bi + Cr) are used to explain doping effects on thermoelectric performance. Notably, Cr behaves nonmagnetically for $\ensuremath{\le}2%\phantom{\rule{0.28em}{0ex}}\mathrm{Cr}$, after which ferromagnetic ordering is favored ($\ensuremath{\le}12.96%$ Cr), despite its elemental antiferromagnetic state. With alloying of Sn (70.4%), ${\mathrm{Mg}}_{2}\mathrm{Si}$ remains an indirect-band-gap semiconductor, but adding small amounts of Bi (3.7%) increases the carrier concentration such that electrons occupy conduction bands, making it a degenerate semiconductor. ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{0.296}{\mathrm{Sn}}_{0.666}{\mathrm{Bi}}_{0.037}$ is found to give the highest thermoelectric figure of merit (ZT) and power factor (PF) at 700 K, i.e., 1.75 and 7.04 $\text{mW}\phantom{\rule{4.pt}{0ex}}{\text{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\text{K}}^{\ensuremath{-}2}$, respectively. Adding small %Cr decreases ZT and PF to 0.78 and 4.33 $\text{mW}\phantom{\rule{4.pt}{0ex}}{\text{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\text{K}}^{\ensuremath{-}2}$, respectively. Such a degradation in thermoelectric (TE) performance is attributed to two factors: (i) uniform doping acting as an electron acceptor, decreasing conduction, and (ii) the loss of low-lying conduction band degeneracy with doping, decreasing the Seebeck coefficients. A study of configurations of Cr doping suggests that Cr has a tendency to form clusters inside the lattice, which play a crucial role in tuning the magnetic and TE performance of doped ${\mathrm{Mg}}_{2}\mathrm{Si}$ compounds.

Physical mechanisms of interface-mediated intervalley coupling in Si

The conduction band degeneracy in Si is detrimental to quantum computing based on spin qubits, for which a nondegenerate ground orbital state is desirable. This degeneracy is lifted at an interface with an insulator as the spatially abrupt change in the conduction band minimum leads to intervalley scattering. We present a theoretical study of the interface-induced valley splitting in Si that provides simple criteria for optimal fabrication parameters to maximize this splitting. Our work emphasizes the relevance of different interface-related properties to the valley splitting.

Electronic properties of a strained ⟨100⟩ silicon nanowire

The effects of uniaxial strain on the electronic properties of silicon nanowires grown in ⟨100⟩ direction are studied using a tight binding sp3d5s∗ orbital basis quantum simulation. Calculations are performed using both Harrison and Boykin formalisms (discussed in Sec. II). The energy difference between the fourfold (Δ4) and the twofold (Δ2) degenerate valleys of conduction bands reduces with compressive strain and the nanowire becomes an indirect band gap material when the compressive strain exceeds a certain value. With tensile strain, this energy difference increases and the nanowire band structures remain direct. The conduction band edge is downshifted with compressive strain and is upshifted with tensile strain. However, the valence band edge is upshifted with both types of strain that results in band gap reduction with strain. The four-valley degeneracy of conduction band at the center of one dimensional wire Brillouin zone is slightly lifted with both types of strain. The energy difference between the top two valence bands is insensitive to tensile strain and is significantly changed with compressive strain. The strain has no effect on conduction band effective mass but changes the valence band effective mass significantly. A 1% strain can change the hole effective mass by ≈53%. Harrison and Boykin formalisms produce very similar valence band edge and hole and electron effective masses and significantly different conduction band edge and band gap. In Boykin formalism, strain affects the energy levels of both the Δ4 and Δ2 valleys of conduction band while the energy level of only Δ2 valleys is affected by strain in Harrison calculations. The direct to indirect transition occurs at a slightly higher compressive strain in Boykin formalism.

Entanglement of static and flying qubits in degenerate mesoscopic systems

The entanglement of flying qubits with static qubits in the solid state is important in the development of quantum computing. It has recently been shown theoretically that the spin-dependent scattering of a propagating electron from a bound electron is sufficient to give full entanglement between the qubits embodied in their respective spins [J. H. Jefferson et al., Europhys. Lett. 74, 764 (2006); D. Gunlycke et al., J. Phys.: Condens. Matter 18, S851 (2006)]. In this paper a generalized, real-space Anderson model is introduced for a quasi-one-dimensional structure consisting of a binding site coupled to ideal leads. Degeneracy of both the binding site and the leads is incorporated to represent, for example, conduction band degeneracy in carbon nanotubes. The model is used to calculate the spin-dependent scattering behavior and resultant static-flying qubit entanglement created by the scattering process. Degeneracy (and more generally, multiplicity) in the binding site gives rise to inelastic scattering processes. In the elastic scattering regime, a degenerate binding site gives rise to antiresonant structures in the transmission spectrum. Additional degeneracy in the leads restricts this effect to the second set of leads, raising the possibility of spin filtration, though this is eliminated in the inelastic scattering regime. Degeneracy in the binding site also gives rise to multiple resonances in transmission that will improve the probability of obtaining entangled pairs relative to the nondegenerate case. This effect is maximized when the components of the degenerate binding site are symmetrically coupled to the leads.

High-energy electron-energy-loss study of sodium-tungsten bronzes.

Single-crystal metallic cubic sodium-tungsten bronzes ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{WO}}_{3}$ (x\ensuremath{\ge}0.25) and ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{Ta}}_{\mathit{y}}$${\mathrm{W}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{O}}_{3}$ (x-y=0.42) and monoclinic reduced ${\mathrm{WO}}_{3\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ have been investigated by high-energy electron-energy-loss spectroscopy (EELS) in transmission. For all electron densities the volume plasmon dispersion appears to be positive quadratic in momentum transfer q. The dispersion coefficient is much smaller than that predicted from the random-phase approximation for one isotropic parabolic band. This deviation can be reduced by recognizing the threefold degeneracy of the conduction-band ${\mathit{t}}_{2\mathit{g}}$ states in an octahedral field and narrowing of these bands with increasing sodium content. Anisotropy of the dispersion between the (100) and (110) direction is not observed. Optical effective masses ${\mathit{m}}^{\mathrm{*}}$(x) of the conduction electrons and background dielectric constants ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$(x) have been determined and compare well with data from optical spectroscopy and EELS in reflection, but not with photoemission results. This discrepancy is a result of the photoemission-data evaluation in which the conduction-band degeneracy was neglected. Na 2p core-level excitation energies argue against an admixture of sodium orbitals to the conduction band near the metal-nonmetal transition at x\ensuremath{\sim}0.2. Na 3s states admixed to O 2p states are observed at about 10--11 eV above the Fermi level in O 1s absorption edges. The x dependence of ${\mathit{m}}^{\mathrm{*}}$ and of the width of the O 1s absorption edge of ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{WO}}_{3}$ supports a model of conduction-band narrowing with increasing Na concentration.

Self-consistent surface calculation of electron-hole drops in gallium phosphide

Self-consistent Kohn-Sham method is used to investigate the surface structure of electron-hole drops (EHD) in GaP. If the conduction bands are located on the X-point and have a degeneracy of 3, the surface tension is found to be 85 × 10 −4 erg cm −2. In the presence of a “camel's-back” structure and a conduction band degeneracy of 6, the surface tension is calculated to be 130 × 10 −4 erg cm −2. The surface charge on the EHD is found to be negative irrespective of whether the conduction band degeneracy is 3 or 6.

Effect of Carrier Concentration on the Raman Frequencies of Si and Ge

The first-order Raman spectrum of Ge and Si has been investigated as a function of carrier concentration. In $p$-type materials we observed large broadenings of the Raman line and large shifts to higher frequencies of the Stokes line. We attribute these effects to the splitting of the valence band produced by the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\simeq}0$ optical phonon in a manner similar to the effects of doping on the ${C}_{44}$ elastic constant discussed by Keyes. From these results it is possible to estimate the coupling constant ${d}_{0}$ between optical phonons and holes. The $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\simeq}0$ phonon should also produce a splitting of the conduction band of Ge (but not of Si). However, for a given impurity concentration, the shifts observed in $n$-type materials are much smaller than those for $p$-type materials. The absence of large effects is probably due to the low rate of intervalley scattering. An effect on $n$-type Si related to the splitting of the ${X}_{1}$ conduction-band degeneracy by the phonon is also discussed and compared with the analogous effect on the elastic constants. It is shown that the internal stress parameter $\ensuremath{\zeta}$ is also affected by doping.