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Small energy gap revealed in CrBr 3 by scanning tunneling spectroscopy

CrBr 3 is a layered van der Waals material with magnetic ordering down to the 2D limit. For decades, based on optical measurements, it is believed that the energy gap of CrBr 3 is in the range of 1.68–2.1 eV. However, controversial results have indicated that the band gap of CrBr 3 is possibly smaller than that. An unambiguous determination of the energy gap is critical to the correct interpretations of the experimental results of CrBr 3 . Here, we present the scanning tunneling microscopy and spectroscopy (STM/S) results of CrBr 3 thin and thick flakes exfoliated onto highly ordered pyrolytic graphite (HOPG) surfaces and density functional theory (DFT) calculations to reveal the small energy gap (peak-to-peak energy gap to be 0.57 ± 0.04 eV; or the onset signal energy gap to be 0.29 ± 0.05 eV from dI/dV spectra). Atomic resolution topography images show the defect-free crystal structure and the dI/dV spectra exhibit multiple peak features measured at 77 K. The conduction band – valence band peak pairs in the multi-peak dI/dV spectrum agree very well with all reported optical transitions. STM topography images of mono- and bi-layer CrBr 3 flakes exhibit edge degradation due to short air exposure (~15 min) during sample transfer. The unambiguously determined small energy gap settles the controversy and is the key in better understanding CrBr 3 and similar materials.

36 MATERIALS SCIENCE↗

False metals, real insulators, and degenerate gapped metals

This paper deals with a significant family of compounds predicted by simplistic electronic structure theory to be metals but are, in fact, insulators. This false metallic state has been traditionally attributed in the literature to reflect the absence of proper treatment of electron-electron correlation (“Mott insulators”) whereas, in fact, even mean-field like density functional theory describes the insulating phase correctly if the restrictions posed on the simplistic theory are avoided. Such unwarranted restrictions included different forms of disallowing symmetry breaking described in this article. As the science and technology of conductors have transitioned from studying simple elemental metals such as Al or Cu to compound conductors such as binary or ternary oxides and pnictides, a special class of degenerate but gapped metals has been noticed. Their presumed electronic configurations show the Fermi level inside the conduction band or valence band, yet there is an “internal band gap” between the principal band edges. The significance of this electronic configuration is that it might be unstable toward the formation of states inside the internal band gap when the formation of such states costs less energy than the energy gained by transferring carriers from the conduction band to these lower energy acceptor states, changing the original (false) metal to an insulator. The analogous process also exists for degenerate but gapped metals with the Fermi level inside the valence band, where the energy gain is defined by transfer of electrons from the donor level to the unoccupied part of the valence band. We focus here on the fact that numerous electronic structure methodologies have overlooked some physical factors that could stabilize the insulating alternative, predicting instead false metals that do not really exist (note that this is in general not a physical phase transition, but a correction of a previous error in theory that led to a false prediction of a metal). Such errors include: (i) ignoring spin symmetry breaking, such as disallowing magnetic spin ordering in CuBi2O4 or disallowing the formation of polymorphous spin networks in paramagnetic LaTiO 3 and YTiO 3 ; (ii) ignoring structural symmetry breaking, e.g., not enabling energy-lowering bond disproportionation (Li-doped TiO 2 , SrBiO 3 , and rare-earth nickelates), or not exploring pseudo-Jahn–Teller-like distortions in LaMnO 3 , or disallowing spontaneous formation of ordered vacancy compounds in Ba 4 As 3 and Ag 3 Al 22 O 34 ; and (iii) ignoring spin–orbit coupling forcing false metallic states in CaIrO 3 and Sr 2 IrO 4 . The distinction between false metals vs real insulators is important because (a) predicting theoretically that a given compound is metal even though it is found to be an insulator often creates the temptation to invoke high order novel physical effects (such as correlation in d-electron Mott insulators) to explain what was in effect caused by a more mundane artifact in a lower-level mean-field band theory, (b) recent prediction of exotic physical effects such as topological semimetals were unfortunately based on the above compounds that were misconstrued by theory to be metal, but are now recognized to be stable insulators not hosting exotic effects, and (c) practical technological applications based on stable degenerate but gapped metals such as transparent conductors or electrides for catalysis must rely on the systematically correct and reliable theoretical classification of metals vs insulators.

36 MATERIALS SCIENCE↗

Biexciton and trion dynamics in InP/ZnSe/ZnS quantum dots

Transient absorption (TA) and time-resolved photoluminescence (PL) spectroscopies have been used to elucidate the hole tunneling and Auger dynamics in biexcitons and negative trions in high-quality InP/ZnSe/ZnS quantum dots (QDs). In a previous paper [Nguyen et al., J. Phys. Chem. C 125, 15405–15414 (2021)], we showed that under high-intensity photoexcitation, two types of biexcitons are formed: those having two conduction band electrons and two valence band holes (designated as an XX state) and those having two conduction band electrons, one valence band hole, and an additional trapped hole (designated as an XT state). In the present paper, we show that both types of biexcitons can undergo Auger processes, with those of the XT state being a factor of four to five slower than those of the XX state. In addition, the trapped holes can undergo tunneling into the valence band, converting an XT state to an XX state. The relative amplitudes of the fast (XX) and slow (XT) components are different in the TA and PL kinetics, and these differences can be quantitatively understood in terms of oscillator strengths and electron–hole overlap integrals of each state. XT to XX hole tunneling rates are obtained from the comparison of the XT state lifetimes with those of the negative trions. This comparison shows that the tunneling times decrease with decreasing core size and shell thickness. Furthermore, these times are about 2 ns for the thinnest shell red-emitting QDs and decrease to 330 ps for QDs that luminesce in the yellow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mixed Tin-Titanium Oxides by Atomic Layer Deposition on Planar Substrates: Physical and Electronic Structure

Ternary atomic layer deposition of Sn-doped TiO x (Sn:TiO x ) and Ti-doped SnO x (Ti:SnO x ) was performed using tetrakisdimethylamidotitanium (IV) and tin(IV) with water at 150 °C on (1 0 0) Si and quartz substrates. The physical structure of the films was investigated using scanning electron, atomic force, and Kelvin probe force microscopies as well as spectroscopic ellipsometry, Raman spectroscopy, and X-ray diffraction. All as-deposited films are amorphous and possessed flat and conformal topographies with low surface roughness (<1 nm). Annealed Sn:TiO x and Ti:SnO x crystallize into the tetragonal anatase TiO 2 and cassiterite SnO 2 structures, respectively, without large variations to the film topography. The chemical composition of the as-deposited and annealed films was investigated through X-ray photoelectron spectroscopy. While dopants are homogenously mixed, the ternary ALD to form Sn:TiO x and Ti:SnO x surprisingly does not follow the rule of mixtures, despite similarities in both the growth rates of binary SnO x and TiO x and the precursors used. This finding is also supported by spectroscopic ellipsometry. Here, we postulate the deviation from the rule of mixtures is due to non-ideal surface chemistry of the binary ALD of SnO x . The optical bandgap of all films was quantified by the Tauc analysis and the valence band position was investigated by valence band X-ray photoelectron spectroscopy. Intra-bandgap states above the valence band maximum were observed for as-deposited Ti:SnO x and Sn:TiO x and ascribed to 5 s states from Sn 2+ ions. The presence of these intra-bandgap states induces enhanced visible absorption and bathochromic shifts to the apparent bandgap for all as-deposited films. Annealing the films removes the intra-bandgap states and increases the optical bandgap. Simplified band diagrams created using the data available demonstrated that the conduction and valence band positions did not vary between the positions of pure TiO 2 or SnO 2 with monotonic increases to the dopant incorporation.

36 MATERIALS SCIENCE↗

Controlled Synthesis of SnO 2 Nanocrystals with Tunable Band Gaps

Tin(IV) oxide nanocrystals (SnO 2 NCs) have significant potential in various applications, with their performance closely related to their band gap. The band gap is influenced by the size and shape of the NCs, which can be precisely controlled by adjusting reaction conditions. In this study, we present deliberately designed synthesis protocols to produce high-quality SnO 2 NCs with tunable band gaps using different methods. Key factors affecting the synthesis include control of the oxidizing agent, reaction temperature, solvent selection, and reaction time optimization. The resulting NCs were characterized by using TEM, XRD, XPS, and optical spectroscopy. Notably, SnO 2 NCs synthesized by controlling the oxidizing agent (air injection) in a hot organic solution were smaller in size and exhibited abundant oxygen vacancies. In contrast, extending the reaction time or using ethanol as a solvent in hydrothermal systems facilitated larger spherical or rod-like SnO 2 NCs with fewer oxygen vacancies. Further analysis of the band gap and valence band maximum energy revealed that the abundant vacancies in SnO 2 NCs synthesized with the air-controlled hot organic solution method resulted in a narrower band gap and an upshifted valence band. These synthetic strategies illustrate the potential for deliberately designing SnO 2 NCs with optimized electronic structures for various applications.

band gap↗

Reversible Interfacial Charge Transfer and Delayed Emission in InP/ZnSe/ZnS Quantum Dots with Hexadecanethiol

The results in this paper show that holes are rapidly and reversibly transferred from red-emitting InP/ZnSe/ZnS quantum dots (QDs) to adsorbed hexadecanethiol (HDT) forming an equilibrium between the thiols and the QD valence band. Photoexcitation results in populations of holes in the valence band and in slightly higher-energy shell-localized traps. Trap to valence band hole tunneling results in a photoluminescence risetime having time constants varying from 300 ps to 2 ns. The presence of adsorbed HDT eliminates the slower risetime component, indicating that hole transfer from the shell-localized traps that are closest to the particle surface efficiently competes with tunneling to the QD core. This shows that the interfacial charge transfer equilibrium is established in less than 2 ns. The population of the shell-localized traps corresponds to a reservoir of hole states that eventually tunnel to the core-localized valence band, resulting in delayed emission. The amount of delayed emission increases rapidly with ZnSe shell thickness and is slightly blue-shifted from the prompt photoluminescence. We propose an energetic model in which the HDT/valence band equilibrium is affected by the extent of valence band quantum confinement and an electric field produced by core–shell interfacial dipoles. Furthermore, this model explains the core size, shell thickness, and photoluminescence (PL) wavelength dependence of this equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photoemission studies of wurtzite zinc oxide.

The electronic structure of wurtzite zinc oxide, investigated over the widest possible photon energy range by means of photoemission techniques, is described. Of particular interest among the results of the photoemission study are the location of the Zn 3rd core states, the width of the upper valence bands, and structure in the conduction-band and valence-band density of states.

Powell, R. A.↗

Comparison of interband related optical transitions and excitons in ZnGeN 2 and GaN

The optical dielectric function of ZnGeN 2 is calculated from the interband transitions using the energy bands calculated in the quasiparticle self-consistent (QS)GW^ method using two different levels of approximation: the independent particle approximation (IPA) and the Bethe-Salpeter Equation (BSE) approach. The first allows us to relate peaks in ε 2 to specific bands and k-points but does not include electron-hole interaction effects. The second includes electron-hole interaction or excitonic effects. The corresponding changes in the shape of ε 2 (ω) are found to be similar to those in GaN. The screened Coulomb interaction W^ is here calculated including electron-hole interactions in the polarization function and gives a band structure already going beyond the random phase approximation. The static dielectric constants including only electronic screening, commonly referred to as ε∞ , were calculated separately by extrapolating the wave vector dependent macroscopic dielectric function in the long-wavelength limit. Below the quasiparticle gap, we find three bound excitons optically active for different polarization. The convergence of these bound excitons with respect to the density of the k-mesh used in the BSE is studied and found to require a fine mesh. It is also found that these bound excitons originate from only the lowest conduction band and the top three valence bands. To incorporate the lattice screening, we include a scaling factor (ε∞/ε 0 ) 2 , which allows us to obtain exciton binding energies of the correct order of magnitude similar to those in GaN. Here, the excitons are related to each of the three fold split valence bands and the splittings of the latter are also studied as function of strain. Finally, a relation between the anisotropic effective masses and the valence band splitting is pointed out and explained.

36 MATERIALS SCIENCE↗

Machine Learning Chemical Guidelines for Engineering Electronic Structures in Half-Heusler Thermoelectric Materials

Half-Heusler materials are strong candidates for thermoelectric applications due to their high weighted mobilities and power factors, which is known to be correlated to valley degeneracy in the electronic band structure. However, there are over 50 known semiconducting half-Heusler phases, and it is not clear how the chemical composition affects the electronic structure. While all the n-type electronic structures have their conduction band minimum at either the Γ - or X -point, there is more diversity in the p-type electronic structures, and the valence band maximum can be at either the Γ -, L -, or W -point. Here, we use high throughput computation and machine learning to compare the valence bands of known half-Heusler compounds and discover new chemical guidelines for promoting the highly degenerate W -point to the valence band maximum. We do this by constructing an “orbital phase diagram” to cluster the variety of electronic structures expressed by these phases into groups, based on the atomic orbitals that contribute most to their valence bands. Then, with the aid of machine learning, we develop new chemical rules that predict the location of the valence band maximum in each of the phases. These rules can be used to engineer band structures with band convergence and high valley degeneracy.

36 MATERIALS SCIENCE↗

Electronic structure of chromium trihalides beyond density functional theory

In this work, we explore the electronic band structure of freestanding monolayers of chromium trihalides Cr X 3 , X = Cl, Br, I, within an advanced ab initio theoretical approach based on the use of Green's function functionals. We compare the local density approximation with the quasiparticle self-consistent GW (QS GW ) approximation and its self-consistent extension ( QS G W ^ ) by solving the particle-hole ladder Bethe-Salpeter equations to improve the effective interaction W . We show that, at all levels of theory, the valence band consistently changes shape in the sequence Cl → Br → I , and the valence band maximum shifts from the M point to the Γ point. By analyzing the dynamic and momentum-dependent self-energy, we show that QS G W ^ adds to the localization of the systems in comparison with QS GW , thereby leading to a narrower band and reduced amount of halogens in the valence band manifold. Further analysis shows that X = Cl is most strongly correlated, and X = I is least correlated (most bandlike) as the hybridization between Cr d and X p enhances in the direction Cl → Br → I . For CrBr 3 and CrI 3 , we observe remarkable differences between the QS GW and QS G W ^ valence band structures, while their eigenfunctions are very similar. We show that weak perturbations, like moderate strain, weak changes to the d - p hybridization, and adding small U , can flip the valence band structures between these two solutions in these materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Probing room temperature indirect and minimum direct band gaps of h-BN

Abstract Hexagonal boron nitride (h-BN) has attracted considerable interest as an ultrawide bandgap (UWBG) semiconductor. Experimental studies focused on the detailed near band-edge structure of h-BN at room temperature are still lacking. We report a direct experimental measurement of the near band-edge structure performed on h-BN quasi-bulk wafers via photocurrent excitation spectroscopy (PES). PES resolved the band-to-band transitions near M- and K-points in the Brillion zone (BZ), from which the room temperature indirect band gap of E g M K ∼6.02 eV, minimum direct bandgap at M-point of E g M = 6.36 eV and next lowest direct energy bandgap at K-point of E g K = 6.56 eV , have been simultaneously determined for the first time experimentally. The measured energy differences between K- and M-points in the conduction band minimum (CBM) and valence band maximum (VBM) are Δ E C M K = 0.54 eV and Δ E V M K = 0.34 eV, respectively, in good agreement with the calculation results. Significantly differing from its III-nitride wurtzite counterparts, in which only electrons and holes in the conduction and valence band extremes at the Γ-point are predominantly involved in the optical and transport processes, the results highlighted that charge carriers associated with both M- and K-valleys control to the optical excitation, recombination and charge transport processes in h-BN.

Physics↗

Generating Bright Emissive States by Modulating the Bandgap of Monolayer Tungsten Diselenide

Transition metal dichalcogenides (TMDs) are essential due to their fascinating electronic and optical properties, strong exciton binding energy, and layer-dependent bandgap. They can be tuned to function as a single-photon emitter, but the quantum yield of photoluminescence of single-layer WSe 2 is low. There is some evidence that a bright emissive state can be produced by introducing local defects through functionalization. In this paper we use spin-polarized periodic density functional theory (DFT) to study the effect of functionalization for the specific case of cyclic carbenes. We find that the simplest of these molecules, cyclopentadiene carbene (Cyc), binds to the surface by a covalent bond leading to a substantial change in the bandgap (1.24 eV compared to 1.64 eV for the pristine surface). Moreover, there are semiflat bands below the Fermi level that originate from σ bonding and the interaction between the lone-pair p orbitals on the carbon of Cyc that bonds with Se on the TMD. Cyc is found to form a Type IIa heterojunction before and after contact with the surface, where the “a” refers to ordering of the energy levels where the TMD levels have the larger splitting and “b” to the reverse. The effect of various electron-withdrawing and electron-donating groups on Cyc is investigated, and it is found that the direct bandgap and heterointerfaces can be chemically tuned with covalently bound functional groups. With an electron-withdrawing group (EWG) such as –CHO, –COCl, and –CN attached to Cyc, a Type III//Type IIa interface is formed, whereas all other EWGs used in this study form a Type IIa junction, before and after contact to the surface. The electron-donating groups (EDG) form Type Ib//Type Ia junctions, and in particular, we find that the system WSe 2 + Cyc-Me band structure consists of semiflat bands at valence band maxima localized on Cyc-Me and the conduction band minimum is coupled between the surface and functional group with a direct bandgap of 0.88 eV. Hence, we predict that the Cyc-Me-functionalized monolayer WSe 2 will produce a red-shifted bright emissive state. Furthermore, we also find that carbenes with the Cyc all-carbon ring have (1) a triplet ground state and (2) form covalent bonds to WSe 2 , while heterocyclic carbenes (1) have a singlet ground state and (2) do not form covalent bonds to WSe 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Resonant and bound states of charged defects in two-dimensional semiconductors

A detailed understanding of charged defects in two-dimensional semiconductors is needed for the development of ultrathin electronic devices. Here, we study negatively charged acceptor impurities in monolayer WS 2 using a combination of scanning tunnelling spectroscopy and large-scale atomistic electronic structure calculations. We observe several localized defect states of hydrogenic wave function character in the vicinity of the valence band edge. Some of these defect states are bound, while others are resonant. The resonant states result from the multi-valley valence band structure of WS$_2$, whereby localized states originating from the secondary valence band maximum at Γ hybridize with continuum states from the primary valence band maximum at K/K$^{\prime}$. Resonant states have important consequences for electron transport as they can trap mobile carriers for several tens of picoseconds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ballistic Electron Emission Microscopy of Metal/Group IV Interfaces

Ballistic electron emission microscopy and spectroscopy, together with related techniques, have been applied with great success to the study of buried interfaces. These probes, known collectively as BEEM, have yielded important information on interface transport, interface band structure, and carrier scattering, with lateral spatial resolution on the nanometer scale. Recent applications of the technique to polycrystalline metal/semiconductor interfaces have demonstrated an ability to spatially map both conduction band and valence band semiconductor structure. BEEM studies of epitaxial silicide/silicon interfaces have been particularly fruitful, as the rich silicide band structure results in complex and often surprising transport behavior...

Hecht, M. H.↗

Band Anticrossing in Highly Mismatched Compound Semiconductor Alloys

Compound semiconductor alloys in which metallic anions are partially replaced with more electronegative isoelectronic atoms have recently attracted significant attention. Group IIIN(sub x)V(sub 1-x) alloys with a small amount of the electronegative N substituting more metallic column V elements has been the most extensively studied class of such Highly Mismatched Alloys (HMAs). We have shown that many of the unusual properties of the IIIN(sub x)V(sub 1-x) alloys can be well explained by the Band Anticrossing (BAC) model that describes the electronic structure in terms of an interaction between highly localized levels of substitutional N and the extended states of the host semiconductor matrix. Most recently the BAC model has been also used to explain similar modifications of the electronic band structure observed in Te-rich ZnS(sub x)Te(sub 1-x) and ZnSe(sub y)Te(sub 1-y) alloys. To date studies of HMAs have been limited to materials with relatively small concentrations of highly electronegative atoms. Here we report investigations of the electronic structure of ZnSe(sub y)Te(sub 1-y) alloys in the entire composition range, y between 0 and 1. The samples used in this study are bulk ZnSe(sub y)Te(sub 1-y) crystals grown by either a modified Bridgman method or by physical vapor transport. Photomodulated reflection (PR) spectroscopy was used to measure the composition dependence of optical transitions from the valence band edge and from the spin-orbit split off band to the conduction band. The pressure dependence of the band gap was measured using optical absorption in a diamond anvil cell. We find that the energy of the spin-orbit split off valence band edge does not depend on composition and is located at about 3 eV below the conduction band edge of ZnSe. On the Te-rich side the pressure and the composition dependence of the optical transitions are well explained by the BAC model which describes the downward shift of the conduction band edge in terms of the interaction between localized Se states and the conduction band. On the other hand we show that the large band gap reduction observed on the Se-rich side of the alloy system is a result of an interaction between the localized Te level and the valence bands. This interaction leads to the formation of a Te-like valence band edge that strongly interacts with the light hole valence band. Calculations based on a modified k(sup dot)p model account for the reduction of the band gap and the large increase of the spin-orbit splitting observed in Se-rich ZnSe(sub y)Te(sub 1-y) alloys. We will also discuss the importance of these new results for understanding of the electronic structure and band offsets in other highly mismatched alloy systems.

Yu, Kin Man↗

Band Anticrossing in Highly Mismatched Compound Semiconductor Alloys

Compound semiconductor alloys in which metallic anions are partially replaced with more electronegative isoelectronic atoms have recently attracted significant attention. Group IIIN(x)V(1-x), alloys with a small amount of the electronegative N substituting more metallic column V elements has been the most extensively studied class of such Highly Mismatched Alloys (HMAs). We have shown that many of the unusual properties of the IIIN(x),V(1-x) alloys can be well explained by the Band Anticrossing (BAC) model that describes the electronic structure in terms of an interaction between highly localized levels of substitutional N and the extended states of the host semiconductor matrix. Most recently the BAC model has been also used to explain similar modifications of the electronic band structure observed in Te-rich ZnS(x)Te(l-x) and ZnSe(Y)Te(1-y) alloys. To date studies of HMAs have been limited to materials with relatively small concentrations of highly electronegative atoms. Here we report investigations of the electronic structure of ZnSe(y)Te(1-y) alloys in the entire composition range, 0 less than or equal to y less than or equal to 1. The samples used in this study are bulk ZnSe(y)Te(1-y) crystals grown by either a modified Bridgman method or by physical vapor transport. Photomodulated reflection (PR) spectroscopy was used to measure the composition dependence of optical transitions from the valence band edge and from the spin-orbit split off band to the conduction band. The pressure dependence of the band gap was measured using optical absorption in a diamond anvil cell. We find that the energy of the spin-orbit split off valence band edge does not depend on composition and is located at about 3 eV below the conduction band edge of ZnSe. On the Te-rich side the pressure and the composition dependence of the optical transitions are well explained by the BAC model which describes the downward shift of the conduction band edge in terms of the interaction between localized Se states and the conduction band. On the other hand we show that the large band gap reduction observed on the Se-rich side of the alloy system is a result of an interaction between the localized Te level and the valence bands. This interaction leads to the formation of a Te-like valence band edge that strongly interacts with the light hole valence band. Calculations based on a modified k p model account for the reduction of the band gap and the large increase of the spin-orbit splitting observed in Se-rich ZnSe(y)Te(l-y) alloys. We will also discuss the importance of these new results for understanding of the electronic structure and band offsets in other highly mismatched alloy systems.

Yu, Kin Man↗

Ultralow Thermal Conductivity, Multiband Electronic Structure and High Thermoelectric Figure of Merit in TlCuSe

The entanglement of lattice thermal conductivity, electrical conductivity, and Seebeck coefficient complicates the process of optimizing thermoelectric performance in most thermoelectric materials. Semiconductors with ultralow lattice thermal conductivities and high power factors at the same time are scarce but fundamentally interesting and practically important for energy conversion. In this work, an intrinsic p-type semiconductor TlCuSe that has an intrinsically ultralow thermal conductivity (0.25 W m -1 K -1 ), a high power factor (11.6 μ W cm -1 K -2 ), and a high figure of merit, ZT (1.9) at 643 K is described. The weak chemical bonds, originating from the filled antibonding orbitals p-d* within the edge-sharing CuSe 4 tetrahedra and long Tl-Se bonds in the PbClF-type structure, in conjunction with the large atomic mass of Tl lead to an ultralow sound velocity. Strong anharmonicity, coming from Tl + lone-pair electrons, boosts phonon-phonon scattering rates and further suppresses lattice thermal conductivity. The multiband character of the valence band structure contributing to power factor enhancement benefits from the lone-pair electrons of Tl + as well, which modify the orbital character of the valence bands, and pushes the valence band maximum off the Gamma-point, increasing the band degeneracy. The results provide new insight on the rational design of thermoelectric materials.

36 MATERIALS SCIENCE↗