Electronic structure properties of CuZn2InTe4 andAgZn2InTe4 quaternary chalcogenides

Cite as: J. Appl. Phys. 125, 155101 (2019); doi: 10.1063/1.5094628

View Online Export Citation CrossMarkSubmitted: 4 March 2019 · Accepted: 1 April 2019 ·Published Online: 16 April 2019

Wencong Shi, Artem R. Khabibullin, Dean Hobbis, George S. Nolas,a) and Lilia M. Woodsa)

AFFILIATIONS

Department of Physics, University of South Florida, Tampa, Florida 33620, USA

Note: This paper is part of the special topic on: Advanced Thermoelectrics. Guest Editors: Ryoji Funahashi, George Nolas,

and Lilia Woods.a)lmwoods@usf.edu and gnolas@usf.edu

ABSTRACT

Quaternary chalcogenides composed of earth-abundant and primarily nontoxic constituents are currently being explored for thermoelectricapplications. The representatives of this class, CuZn2InTe4 and AgZn2InTe4, have been synthesized, and here, we present a comparativestudy of their structure–property relations using first principles simulations. Our calculations show that the lattice structure for both materi-als is very similar in terms of characteristic atomic distances and lattice structures, which compare well with experimental data. The elec-tronic structure results indicate that both materials are direct gap semiconductors whose electron localization and charge transfer propertiesreveal polar covalent bonding in the lattice. The calculated phonon structure shows dynamic stability with unique vibrational properties foreach material.

Published under license by AIP Publishing. https://doi.org/10.1063/1.5094628

I. INTRODUCTION

Environmentally friendly routes and novel materials forrenewable energy production are at the forefront of research andpractical applications. Thermoelectricity has a unique place in thisquest. Thermoelectric (TE) phenomena rely on direct solid-statemechanisms, which include converting waste heat to electricalpower and cooling based on the consumption of electric energy.Efficient TE devices rely on materials with a large internal figure ofmerit defined as ZT = S2σT/κ, where S is the Seebeck coefficient, σis the electrical conductivity, and κ is the thermal conductivity.1–3

Most materials with large ZT, however, are semiconductors com-posed of toxic, expensive, and scarce elements. This may be prob-lematic for large scale devices; thus, the search for new materialssuitable for thermoelectricity has expanded to systems with earth-abundant and/or nontoxic constituents.4

Quaternary chalcogenides with benign and naturally abundantatoms have been identified as promising TE materials mostly dueto their low thermal conductivity arising as a result of a complexcrystal structure and anharmonic phonon scattering processes.5–11

These compounds can also accommodate different types ofdopants at various lattice sites that can be used for optimization ofelectronic and vibrational properties. The design of quaternary

chalcogenides via a cation cross-substitution, a method pioneeredin Refs. 12 and 13, has created a pathway for the synthesis ofseveral related chalcogenide classes that are of fundamental andpractical interest.

Materials with the general chemical composition I2–II–IV–VI4(I = Cu, Ag; II = Zn, Cd; IV = Si, Ge, Sn; VI = S, Se, Te) can befound in several types of crystal structures, including kesterite,stannite, wurtzite–kesterite, and wurtzite–stanite.14–16 Other qua-ternary chalcogenides with the chemical formula I–II–III–VI3(I = Na, K, Cu, Ag; II = Si, Ge, Sn, Pb; III = N, P, As, Sb, Bi; VI = S,Se, Te) synthesized in a bournonitelike lattice have also beenstudied.17–21 Experimental and computational studies have shownthat these systems can serve as templates for fundamental discover-ies in transport as well as applications in solar cell devices and ther-moelectricity among others.22–31

The above-mentioned materials can be derived via cationcross-substitutions from simpler, II–VI binary compositions.Additionally, starting from a II–VI zinc-blende structure, one mayobtain a new family of quaternary chalcogenides with the chemicalformula I–II2–III–VI4. This is a relatively unexplored class ofsystems with the majority of current reports focusing on theirsynthesis,32–34 and only very recently, studies have presented

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transport measurements for CuZn2InSe4, CuZn2InTe4, andCuCd2InTe4 that show low thermal conductivity and semiconduct-ing behavior that can be altered by doping.35,36

In this work, we present a comparative study includingsynthesis and computation of structure–property relations ofCuZn2InTe4 and AgZn2InTe4 quaternary chalcogenides. Using abinitio simulations based on density functional theory (DFT), thecrystal structures are calculated and compared with our experimen-tal results for polycrystalline specimens synthesized by direct reac-tion and solid-state annealing, as described previously.31 Theelectronic structure in terms of density of states (DOS), electronlocalization function (ELF), and charge transfer is analyzed inorder to understand the characteristic behaviors in these materials.Phonon band structure and phonon density of states (PDOS) arealso computed.

II. RESULTS AND DISCUSSION

A. Crystal structure

Quaternary compounds with the I–II2–III–VI4 composition(I = Cu, Ag; II = Zn, Cd; III = Ga, In; VI = S, Se, Te) are relativelyunexplored materials. The relations between the diversity of atomicconstituents and atomic structure are not established yet. It hasbeen reported that AgCd2GaS4 and AgCd2GaSe4 crystallize in anorthorhombic lattice with the space group Pmn21, which can becharacterized as a wurtzite-type lattice with tetragonal coordina-tion.32 Also, CuFe2InSe4, CuTa2InTe4, CuV2InSe4, and CuCo2InSe4have been reported with a sphaleritelike lattice with the I�42mtetragonal space group.33,34,37 In our previous results, it was foundthat CuCd2InTe4, CuZn2InTe4, and CuZn2InSe4 are synthesized ina modified zinc-blende structure with the F�43m space group.35,36

In this study, we synthesize polycrystalline CuZn2InTe4 andAgZn2InTe4. The specimens were weighed in the nominal composi-tions from the high-purity elements and were placed into a silicaampoule to be sealed in an evacuated quartz tube, before beingreacted in a furnace at 973 K for 7 days. The product was thenfinely ground, cold pressed, and placed in an evacuated quartz tubefor annealing at 773 K for 21 days. After annealing, the specimenswere finely ground, sieved through (325 mesh), and placed in acustom-built graphite die and molybdenum alloy TZM punchassembly for hot press densification. The structure and homogene-ity of the specimens were analyzed using powder x-ray diffraction(XRD) and energy dispersive spectroscopy (EDS). The XRD dataindicate that both specimens are phase-pure and form in themodified zinc-blende structure with the F�43m space group (seeFig. S1 in the supplementary material). Furthermore, the quanti-tative EDS data indicate that the specimens are very close tonominal composition and homogeneous.

The reported experimental structures are further investigatedusing first principles simulations with the DFT Vienna ab initioSimulations Package (VASP), which is a state of the art computa-tional tool based on the projector-augmented wave method that usesa plane-wave basis set and periodic boundary conditions.38,39 Theexchange–correlation energy was taken into account using the gener-alized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional and with the Heyd–Scuseria–Ernzerhof(HSE06) screened Coulomb hybrid density functional.40,41 The

HSE06 functional is expected to yield more accurate energy bandg-aps for semiconducting materials with strong p–d hybridizationwhen compared with experiments. Here, we present results for thedensity of states (DOS) for both functionals, which help us betterevaluate the role of electron correlations in the considered com-pounds. The convergence criteria for the atomic relaxationprocess are 10−5 eV (total energy criteria) and 10−4 eV Å−1 (forcecriteria). The starting conventional unit cell was reduced to theprimitive cell for the lattice with the F�43m space group, whichwas also allowed to change shape and volume during the relaxa-tion process. The energy cutoff in the calculations is 384 eVfor CuZn2InTe4 and 360 eV for AgZn2InTe4. Also, we use thetetrahedron integration method with Blöchl corrections with a12 × 12 × 12 k-point mesh for both structures. Spin orbit coupling(SOC) effects are also considered within GGA-PBE. Crystal struc-tures, electron localization functions (ELF), and charge transferare visualized using the VESTA software.42

The lattice structure of the synthesized compounds is found tobe zinc blende with the F�43m crystal symmetry. The conventionalcells for both materials are identical and are shown in Fig. 1, wherethe primitive cell is also denoted in the bottom left corner of eachpanel. The Wyckoff positions for the cation atoms (Cu, Ag, Zn, In)are at the 4a (0, 0, 0) site and the chalcogen atom (Te) is at the4c (0.25, 0.25, 0.25) site. In this arrangement, each Te atom is sur-rounded by cation atoms (Fig. 1). Using standard XRD methods, itis not possible to discern the specific positions that the cationatoms occupy, and they appear to be randomly distributed.Examining the lattice structure in Fig. 1 shows that the cationatoms have interchangeable locations, such that by simple transla-tions, the unit cell with In atoms in the corners can be mappedinto an equivalent unit cell with In atoms residing in the faces ofeach site interchanging locations with the Zn atoms. Similar obser-vations of location interchangeability are observed for all cationatoms. This situation makes the F�43m zinc blende structurallyquite interesting.

Our results for the lattice parameters and cation–chalcogennearest-neighbor atomic distances are summarized in Table I.As described above, the lattice sites (Wyckoff positions) are fixedin this structure, and, therefore, bond lengths cannot be varied,based on our XRD data, without reducing the lattice symmetry.From our theoretical analyses, we find that after relaxation,the lattice parameters for the Cu-based material are the samea = b = c; however, for the Ag-based chalcogenide, the a latticeconstant is obtained to be slightly bigger (by 0.01 Å) when com-pared to the b = c constants. This implies that the lattice has amodified zinc-blende (F�43m) structure whose cubic symmetry isapproximately preserved in AgZn2InTe4. It is also found that thelattice parameters for the AgZn2InTe4 are larger than the latticeparameters for the Cu-based compound, which is explained bythe larger size Ag atom as compared to the Cu atom. There isgood agreement between the experimental and computationalresults obtained via DFT-GGA, but the computational values areabout 1.5% and 2% larger than that from the experiment forCuZn2InTe4 and AgZn2InTe4, respectively.

Interestingly, the inclusion of SOC does not significantlychange the lattice parameters for CuZn2InTe4; however, forAgZn2InTe4, these are reduced by ∼1.9% for AgZn2InTe4 when

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compared with the values found via DFT-GGA. Actually, theDFT-GGA + SOC results for the AgZn2InTe4 lattice parametersagree very well with the experimental results, as shown inTable I. The bonds between a given cation and all four inequi-valent Te atoms are found to be the same, which is directlyrelated to the underlying cubic zinc-blende lattice. The Zn–Teand In–Te distances obtained via GGA are very similar for bothcompounds; however, the Ag–Te bonds are obtained to be∼0.17 Å larger than the Cu–Te bonds using DFT-GGA. TheSOC does not result in significant changes in the characteristiccation–chalcogen bonds with the exception of Ag–Te for whichthe GGA + SOC value is obtained to be 0.166 Å smaller than

the GGA value. We note that overall, both lattices are verysimilar, although the lattice constant in the Ag-based compoundis larger than the Cu-based material, and the Ag–Te bonds arelarger than the Cu–Te bonds, which is directly associated withthe different ionic radii of Cu and Ag.

B. Electronic structure

The electronic structure calculations for CuZn2InTe4 andAgZn2InTe4 are shown in Fig. 2, illustrating the obtained density ofstates results. Both materials are found to be semiconductors withdirect energy gaps, Eg, at the Γ point. Standard DFT-GGA yieldssimilar gaps for both systems with Eg = 0.262 eV for CuZn2InTe4and Eg = 0.269 eV for AgZn2InTe4, as shown in Figs. 1(a) and1(d). Including SOC reduces the gaps resulting in Eg = 0.163 eV forboth materials. Current research shows that standard DFT is inade-quate to correctly capture the magnitude of bandgaps for manysemiconductors, especially for chalcogenides characterized withstrong p–d hybridization around the Fermi level.43 DFT calcula-tions using hybrid functionals usually yield results that comparewell with experimental data. Our simulations with the HSE06hybrid functional show that the bandgaps at the Γ point becomeEg = 1.065 eV for CuZn2InTe4 and Eg = 1.121 eV for AgZn2InTe4,as shown in Figs. 1(c) and 1(d). This is consistent with Refs. 35and 36 as reported in our previous work, in addition to the increasein room-temperature resistivity observed for AgZn2InTe4 comparedto CuZn2InTe4.

Our analysis further shows that the DOS around the Fermilevel is mainly composed of the Cu (Ag) d states hybridized withTe p states in the valence range. There is also admixture betweenthe Cu (Ag) d states and In p states. In fact, the cation d state–chal-cogen p state composition characterizes the (−6, 0) eV region inthe DOS for both materials. The conduction band edge, on theother hand, is mainly composed of In s states and Te p states. Thestrong and well defined peak at approximately −7 eV, as shownin Figs. 2(a) and 2(d), is due entirely to Zn, which splits afterincluding SOC according to Figs. 2(b) and 2(e). Calculations viathe HSE06 hybrid functional show a significant shift (∼1.5 eV) inthe Zn peak toward lower values in the valence region for bothmaterials.

FIG. 1. Crystal structure for CuZn2InTe4and AgZn2InTe4. The unit cells contain-ing eight distinct atoms are also outlinedin the bottom left corner of each panel.

TABLE I. Summary of experimental and calculated lattice parameters a, b, and cand cation–chalcogen atom distances for CuZn2InTe4 and AgZn2InTe4 in Å.

Latticeparameters (Å)

CuZn2InTe4 AgZn2InTe4

Exp. GGAGGA +SOC Exp. GGA

GGA +SOC

a 6.15 6.24 6.24 6.24 6.37 6.25b 6.15 6.24 6.24 6.24 6.36 6.24c 6.15 6.24 6.24 6.24 6.36 6.24

Characteristic nearest-neighbor interatomic distances (Å)

Te1, Te2, Te3, Te4

Cations CuZn2InTe4 AgZn2InTe4

Cu GGA 2.601 …SOC 2.602 …

Ag GGA … 2.768SOC … 2.602

Zn1 GGA 2.688 2.690SOC 2.690 2.691

Zn2 GGA 2.689 2.696SOC 2.690 2.691

In GGA 2.839 2.849SOC 2.840 2.839

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C. Electron localization and charge transfer

The bonding in the materials is further studied by calcu-lating their electron localization function. Our results areshown in Fig. 3 for both materials. ELF takes typical values inthe range of 0 ≤ ELF ≤ 1 with ELF ≅ 1 corresponding to stronglocalization (red color) and ELF ≅ 0.5 corresponding to an elec-tron gas (green color). The chosen plane projection of theplots, below each panel in Fig. 3, provides information for theELF involving different cations and the chalcogen atom.Specifically, Fig. 3(a) shows one prospective view where theTe atom is surrounded by Cu, Zn, and In atoms. The intenselyred regions around Te characterize strong electron localization.The situation in Fig. 3(c) depicting ELF for Ag, Zn, In, andTe atoms is very similar. The projection views in Figs. 3(b)and 3(d) also reveal the strong electron localization around theTe atom as well as charge distribution around the cations remi-niscent of an electron gas.

Considering the shell structure of each atom, one findsthat to maintain charge neutrality within each material, the 4s1

electron from Cu (5s1 electron from Ag), the 4s2 electrons fromZn, and the 5s25p1 electrons from In are donated to fill up the5p4 shell of the Te atoms. The type of bonding for these materi-als can further be analyzed by examining the electronegativitydifferences ΔχA−Te = |χA− χTe| (where χA is the electronegativityof cation A and χTe is the electronegativity of Te)17,44,45 betweenthe atoms in each bond. Given that χCu = 1.9, χAg = 1.93,χIn = 1.78, χZn = 1.65, and χTe = 2.1, we find that ΔχCu−Te = 0.2,ΔχAg−Te = 0.17, ΔχIn−Te = 0.32, and ΔχZn−Te = 0.45. This is anindication of covalent bonds with different degrees of polarity.The unequal ability of the involved atoms in each bond to shareelectrons is reflected in the different values of Δχ, which will alsoresult in a dipole moment whose largest value is obtained for theZn–Te bond.

To further study the type of chemical bonding in these materi-als, we calculate the charge density difference, Δρ, between each

FIG. 3. Electron localization functionfor [(a) and (b)] CuZn2InTe4 and [(c)and (d)] AgZn2InTe4. The different pro-jections are shown at the right topcorner next to each panel. The atomiccomposition and ELF color scale arealso shown.

FIG. 2. Total and atomically projectedDOS plots for CuZn2InTe4 obtainedusing (a) standard DFT-GGA, (b) stan-dard DFT-GGA with SOC included,and (c) with HSE hybrid functional.Total and atomically projected DOSplots for AgZn2InTe4 obtained using(d) standard DFT-GGA, (e) standardDFT-GGA with SOC included, and (f )with HSE06 hybrid functional.

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cation and the rest of the lattice structure using Δρ = ρtot− (ρX +ρtot−X), where ρtot is the charge density of the material, ρX is thecharge density of the cation atom X = Cu, Ag, Zn, or In, and ρtot−Xis the charge density of the lattice structure without the cationX. The results are shown in different perspectives in Fig. 4, wherethe turquoise regions correspond to electronic depletion and theyellow regions correspond to charge accumulation. Our findings(Fig. 4) indicate that for both materials, the electrons are covalentlyshared between each cation and chalcogen atom. Each bond ischaracterized by the electrons being shifted toward the Te atom, thelargest shift obtained for the Zn–Te bond in both materials. This isalso consistent with the ELF results shown in Fig. 3. We also showresults for charge transfer associated with each atom computed viaBader analysis,46–48 given in Table II. The values for Δe for thecations and chalcogen atoms are a measure of the charge inside thesurrounding Bader volume. Similar trends are observed for bothmaterials, although bigger charge values are found for AgZn2InTe4. Ithas been suggested that ratios of Δe for atoms comprising a bond canbe used as an estimate of their oxidation states.49,50 For example, wefind that the average ratios are Δe(Cu):Δe(Zn):Δe(In):Δe(Te) = (− 1):(− 2):(− 3):2 for the Cu-based system; the same ratios are obtainedfor the Ag-based material using Δe(Ag) instead of Δe(Cu).This confirms that the computed oxidation states coincide with theoriginally assigned oxidation states of each atom, such that Cu+, Ag+,Zn2+, In3+, and Te2− are in two structures.

Our calculations show these quaternary chalcogenides arepolar covalent semiconductors since their crystal structures contain

only polar covalent bonds. These findings are consistent with thefact that many materials that belong to the III–V and II–VI binarycompounds, as well as others that have zinc-blende structure, havebeen characterized as covalent semiconductors.51–54

D. Phonon structure

The phonon band structure and phonon density of states(PDOS) are also calculated, and the results are shown in Fig. 5 forboth materials. CuZn2InTe4 and AgZn2InTe4 are found to bedynamically stable since there are no imaginary frequencybranches. There are small numerical inaccuracies around Γ forCuZn2InTe4 [Fig. 5(a)], which frequently occur in phonon simu-lations of many materials. Using the results in Figs. 5(a) and 5(c),the sound velocities for the longitudinal and transverse acousticmodes vLA, vTA are found by calculating the slopes of thelinear phonon dispersions starting at the Γ point. We obtainthat vLA = 3332 m/s and vTA = 1650 m/s for CuZn2InTe4 andvLA = 3185 m/s and vTA = 1729 m/s for AgZn2InTe4 showing thatthe sound velocities for these systems are quite similar.

Figures 5(a) and 5(b) also show that the lowest opticalphonon branches are in the (1,2) THz frequency range for bothmaterials; however, there is a greater degree of degeneracy forCuZn2InTe4. The atomically resolved PDOS indicates that thevibrations of all atoms in this region for CuZn2InTe4 [Fig. 5(c)] arecoupled, thus contributing to a broad peak centered at ∼1.6 THz.The atomically resolved PDOS for AgZn2InTe4 [Fig. 5(d)] showsthat the (1,2) THz frequency range is comprised of three peaks at∼1 THz, ∼1.4 THz, and ∼1.8 Hz with Ag almost exclusively con-tributing at ∼1 THz. Figure 5(d) further shows that the vibrationsof the different atoms in this optical range are much more decou-pled from each other when compared with the correspondingsituation in Fig. 5(c). There are also significant differences in thehigher optical range for both materials. For example, there is a gapat ∼4 THz frequency for CuZn2InTe4, which is not present inAgZn2InTe4, as seen in Figs. 5(c) and 5(d). In fact, in the (4,5.5)THz frequency range, the vibrations of the different atoms inCuZn2InTe4 are decoupled, as evident from the different PDOSpeak locations in Fig. 5(c), compared to the atomic vibrations inAgZn2InTe4 in which the phonon density of states peaks for thedifferent atoms coincide, particularly in the (4.5; 5) THz frequencyrange. These results indicate that AgZn2InTe4 should have a lower

FIG. 4. Charge transfer between eachcation and the rest of the network ofatoms for [(a) and (b)] CuZn2InTe4 and[(c) and (d)] AgZn2InTe4. The isosur-face value is 0.006 e/Bohr3.

TABLE II. Bader analysis of charge transfer for CuZn2InTe4 and AgZn2InTe4. Here,Δe = efinal− einitial, where einitial is the charge provided initially by the VASP pseudo-potential and efinal is the computed charge after relaxation.

Sites Δe for CuZn2InTe4 Sites Δe for AgZn2InTe4

Cu −0.204 Ag −0.285Te1 0.456 Te1 0.579Te2 0.549 Te2 0.570Te3 0.439 Te3 0.601Te4 0.437 Te4 0.600Zn1 −0.482 Zn1 −0.583Zn2 −0.482 Zn2 −0.591In −0.713 In −0.891

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thermal conductivity than CuZn2InTe4, as corroborated experimen-tally and shown in Fig. S2 of the supplementary material.

III. SUMMARY

In this paper, we present results for structure–property relationsof structurally related quaternary chalcogenides CuZn2InTe4 andAgZn2InTe4 synthesized with zinc-blende lattices. Our detailed firstprinciples simulations show that interatomic distances and latticeparameters are in good agreement with the experimental data. Theelectronic structure calculations reveal that both materials are directgap semiconductors, and hybridized DFT functionals need to be uti-lized that take into account electron correlation effects especiallyprominent in materials with strong p–d orbital hybridization aroundthe Fermi level. The in-depth analysis of the computed ELF andcharge transfer shows that the chemical bonding is mainly of polarcovalent character, suggesting that both materials can be classified aspolar covalent semiconductors. The calculated vibrational propertiesshow that these systems are dynamically stable with similar soundvelocities. The atomically resolved phonon density of states showproperties that are specific to each material’s vibrational modes withdecoupling in different ranges for the optical phonon modes. Thethermal conductivity of these materials is intrinsically low,AgZn2InTe4 being lower than that of CuZn2InTe4.

SUPPLEMENTARY MATERIAL

See the supplementary material for experimental data for powderXRD spectra and thermal conductivity for both materials.

ACKNOWLEDGMENTS

The authors acknowledge financial support from theU.S. National Science Foundation (NSF) under Grant No.DMR-1748188. D.H. and G.S.N. also acknowledge the II-VIFoundation Block-Gift Program. The use of the University of SouthFlorida Research Computing facilities is also acknowledged. The

authors thank H. Wang at Oak Ridge National Laboratory fortransport measurements.

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FIG. 5. Vibrational properties forCuZn2InTe4: (a) phonon band structureand (b) total and atomically resolvedphonon density of states. Vibrationalproperties for AgZn2InTe4: (c) phononband structure and (d) total and atomi-cally phonon density of states.

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J. Appl. Phys. 125, 155101 (2019); doi: 10.1063/1.5094628 125, 155101-7

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