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Article Cite This: Chem. Mater. 2018, 30, 3395−3409

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Ultralow Thermal Conductivity in Diamond-Like Semiconductors: Selective Scattering of Phonons from Antisite Defects Brenden R. Ortiz,*,† Wanyue Peng,‡ Lídia C. Gomes,§,# Prashun Gorai,†,∥ Taishan Zhu,§ David M. Smiadak,‡ G. Jeffrey Snyder,⊥ Vladan Stevanović,†,∥ Elif Ertekin,§ Alexandra Zevalkink,‡ and Eric S. Toberer*,†,∥ †

Colorado School of Mines, Golden, Colorado 80401, United States Michigan State University, East Lansing, Michigan 48824, United States § University of Illinois at Urbana−Champaign, Urbana, Illinois 61820, United States # National Center for Supercomputing Applications, Urbana, Illinois 61801, United States ∥ National Renewable Energy Laboratory, Golden, Colorado 80401, United States ⊥ Northwestern University, Evanston, Illinois 60208, United States

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‡

S Supporting Information *

ABSTRACT: In this work, we discover anomalously low lattice thermal conductivity (50 cm2/(Vs) at 300 °C) in Hg-containing systems, leading to predicted zT > 1.5 in Cu2HgGeTe4 and Cu2HgSnTe4 under optimized doping. In addition to introducing a potentially new p-type thermoelectric material, this work provides (1) a strategy to use the proximity of phase transitions to increase point defect phonon scattering, and (2) a means to quantify the power of a given point defect through inexpensive phonon calculations.

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Database (ICSD)30 has culminated in the identification of several new material classes for thermoelectric applications, including the n-type Zintl phases.38,39 Here, we focus on the ptype quaternary diamond-like semiconductors (DLS), another promising class of materials that consistently appears in our set of candidate thermoelectrics. The DLS are a chemically rich family of compounds that can be derived from the diamond silicon prototype via simple electron counting rules (i.e., Grimm−Sommerfeld rule).40 Figure 1 shows the derivation of the binary, ternary, and quaternary DLS from the diamond prototype. The diverse chemistry observed in the DLS is fundamentally tied to the number of cation mutations that preserve tetrahedral

INTRODUCTION Widespread application of the Material Genome Initiative (MGI) promises to revolutionize the discovery and realization of next-generation materials for a diverse set of applications including photovoltaics,1−9 batteries,1,2,10−20 catalysis,1,2,21−29 and thermoelectrics.1,2,30−37 Fundamental to the success of MGI-inspired approaches is the leveraging of computational material science and ab initio calculations to survey a broad chemical space for a desired suite of properties. Our prior work in thermoelectrics led to the development of a computationally efficient figure of merit, which can be evaluated in a highthroughput fashion.30,31 Our approach combines semiempirical analysis of experimental data and density functional theory (DFT) electronic structure calculations to predict complex, scattering-dependent transport coefficients (e.g., the intrinsic carrier mobility μ0 and lattice thermal conductivity κL). Our high-throughput search of the Inorganic Crystal Structure © 2018 American Chemical Society

Received: February 28, 2018 Revised: April 16, 2018 Published: May 2, 2018 3395

DOI: 10.1021/acs.chemmater.8b00890 Chem. Mater. 2018, 30, 3395−3409

Article

Chemistry of Materials

Figure 1. Zincblende, chalcopyrite, stannite, and kesterite structures are derivatives of the diamond lattice. Simple electron counting rules permit cation mutation so long as the net valence electron count is unchanged. All structures are tetrahedrally coordinated with a 1:1 cation:anion ratio (e.g., GaAs, ZnS, ZnSiP2, CuInSe2, Cu2ZnSnTe4). The quaternary DLS exhibit multiple cation ordering motifs (e.g., stannite and kesterite), which are in close energetic proximity to one another. As expected from the relative stability of the structures, the DLS can be particularly prone to cation disorder and antisite defects. For simplicity, we do not consider other modifications to the diamond lattice that preserve tetrahedral coordination but shift the unit cell away from the cubic and tetragonal Bravais lattices (e.g., wurtzite, wurtz-stannite).

coordination. Because of the flexibility of the cation sublattice, it is common to see multiple cation ordering motifs exist within close energetic proximity to each other.41 This is most evident in the quaternary systems, where the principle ordered variants stannite (I4̅2m) and kesterite (I4̅) rarely differ in total energy calculations by 10 meV/atom.42−47 Note that other cation orderings are observed in the literature, and alloys between the stannite and kesterite structures invoke nontrivial changes in atomic occupancies and ordering.48 Further, distinguishing between the kesterite and stannite structures without high-level structural characterization (e.g., neutron, resonant X-ray diffraction) can be difficult in cases where the elements share similar atomic numbers.41,49 The close proximity of multiple cation ordering motifs naturally extends to the concept of cation disorder. There is a plethora of experimental evidence from the photovoltaic community evidencing disorder and the impact on optical and electronic properties in the sulfide and selenide DLS (e.g., CZTS, CZTSe).50−58 While the photovoltaic community must often contend with disorder as a challenge (e.g., reduced carrier lifetime, recombination), there exists an opportunity to leverage the disorder within the quaternary DLS to impede phonon transport and reduce the lattice thermal conductivity. Despite heavy investment into CZTS and CZTSe by the photovoltaic community, DLS with heavier group IIB (e.g., Cd, Hg) elements and heavier chalcogenides (e.g., Te) have not been well characterized within other fields. The potential for strong point defect phonon scattering arising from increased disorder, combined with our prior high-throughput predictions,30 make the quaternary telluride DLS a particularly interesting search space for thermoelectric materials. To date, the thermoelectric community has seen limited success in bulk, polycrystalline DLS. The most notable exception is Si0.8Ge0.2, although the innately high lattice thermal conductivity and low anharmonicity of Si and Ge have required extensive materials engineering (alloying, nanostructuring, grain boundary engineering) to produce successful high-temperature thermoelectric modules.59−64 The literature is also ripe with studies investigating the thermoelectric properties of individual nanowires or nanodots,65−75 although such form factors are generally prohibitive for practical thermoelectric applications. Literature also predominantly focuses on the binary DLS, with comparatively infrequent mention of the ternary and quaternary analogues. Existing literature on some selenide

materials (e.g., Cu2FeSnSe4, Cu2CdSnSe4, Cu2ZnGeSe4) indicates that the quaternary materials do possess significantly reduced lattice thermal conductivity (∼1 W/mK at 300 °C) as compared to the binary and ternary counterparts.41,76−83 On average, the reduction of the lattice thermal conductivity is consistent with the introduction of more complex cells and the increased potential for disorder. Existing searches have failed to find any quaternary DLS with zT exceeding unity. Notable compositions include Cu2.15Co0.8Mn0.05SnS4 (zT ≈ 0.8, 500 °C), 81 Cu 2.10 Cd 0.90 SnSe 4 (zT ≈ 0.6, 425 °C), 77 and Cu2.2Fe0.6SnSe4 (zT ≈ 0.4, 475 °C).76 Current literature is heavily biased toward research on the selenide and sulfide DLS, with a dearth of telluride research. Additionally, there are no works that attempt to correlate chemistry with transport beyond a singular compound or alloy. In this work, we begin by performing a computational assessment of all DLS (>140 unique calculations) within the ICSD adhering to the diamond, zincblende, chalcopyrite, or stannite prototypes. Note that all calculations are uploaded to our open-access Web site www.tedesignlab.org. We find that the most promising candidates include a set of quaternary tellurides Cu2IIBIVTe4 (IIB: Zn, Cd, Hg) (IV: Si, Ge, Sn). As this series spans a wide enough chemical space to begin to resolve the connection between chemistry and transport, these nine materials will serve as our model system for this study. Experimentally, we observe that bulk samples of the DLS present as heavily doped p-type semiconductors with assynthesized carrier densities in the 1019−1021 cm−3 range. Some compounds exhibit relatively high hole mobilities (>50 cm2/ (Vs) at 300 °C) alongside exceptionally low lattice thermal conductivity ( 1.5 at 300 °C under optimized doping. A combination of high-temperature X-ray diffraction (XRD), synchrotron XRD, high-temperature resonant ultrasound spectroscopy (RUS), and high-temperature transport measurements indicates that cation disorder plays a fundamental role in the reduction of the lattice thermal conductivity in the Hgcontaining samples. In particular, the antisite defects HgCu and CuHg appear to possess unusually strong phonon scattering strength, significantly reducing phonon lifetimes when compared to the lighter Zn and Cd analogues. The propensity of these materials to form antisite defects between relatively 3396


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flowing argon to minimize oxidation. The elastic moduli were determined using the Quasar2000 CylModel software package. Hall effect and resistivity measurements were performed using the Van der Pauw geometry on a home-built apparatus.84 Measurements were conducted up to 300 °C under dynamic vacuum (5 μm) in size and are unlikely to contribute to the thermal conductivity appreciably (e.g., nanostructuring). All high-temperature XRD patterns can be found in Figures S8−S16. The Zn-containing compounds (Figures S8−S10) show a linear peak shift toward lower angles, consistent with the expected thermal expansion behavior. To a small extent, the Cd-containing compounds (Figures S11−S13) begin to exhibit nonlinear behavior at elevated temperatures. By far, however, the Hg-containing samples show the most nonlinear behavior. To visualize the high-temperature evolution of the structure, Figure 5 shows the peak shift for the (112), (220), (204),

Figure 4. Predicted thermoelectric performance (color) for the quaternary Cu2IIBIVTe4 DLS compounds using the single parabolic band (SPB) model at 300 °C. Compounds generally present as near degenerately doped (1020−1021 cm−3) p-type semiconductors. Experimentally realized zT with as-synthesized carrier concentration (black) is overlaid on the predictions. The improved zT in all Hgcontaining samples can be attributed to the significantly reduced lattice thermal conductivity, although the improvement in Cu2HgGeTe4 and Cu2HgSnTe4 is also due to improved electronic mobility. Optimization of zT will require an order of magnitude reduction in carrier density for the Hg-containing samples.

PGEC behavior in these samples. We first turn our attention to the connection between crystal structure, elastic properties, thermal transport, and phonon structure to understand the origins of the abnormally low lattice thermal conductivity in the Cu2IIBIVTe4 family of materials. Structure and Phase Transitions. The DLS are nominally ordered variants of the diamond prototype, although the literature is ripe with reports of native disorder, antisite defects, order−disorder transitions, and off-stoichiometry.50−58,99−103 The possibility of strong cation disorder may influence the strength of point-defect scattering in the DLS, particularly in the quaternary systems (greater number of cation combinatorics). As such, we begin by applying a combination of hightemperature diffraction and Rietveld analysis to characterize any structural features, which may explain the abnormally low lattice thermal conductivity exhibited by the DLS. As noted before, it can be nontrivial to distinguish between the stannite and kesterite structures via lab X-ray diffraction, particularly in cases where the Z-number of elements is similar (e.g., Cu−Zn disorder in CZTS or CZTSe). Consistent with our total energy calculations (Table S1), all members of the Cu2(IIB)(IV)Te4 family of materials are reported as stannite within the ICSD, although there are reports suggesting that both Cu2ZnGeTe4 and Cu2HgSnTe4 may possess hightemperature transformations to either wurtz-stannite or kesterite, consistent with a disordering process.100,101,103 Unlike CZTS or CZTSe, however, the Hg-containing samples should have the necessary Z-number contrast to resolve the subtle difference between the stannite and kesterite refinements. A powder sample of the most promising sample, Cu2HgGeTe4, was sent to Argonne National Lab (BM-11) for high-resolution synchrotron data. The associated Rietveld refinement and associated structural data can be found in Figure S7. The sample is predominantly Cu2HgGeTe4 with a minor ( 1.5 at 300 °C under optimized doping. The transport behavior of these compounds is reminiscent of the phonon-glass-electron-crystal concept, although the DLS possess markedly simpler structure when compared to most PGEC materials. A combination of high-temperature resonant ultrasound spectroscopy, high-temperature XRD, high-temperature transport, and synchrotron XRD suggests an abundance of antisite defects in the Cu2IIBIVTe4 family of materials. Likely driven by the energetic proximity of the stannite and kesterite cation orderings, the defects contribute strongly to the suppressed lattice thermal conductivity in the Hg-containing systems via point-defect phonon scattering. Remarkably, the seemingly high density of antisite defects does not appear to degrade the hole transport within these materials. Our investigation used phonon calculations to probe the strength of particular antisite defects by calculating the overlap integral between the atom-decomposed phonon density of states. This demonstrates the unusually strong point-defect scattering potential of HgCu and CuHg antisite defects, which qualitatively match our observations regarding the unusually low lattice thermal conductivity in Hg-containing systems. Thus, this work not only introduces a potentially relevant p-type thermoelectric material, but also provides strategies for harnessing shallow energy landscapes (e.g., energetic proximity of stannitekesterite) for reducing κL through point-defect phonon scattering.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b00890. Additional structural, computational, and experimental transport data to augment the results (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Brenden R. Ortiz: 0000-0002-1333-7003 Taishan Zhu: 0000-0001-9462-5666 3406


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