Chemical Tuning of Carrier Type and Concentration in a Homologous

Article pubs.acs.org/cm

Chemical Tuning of Carrier Type and Concentration in a Homologous Series of Crystalline Chalcogenides Tobias Schaf̈ er,† Philipp M. Konze,‡ Jonas D. Huyeng,† Volker L. Deringer,#,‡ Thibault Lesieur,† Paul Müller,‡ Markus Morgenstern,∥,§ Richard Dronskowski,*,‡,§ and Matthias Wuttig*,†,§ †

Institute of Physics IA, ‡Institute of Inorganic Chemistry, ∥Institute of Physics IIB, and §Jülich−Aachen Research Alliance (JARA-FIT and JARA-HPC), RWTH Aachen University, 52056 Aachen, Germany S Supporting Information *

ABSTRACT: Tellurium-based phase-change materials (PCMs) enable applications from optical and electronic data storage to thermoelectrics and plasmonics, which all demand precise control of electronic properties. These materials contain an unusually large number of vacancies: “stoichiometric” ones that stem from the chemical composition and “excess” vacancies that act like classical dopants. Here we show how both types of vacancies can be controlled independently in the solid solution Sn(Sb1−xBix)2Te4. We vary x in small steps over the entire compositional range and show that this has a profound effect on the material’s electronic nature: remarkably, we observe a change from p- to n-type conduction at x ≈ 0.7, solely controlled by composition. Our findings lead to a new compositionally (that is, chemically) tunable materials platform that enables precise control of electrical properties.

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phase (high resistance, “zero bit”) and a metastable rocksaltlike crystalline one (low resistance, “one bit”) by heating and quenching cycles. Further, extended heating of the metastable phases leads to structural reordering and results in stable, layered trigonal structures.18 The second aforementioned field where chalcogenides are used is thermoelectric power generation (waste-heat recovery).3 By construction, thermoelectric devices require both pand n-type materials, of which the former are generally more abundant. Materials are typically alloyed or nanostructured to lower the thermal conductivity (“electron crystal, phonon glass” concept; ref 19). Again, disorder in the crystalline phases has substantial impact on thermal transport,20,21 which is relevant for thermoelectric applications. Besides low thermal conductivity, a high Seebeck coefficient S and large electrical conductivity σ are mandatory: the carrier concentration (that influences all three quantities) must be chosen to yield a good trade-off. An important difference compared to data-storage applications (switching between amorphous and metastablecrystalline states) is that thermoelectric materials are chiefly used in their thermodynamically stable crystal phase. This is because the application exposes devices and materials to extended periods of high temperature. Finally, in recent years, several telluride compounds have been predicted and proven to develop topologically nontrivial

INTRODUCTION Chalcogenide materials enable a wealth of applications from digital data storage1,2 to thermoelectrics3 and topological insulators.4−6 In all these, a decisive role is played by the materials’ electrical conductivity, which is proportional to the concentration n of charge carriers and to their mobility μ. Ultimately, independent control of both properties would be highly beneficial for applications. In the field of data storage, rapidly evolving research is concerned with phase-change random access memory (PCRAM), a nonvolatile and fast memory technology.1,2,7−9 Many phase-change materials (PCMs) are quasibinary alloys of maingroup IV and V chalcogenides, such as the widely studied Ge2Sb2Te5 and GeSb2Te4 (often colloquially referred to as “GSTs”). These materials are semiconductors for which one would expect, due to stoichiometry,10,11 the Fermi energy EF to reside within the band gap. Experimentally, by stark contrast, they have been shown to be hole-conducting (p-type) degenerate semiconductors with EF pinned in the valence band. There is a large carrier concentration in the samples, which first-principles computations traced back to a self-doping mechanism.12,13 Besides, the materials are sensitive to disorder, which strongly influences carrier mobility. If carefully controlled, disorder can be exploited to tune electronic properties14−17for example, by annealing samples at different temperatures and thus inducing different degrees of ordering. Materials such as the “GST” family with many empty lattice sites (vacancies) are particularly suitable for this. In applications, PCMs are switched between an amorphous © 2017 American Chemical Society

Received: April 18, 2017 Revised: July 18, 2017 Published: July 24, 2017 6749

DOI: 10.1021/acs.chemmater.7b01595 Chem. Mater. 2017, 29, 6749−6757

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Chemistry of Materials or topologically insulating (TI) surface states.4−6,22−27 Here, bulk conductivity is regarded as a parasitic effect and neither pnor n-type bulk conductivity is desired, as both self-doping and disorder are unwanted sources of carriers. Hence, for TI-based devices, 26 doping approaches are employed to reduce conductivity in the bulk: the aim is different, but once more a careful control of the electronic nature is crucial to enable future applications. In this work, we move from the concept of disorder tuning known in the PCM community to a more general picture including ideas from thermoelectrics and TI research, and we show how chemical control (that is, varying the composition rather than physical parameters) is crucial to enable new properties. We synthesize and study the pseudoternary compounds Sn(Sb1−xBix)2Te4; the end members of this pseudoternary line (SnSb2Te4 and SnBi2Te4) have both been used in thermoelectrics and shown to develop TI surface states.28−31 By adjusting the chemical composition, we are able to continuously tune the electronic nature of the solid solution and, ultimately, to turn it from a p-type into an n-type conductor. This provides new general insight into chalcogenide materials and helps to realize a chemically tunable materials platform.

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RESULTS AND DISCUSSION Synthesis and Structure of Sn(Sb1−xBix)2Te4. The materials investigated here are heavier homologues of the aforementioned PCMs. One of the parent compounds, SnSb2Te4, is isostructural to GeSb2Te4 and similar in chemical and electronic properties.10,32−40 From there on, one may substitute the main-group V element, by moving to the heavier homologue, formally written as SnSb2Te4 + 2x Bi → Sn(Sb1 − x Bix)2 Te4 + 2x Sb

In a first step, we synthesized three powder samples, namely, SnSb2Te4 (x = 0), a material close to SnBiSbTe4 (x = 0.57 as determined by EDX), and SnBi2Te4 (x = 1), and investigated their structures. Sputter deposition initially yields rocksalt-like phases in all cases, and powder XRD patterns and refinement results are provided as Supporting Information (Figure S2 and Tables S1 and S2). As expected, the lattice parameter increases from 6.1906(4) Å (x = 0) via 6.224(5) Å (x = 0.5) to 6.3251(4) Å (x = 1). Upon heating, the samples transform to stable trigonal polymorphs (Figure 1a). Here, the in-plane lattice parameter a rises from 4.3158(1) Å via 4.3711(1) Å to 4.4085(1) Å, while the out-of-plane parameter c stays almost constant upon Sb → Bi replacement (to within 0.02 Å). This anisotropy can be explained by first-principles computations, showing that the octahedral distortion around Sn is lower in SnBi2Te4 than in SnSb2Te4 (due to the difference in ionic radii, Figure S1); in consequence, the height of the septuple-layer building block remains largely unchanged. The structures of the end members SnSb 2 Te 4 and SnBi 2 Te 4 agree well with literature data.33,35,39,41,42 No syntheses or structural data of rocksalttype SnBi2Te4 and of the intermediate phases have been reported to our knowledge. This transformation from a rocksalt-like metastable to a trigonal stable structure is in accord with previous observations for GeSb2Te4, which suggests similar principles for the occupation of the lattice. Assuming that GeSb2Te4, SnSb2Te4, and SnBi2Te4 are structurally analogous, one can infer the following occupancy of the crystalline unit cell: in the

Figure 1. (a) Structure models of metastable (lef t) and stable (right) Sn(Sb1−xBix)2Te4, with exemplary environments of Te shown as closeups. Sn, Sb, and Bi are dark gray, red, and blue, respectively; Te atoms are light gray, and an exemplary vacancy site on the rocksalt-like lattice is indicated (□). (b) Grazing-incidence XRD for the homologous series. The scans on the left represent the cubic “as-deposited” (that is, nonannealed) state, while the samples characterized on the right have been annealed to 325 °C. The Bi content increases from bottom (red; pure SnSb2Te4) to top (blue; pure SnBi2Te4). (c) Application of Vegard’s Law, comparing experimental volumes per formula unit Sn(Sb1−xBix)2Te4 (additional powder samples as open circles) to computed ones (Methods section).

metastable rocksalt-type phase, the anionic-like sublattice is fully occupied with Te atoms, whereas on the interpenetrating second sublattice, Sn, Sb, and Bi, as well as 25% vacancies are statistically distributed.43 A different way to describe the structure is as a dense stacking of {111} planes, of which every second is filled with Te, while those in between are occupied by Sn, Sb, Bi, and vacancies. Upon heating, the vacancies assemble into layers along {111}, concomitant with increased cation ordering.14,44 While this vacancy ordering proceeds continuously during heating, the rocksalt-to-trigonal transition is furthermore characterized by a displacement of the septuplelayers (yielding the long c-axis) and by a narrowing of the 6750


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state to another (“hopping”). This is known as Anderson localization and has been observed in PCMs.17,46 Both in the localized and delocalized transport regime, many PCMs have extremely low mobilities of the order of 0.2−25 cm2/(V s), which are more common for amorphous than for crystalline materials. There are two different mechanisms for vacancy formation in PCMs. We will, in the following, speak of “stoichiometric” and “excess” vacancies (Figure 2); the former term is used for the

vacancy layers. This causes the denser packing in the trigonal form (smaller volume in Figure 1c). This process can be directly tracked in XRD experiments. A capillary filled with nonannealed powder is heated step by step, and X-ray patterns are recorded at each temperature. SnSb2Te4, SnSbBiTe4, and SnBi2Te4 retain their metastable structure up to 280 ± 5, 270 ± 5, and 275 ± 5 °C, respectively, followed by a relatively sharp transition. Summarizing thus far, we synthesized Sn(Sb1−xBix)2Te4 by an alternating codeposition sputtering process. The samples initially have rocksalt-like structures and on annealing convert to stable trigonal phases. Our data so far suggest that Sn(Sb 1−x Bi x ) 2 Te 4 behaves similarly to the well-known GeSb2Te4 in terms of structure. The subsequent discussion will center on electrical data recorded on thin films (∼250 nm), rather than bulk samples. Therefore, thin-film samples were synthesized and verified to exhibit similar structure: grazing-incidence XRD patterns for the thin films (Figure 1b) agree well with powder-diffraction results (Figure S2) and evidence that rocksalt-like as well as trigonal structures were successfully produced along the entire line. We note in passing that the lattice parameter of the asdeposited thin-film samples varies slightly compared to that determined for the bulk powder, due to necessary adjustments in the production process; this is much less pronounced for the stable structures. To verify Vegard-like behavior, the experimentally determined cell volumes are shown in Figure 1c. We furthermore performed first-principles computations for structural models of the quasi-ternary series: the results are well in line with the thin-film data (Figure 1c) and discussed in the Supporting Information. In particular, no pronounced structural rearrangements were observed during computations: one can hence conclude complete mixing along the Sn(Sb1−xBix)2Te4 line; this holds for both the rocksalt and the trigonal phases and for all samples produced in this work. The composition of all samples was verified by EDX, yielding just a minor Te deficit independent of x (Figure S5). This is common for sputter-deposited PCMs.45 How Disorder and Doping Control Electronic Properties. So far, we have shown that Sn(Sb1−xBix)2Te4 is structurally similar to typical PCMs such as GeSb2Te4what, now, about the electronic nature of both material systems? As reported before, the electronic properties of PCMs are rather intricate and dominated by the distribution of vacancies. In the metastable phase, vacancies randomly occupy the cation lattice, but upon annealing they order into clusters or planes.14 This strongly influences the localization of the electronic wave function: ordered vacancy planes do not interrupt extended Bloch states in the crystal, but disordered vacancies do.14 Besides providing scattering centers, they can also generate localized states that mostly concentrate on the band edges. Localized states at the band edges are mostly known from amorphous semiconductors, but crystalline PCMs can feature localized states for at least the first 130 meV from the band edge.17 These localized states at the band edge alter the transport mechanism, from a Drude-like propagation of Bloch waves to a temperature-activated transport regime. While the former is the typical transport mechanism in metals, providing conductivity by nearly free electrons, the latter relies on carriers localized in the defect states. To participate in transport, those localized carriers either get thermally activated into a delocalized state, or the carrier tunnels from one localized

Figure 2. Simplified schematic of how disorder and self-doping control the electrical conductivity in crystalline PCMs. In the metastable phases (lef t), both stoichiometric and excess vacancies are present; they localize carriers, reducing the mobility μ (the stoichiometric vacancies dominate due to higher abundance). In the stable phases (right), vacancies arrange into well-ordered van der Waals gaps, and only the excess vacancies remain. This allows one to separate both “types” of vacancies and to study them independently.

empty cation sites arising directly from composition (on the cation sublattice of GeSb2Te4, one-quarter of the sites is empty). The formation of these in GeSb2Te4 was previously explained using chemical-bonding analyses:11 vacancy formation lowers EF, depleting previously filled, antibonding regions of the band structure. In addition, there are “excess vacancies”, less abundant in numbers, but it is those vacancies that cause ptype conductivity (approximately 1% of cation sites in GeSb2Te4 and GeTe; Supporting Information). The occurrence of excess vacancies is often referred to as “self-doping”: the material adjusts the number of carriers without external influence, and a self-doped solid often is insensitive to additional doping. Note that this is also irrespective of the sputtering process, which induces a minor Te deficiency (see above) which would intuitively be expected to lead to Te vacancies; instead, the formation of Ge vacancies is energetically much more favorable, resulting in p-type conductivity.12 6751


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each step. The results for SnSb2Te4 resemble earlier ones for GeSb2Te4.17 With each annealing step, the resistance drops further, and the temperature coefficient of resistivity (TCR = dρ/dT) gradually changes from temperature-activated insulator-like (TCR < 0, indicating Anderson localization) to metallike behavior (TCR > 0).47 Hall measurements at room temperature of the as-deposited state (point (A) in Figure 3), an intermediate (B), and a highly annealed one (C) reveal that the drop in resistivity (increase in conductivity) is solely due to increased mobility (from 0.1 to 13 cm2/(V s)), while the carrier concentration does not change considerably (Figure S3). This is consistent with previous findings for GeSb2Te4.17 In Figure 2, it would be visualized as a gradual ordering of stoichiometric vacancies. As expected for an Anderson-localized material, similar to GeSb2Te4, SnSb2Te4 shows low mobilities compared to typical crystalline materials.17 During annealing, both conductivity and crystal structure change but in a fundamentally different way. While the change from rocksalt to trigonal structure does not occur below 270 °C, the increase in conductivity progresses throughout the entire annealing process (Figure 3) without any specific correlation with structural changes. Both effects thus go back to separate processes, even though they are both linked to vacancy ordering. Compared to SnSb2Te4, the resistivity of SnBi2Te4 behaves very differently (Figure 3b): it shows only a moderate annealing effect, and its resistivity increases during annealing. However, again decoupling carrier concentration and mobility, one can establish an increase of mobility upon annealing (from 1.6 to 6.6 cm2/(V s); Figure S3). This remains in line with an ordering of stoichiometric vacancies that promotes mobility and eventually leads to a structural transition as well. But here, the increase in mobility is overcompensated by a severe reduction in carrier concentration, from 5 × 1021 cm−3 (A) to 7 × 1020 cm−3 (C) at room temperature. This might stem from the excess vacancies being metastable upon annealing and hence a synchronous and countervailing tuning of carriers and mobility. Anderson physics and its relief by annealing play a role in both SnSb2Te4 and SnBi2Te4 as indicated by the low mobilities; however, the initially high number of carriers in SnBi2Te4 overshadows this effect by pushing the Fermi-level deep into the band. As stated above, the thin-film samples have a thickness of around 250 nm, and in principle finite-size effects can influence electronic property measurements. However, even for our highest-mobility samples, the mean free path stays well below 2 nm, more than 2 orders of magnitude below the film thickness. Our samples can therefore be regarded as bulk-like in terms of transport properties. Tuning Carrier Concentration, the Chemical Way. To decouple the influence of both vacancy types, we next aim to vary the number of excess vacancies only. All compounds under study have isovalent IV1V2VI4 compositions, so the concentration of stoichiometric vacancies is constant. As shown in Figure 4a, the resistivity of the as-deposited samples (purple) continuously decreases with increasing Bi content, and the initial mobility of SnBi2Te4 is 16× that of SnSb2Te4 as discussed before. The TCR becomes less insulating-like at the same time; it is therefore obvious that the ordering of stoichiometric vacancies plays an important role.

A different perspective on the effect of excess vacancies is that they shift the Fermi energy EF into one band (for p-type materials, the valence band). This renders the material a degenerate semiconductor, which in turn generates carriers. Both views describe the same underlying phenomenon despite focusing on different aspects. The two “types” of vacancies are encoded by separate colors in Figure 2, although it is of course impossible to assign an individual vacancy to one “type”; all implications of the diagram should be in a statistical manner. While only excess vacancies (green) provide carriers, all vacancies may serve as scattering centers if randomly distributed. Due to their overwhelming number, stoichiometric vacancies (purple) govern disorder and localization and hence mobility in the metastable phase. During annealing, the stoichiometric vacancies order into planes, enhancing mobility. Eventually, upon transition to the stable phase, the vacancies form vdW gaps which renders them irrelevant for mobility tuning. Consequently, there are two approaches to tailor conductivity: either to control the mobility by changing the ordering17 and/or number45 of stoichiometric vacancies or to vary the number of excess vacancies and hence carrier concentration. An approach for the latter is presented in the following. Figure 3 shows the resistivity during annealing of the parent compounds SnSb2Te4 and SnBi2Te4. In this experiment, the same sample has been heated to progressively higher temperatures and cooled down to room temperature after

Figure 3. Resistivity of the stoichiometric end members during progressive annealing. The resistivity of SnSb2Te4 (a) decreases upon stepwise annealing at increasingly large temperatures, similar to Ge− Sb−Te PCMs (see text). By contrast, that of SnBi2Te4 (b) stays almost constant. 6752


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Figure 4. Changes in electronic properties with chemical composition. (a) Electrical resistivity at 300 K with increasing Bi content for asdeposited cubic (purple) and annealed trigonal (green) samples. (b) Temperature coefficient of resistivity (TCR) for as-deposited and annealed samples at 300 K, respectively. A positive value indicates metal-like behavior (resistivity rising with temperature), while negative values point toward a temperature-activated conduction mechanism.

Figure 5. Experimental verification of the p-to-n transition. For the annealed homologous series, measurements are reported of (a) Hall carrier concentration nH, (b) Seebeck coefficient S, and (c) location of the Fermi energy, EF, as calculated from S. In the latter case, negative values indicate that EF is located in the valence band. Data measured at room temperature (green) and low temperature (gray) are shown.

We are here concerned with compositional, chemical control, and it is therefore desirable to eliminate the influence of vacancy disorder (which overshadows the role of the less abundant excess vacancies). For this, the annealed samples in their stable phase are more promising subjects of study: here, no “stoichiometric vacancies” can hamper the mobility (Figure 2, right). In this case, lower resistivity is seen at both ends of the stoichiometric line than in the mixed region (green in Figure 4a). The end members exhibit a metal-like TCR, while samples at intermediate x show insulator-like resistivity. Resistivity values alone cannot disentangle the influence of disorder from a change in number of carriers. Therefore, Hall and Seebeck effect measurements are needed for deeper insight (Figure 5). While SnSb2Te4 is hole-conducting (p-type) with a high carrier concentration on the order of 1021 cm−3, SnBi2Te4 is an electron conductor (n-type) with comparable carrier density, and hence the majority carrier type changes at an intermediate composition (around x = 0.7). We discuss these three regions in sequence, beginning with the p-type one (0 ≤ x ≪ 0.7). Starting from p-type SnSb2Te4 and moving to larger x, the number of carriers decreases as does the conductivity. Interpreting this in the framework of Figure 2 suggests a reduction in “excess vacancies” by Bi introduction. Roomtemperature and low-temperature Hall data are nearly superimposable: together with absolute values of 1020−1021 cm−3, this is typical for degenerate semiconductors. This indicates that the Fermi energy of the semiconducting material has been shifted into the valence band. Almost no carriers are generated by increasing the measurement temperature; hence the transport is not temperature-activated, as already indicated by

the TCR (Figure 4b). A Drude-like transport model is indeed suitable here. Location of the Fermi Energy. So far, the location of the Fermi energy has been inferred qualitatively, but Seebeck measurements (Figure 5b) can also provide a direct, quantitative determination of EF in a Drude-like regime. In the textbook case of EF in a single isotropic parabolic band, the Seebeck coefficient S can be used to calculate EF using |S | =

kB π 2 ⎛ 3 ⎞k T ⎜ + γ⎟ B ⎝ ⎠ |EF | e 3 2

where γ is chosen depending on the scattering mechanism (the most common values chosen are γ = −1/2 for acoustic phonons and γ = +1.5 for ionized impurities). As the temperature dependence of resistivity and Seebeck coefficient in our materials is metal-like (Figure 6), the scattering at room temperature is dominated by phonons, and γ = −1/2 was chosen accordingly.48 The overall term in parentheses in the above equation is positive, and so the absolute Seebeck coefficient rises with increasing temperature. Starting from SnSb2Te4 and adding Bi, the magnitude of S rises, indicating a reduction in carrier concentration. The temperature dependence of this allows additional insight: in metals (and well-ordered degenerate semiconductors), S increases with temperature. This is visible here as well, justifying the model introduced above to calculate EF. As 6753


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semiconductors. Additionally, the carrier concentration at x ≈ 0.7 follows the trend of the surrounding compositions only at low temperatures. By contrast, at room temperature, the carrier density exceeds that in Bi-richer samples. This might be due to the excitation of carriers into a second band, so that electrons and holes compensate in the Hall signal, which requires a small band gap. In fact, estimates from the Seebeck coefficient point to 60−90 meV (Supporting Information), which agrees with findings in the related materials series (Sb,Bi)2Te3.24,49−51 The data in direct vicinity of the transition show remarkable features in the Seebeck coefficient as well. The temperature coefficient decreases with temperature, suggesting a transition from the degenerate to the nondegenerate case or disorder localizing the carriers at reduced temperatures. The Seebeck coefficient of insulators drops with increasing temperature as their carrier densities rise. Although the standard reasoning here is made for band insulators, the predictions likewise hold for Anderson insulators.52,53 Additionally, the magnitude of the Seebeck coefficient is lower than expected from neighboring compositions. This coincides with the overestimated Hall carrier concentration and might be an additional sign of a twochannel transport, where both electrons and holes participate (and partly cancel each other) in Hall and Seebeck coefficients. Recalling the low mean free path (1(Bi2Te3)m=1 compounds. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 245145. (31) Menshchikova, T. V.; Eremeev, S. V.; Chulkov, E. V. Electronic structure of SnSb2Te4 and PbSb2Te4 topological insulators. Appl. Surf. Sci. 2013, 267, 1−3. (32) Matsunaga, T.; Yamada, N. Structural investigation of GeSb2Te4: A high-speed phase-change material. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 104111. (33) Talybov, A. G. Electron diffraction study of the structure of SnSb2Te4. Sov. Phys. Crystallogr. 1961, 6, 40−44. (34) Agaev, K. A.; Talybov, A. G. Electron-Diffraction Analysis of the Structure of GeSb2Te4. Sov. Phys. Crystallogr. 1966, 11, 400−402. (35) Zhukova, T. B.; Zaslavskii, A. I. Crystal structures of the compounds PbBi4Te7, PbBi2Te4, SnBi4Te7, SnBi2Te4, SnSb2Te4, and GeBi4Te7. Sov. Phys. Crystallogr. 1972, 16, 796−800. (36) Mao, Z. L.; Chen, H.; Jung, A. l. The structure and crystallization characteristics of phase change optical disk material Ge1Sb2Te4. J. Appl. Phys. 1995, 78, 2338−2342. (37) Karpinskya, O. G.; Shelimova, L. E.; Kretova, M. A.; Fleurial, J. P. An X-ray study of the mixed-layered compounds of (GeTe)n(Sb2Te3)m homologous series. J. Alloys Compd. 1998, 268, 112− 117. (38) Shelimova, L. E.; Karpinskii, O. G.; Kretova, M. A.; Kosyakov, V. I.; Shestakov, V. A.; Zemskov, V. S.; Kuznetsov, F. A. Homologous series of layered tetradymite-like compounds in the Sb-Te and GeTeSb2Te3 systems. Inorg. Mater. 2000, 36, 768−775. (39) Oeckler, O.; Schneider, M. N.; Fahrnbauer, F.; Vaughan, G. Atom distribution in SnSb2Te4 by resonant X-ray diffraction. Solid State Sci. 2011, 13, 1157−1161. (40) Volker, H. Disorder and electrical transport in phase change materials, Dissertation, RWTH Aachen University, 2013. (41) Kuznetsova, L. A.; Kuznetsov, V. L.; Rowe, D. M. Thermoelectric properties and crystal structure of ternary compounds in the Ge(Sn,Pb)Te−Bi2Te3 systems. J. Phys. Chem. Solids 2000, 61, 1269− 1274. (42) Karpinskii, O. G.; Shelimova, L. E.; Kretova, M. A.; Avilov, E. S.; Zemskov, V. S. X-ray Diffraction Study of Mixed-Layer Compounds in the Pseudobinary System SnTe−Bi2Te3. Inorg. Mater. 2003, 39, 240− 246. (43) A numerical prediction of defect concentrations, including antisite defects and vacancies, would be of interest but requires much further computational effort, including at minimum the treatment of charged defects and likely that of defect complexes. 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