Manipulating the Bulk Band Structure of Artificially Constructed van

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Manipulating the bulk band structure of artificially constructed van der Waals chalcogenide heterostructures Yuta Saito, Kotaro Makino, Paul Fons, Alexander V. Kolobov, and Junji Tominaga ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b04450 • Publication Date (Web): 26 Jun 2017 Downloaded from http://pubs.acs.org on June 27, 2017

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ACS Applied Materials & Interfaces

Manipulating the bulk band structure of artificially constructed van der Waals chalcogenide heterostructures Yuta Saito∗, Kotaro Makino, Paul Fons, Alexander V. Kolobov, and Junji Tominaga

Nanoelectronics Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 5, 1-1-1 Higashi, Tsukuba 305-8565, Japan

KEYWORDS. Topological insulator, chalcogenide heterostructure, layered compound, density functional theory, switching device.

ABSTRACT

The bulk band structures of a variety of artificially constructed van der Waals chalcogenide heterostructures IVTe/V2VI3 (IV: C, Si, Ge, Sn, Pb; V: As, Sb, Bi; VI: S, Se, Te) have been systematically examined using ab initio simulations based on density functional theory. The crystal structure and the electronic band structure of the heterostructures were found to strongly depend on the choice of elements as well as the presence of van der Waals corrections. Furthermore, it was found that the use of the modified Becke-Johnson local density approximation functional demonstrated that a Dirac cone is formed when tensile stress is applied to a GeTe/Sb2Te3 heterostructure and the band gap can be controlled by tuning the stress. Based on these simulation results, a novel electrical switching device using a chalcogenide heterostructure is proposed.

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INTRODUCTION Topological insulators are insulators with an energy band gap in the bulk and yet possess conductive surface or edge states protected by time reversal symmetry.1 After the theoretical prediction of the presence of this new phase of matter,2 and subsequent experimental confirmation,3-5 extensive research has been carried out to reveal the fundamental properties of topological insulators leading to novel functional devices being proposed to exploit their exotic properties.6-8 On the other hand, since the unusual properties of topological insulators are limited to surface or edge states, it is difficult to use them for applications. For instance, a nondissipative surface current can be hidden by a larger current due to carriers associated with bulk defects. In order to effectively utilize the attractive properties of topological insulators in bulk form, a promising technique is to fabricate a film consisting of alternately stacked layers of a topological insulator and a normal insulator, where each interface plays the role of generating a nontrivial electronic state, resulting in the enhancement of topological insulating properties.9,10 Recently, two dimensional (2D) materials have attracted a great attention for the realization of novel devices beyond graphene.11 A van der Waals (vdW) heterostructure of different 2D materials is one possible way to realize such novel devices using the unique properties of the constituent materials.12-17 Since 2D materials have strong chemical intralayer bonds but show weak interaction between layers, the usual constraint of lattice mismatch, which often leads to challenges in fabricating compound semiconductor heterostructures, is not crucial, and investigations of a large number of new combinations of different materials are feasible. Representative topological insulators, such as Bi2Se3, Bi2Te3 and Sb2Te3, are also layered compounds, where chalcogen atoms (Se, Te) terminate a layer at the van der Waals gap.18


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GeTe/Sb2Te3 superlattice structures have been developed to replace conventional Ge-Sb-Te ternary alloys for use in phase change random access memory (PCRAM). PCRAM is a promising candidate for next-generation non-volatile memories19 and this superlattice-based memory exhibits improved device performance in areas such as power consumption, switching speed, and cyclability.20 Subsequent to the use of superlattices for memory applications, it was realized that the superlattice memory structure consisted of alternate stacking of a topological insulator and a normal insulator. Unusual physical properties have been reported from these superlattices experimentally21-23 and they were speculated to be related to the topological insulating nature of the constituent layers and this speculation was supported by theoretical predictions of this material being a Dirac semimetal with a gapless Dirac cone in the bulk state.24,25 In spite of the promise of such exotic properties, the current state of knowledge of appropriate compositions is limited,26 and feasibility studies of different superlattice materials are required for future device applications. In this paper, a systematic study of the crystal structures and corresponding electronic band structures of IVTe/V2VI3 (IV: C, Si, Ge, Sn, Pb; V: As, Sb, Bi; VI: S, Se, Te) chalcogenide heterostructures have been comprehensively evaluated based on ab initio density functional theory (DFT) simulations. We reveal that the crystal structure as well as electronic band structure strongly depend on the choice of elements and in addition the effects of van der Waals corrections were also systematically examined. Furthermore, the modified Becke-Johnson (MBJ)-local density approximation (LDA), which allows for more accurate band gap predictions, was used for a GeTe/Sb2Te3 heterostructure as a function of external stress. Based on these results, a switching device based upon a GeTe/Sb2Te3 heterostructure, which exploits the properties of the Dirac cone, is proposed.


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EXPERIMENTAL SECTIONS The ab initio density functional theory (DFT) code CASTEP was used for carrying out the structural relaxation of hypothetical chalcogenide heterostructures.27 The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) was used.28 A 7×7×2 Monkhorst-Pack grid was utilized for Brillouin zone integrations along with ultrasoft pseudopotentials; a cut-off energy of 230 eV was used.29 The effects of van der Waals forces on a hypothetical chalcogenide heterostructure were examined by inclusion of the DFT-D correction proposed by Tkatchenko and Scheffler (TS).30 The WIEN2k code was used for all electronic structure simulations; an augmented plane wave basis was utilized.31 A value of RMTKmax = 7.0 was used for the planewave component between augmentation spheres. (8×8×1) Monkhorst-Pack grids were used for Brillouin zone integrations based upon a convergence study carried out using29 a GeTe/Sb2Te3 heterostructure. As can be seen in Figure S1 (Supporting Information), both the total and Fermi energies showed higher values for smaller k point grids and converged with increasing k. It was found that k = 10 (8×8×1) was sufficient for reliable simulations, so all simulations was carried out using this grid. The energy convergence criterion used was 0.1 mRy. Spin-orbit coupling (SOC) effects were included to clarify the effect of relativity on the band structure. Figure 1a shows a model structure of a IVTe/V2VI3 heterostructure and Figures 1b, c, and d show views along the x-, y- and z-axes, respectively. The blue framework represents the unit cell. In this work, a heterostructure with the so-called inverted Petrov structure25 with a c-axis stacking sequence -VI2-V-VI1-Te-IV-IV-Te-VI1-V-VI2- was considered as is shown in Figure 1a because this structure was reported to show a topologically non-trivial Dirac semimetal-like band structure. The group VI atoms assume two different positions and are indicated by the symbols VI1 and VI2; the atoms are located at the van der Waals gap and at the center of the quintuple


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layer (QL, VI1-V-VI2-V-VI1), respectively. The space group (SG) of the heterostructure was 164 (P3m1) and the lattice constants were defined as a and c in the hexagonal representation. This structure can be viewed as one V2VI3 QL intercalated by two IVTe layers, leading to the speculation that topological insulating properties may be present. Even though there have been no reports that As2S3 (SG: 14), As2Se3 (SG: 14), As2Te3 (SG: 12), Sb2S3 (SG: 62), Sb2Se3 (SG: 62), and Bi2S3 (SG: 62) assume a quintuple layered structure (SG: 166) and different crystal structure in the bulk, here we speculate that the QL structure may be metastable in thin film form32. Recently, rhombohedral Sb2Se3 was theoretically predicted to be a topological insulator.33 Furthermore, even though the electronic structures of two-dimensional IV-VI mono chalcogenides have been reported, the model structures used in those works are different from those used in the current study.34

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Figure 1. (a) Model structure for the chalcogenide heterostructure, where V represents As, Sb, or Bi, and VI1 and VI2 shows S, Se, or Te. View along (b) x axis, (c) y axis, and (d) z axis.


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RESULTS AND DISCUSSION The lattice parameters and bond lengths of the relaxed IVTe/V2VI3 heterostructures are summarized in Figures 2a-e. The lattice constant a was found to increase with increasing atomic number, e.g. from carbon to lead when the choice of V2VI3 compound was fixed or from sulfide to telluride when the choice of IVTe was fixed (Figure 2a), whereas the c values were scattered and did not show a clear dependence on atomic number (Figure 2b). This will be discussed later. The IV-Te bond lengths were found to strongly depend on the choice of the IVTe compound, but showed little dependence on the choice of the V2VI3 compound (Figure 2c). This indicates that the choice of IVTe compound dominates the bond lengths rather than the surrounding V2VI3 QL. Figure 2d shows the VI1-V bond lengths. Contrary to the trend seen in Figure 2c, these bond lengths only showed a weak dependence on the choice of IVTe compound, but increased with increasing atomic number of the V2VI3 compound. The Te-VI1 bond length corresponds to the van der Waals (vdW) gap distance (Figure 2e) and showed strong scatter similar to the c axis values. A clear linear correlation between c and the vdW gap can be seen in Figure 2f, where c increases with increasing Te-VI1 bond length. This result supports the premise that the vdW gap largely determines the lattice constant c. In Figure 2f, results without the DFT-D vdW correction are also shown for comparison. It can be clearly seen that the vdW gap as well as the values of c are distributed over a much wider range, some of the values of which are unrealistic for bond lengths. These results indicate that the DFT-D correction is crucial for the proper simulation of van der Waals heterostructures. Other bond lengths as a function of the choice of compound are summarized in Figure S2. It was found that the effect of DFT-D was more pronounced in heterostructures containing heavier elements such as PbTe, the results being consistent with a


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previous report.35 We also have performed phonon calculations for several heterostructures in order to investigate the stability of artificially constructed heterostructures. The results are shown in Figure S3. It was found that the phonon density of states of the three selected heterostructures did not possess imaginary modes indicating the structures are dynamically stable. Further studies for other heterostructures will be a topic of future work.

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Figure 2. Lattice constants (a) a and (b) c for various heterostructures. Bond lengths of (c) IV-Te, (d) VI1 -V, and (e) Te-VI1 . (f) Correlation between the lattice constant c and the Te-VI1 bond length at van der Waals gap. The effect of DFT-D correction was compared.


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In order to investigate the effects of SOC on the electronic structure of the chalcogenide heterostructure, band structure simulations were carried out. A GeTe/Sb2Te3 heterostructure is chosen here as an example and the DFT-D correction is not included here. The effect of DFT-D on the electronic structure is discussed in the next paragraph. Figure 3a shows a schematic of the Brillouin zone of the heterostructure along with the associated high symmetry points. Figures 3b and 3c show simulated band structures without and with SOC, respectively. It can be seen that the overall band structures look similar, however significant differences can be found in the vicinity of the Γ point. It was found that including SOC resulted in the closing of the bandgap at the Γ point (Figure 3d), a feature found in topological insulators, where the band closing occurs as a result of inclusion of the SOC term. Such linear dispersion of the band structure is referred to as a Dirac cone. Therefore, hereafter, all band simulations were carried out with the SOC term.

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Figure 3. (a) Schematic Brillouin zone of the heterostructure. Band structures of a GeTe/Sb 2 Te 3 heterostructure simulated (b) without and (c) with SOC. (d) Comparison of the band structures around the Γ point simulated with and without SOC.


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The composition as well as the crystal structure dependence of the band structures of the IVTe/V2VI3 chalcogenide heterostructures studied in this work are summarized in Figure 4 (and a full set of the results are shown in Figure S4). The band structures could be categorized into three groups, namely, a metal-like gap closed (blue), an insulator-like gap open (green), and a Dirac semimetal-like gap contacted at the Γ point (red) as can be seen in Figure S4. Figure S4a shows the band structures of heterostructures relaxed without DFT-D, while the DFT-D correction was applied for the results shown in Figure S4b. As can be seen in Figure S4a, the CTe/V2VI3, IVTe/As2S3, IVTe/As2Se3, and IVTe/Sb2S3 heterostructures exhibited metallic behavior, and hence no band gap but the Fermi energy was found to be in the valence or conduction bands. Some heterostructures exhibited insulator like behavior with a band gap. It should be noted that in this study the Z2 invariant of each structure was not calculated and thus it was not confirmed if the band structures showing insulator-like behavior were trivial or nontrivial. Therefore, it may be possible that some insulator-like heterostructures are topological insulators. However, since the purpose of this study is to find novel heterostructures that appear to be Dirac semimetals, gapped band structures including both normal and topological insulators are not focused upon here. Interestingly, a limited number of combinations displayed Dirac conelike features. Among these materials, Sb2Te3, Bi2Se3, and Bi2Te3 are known to be 3D topological insulators,21,36 while SnTe is also known to be a 3D topological crystalline insulator,37 however PbTe is not a topological insulator.38 On the other hand, recently fluorinated PbX (X=C, Si, Ge, and Sn) are two-dimensional compounds that have been reported to be large band gap topological insulators.39 When Sb2Te3 is chosen to be a component of the heterostructure, calculations suggest that SiTe or GeTe are promising candidates that exhibit Dirac cone-like features, but the choice of SnTe and PbTe results in a bulk insulator. Very recently, two-


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dimensional SiTe has been theoretically predicted to become a topological insulator.40 When Bi2Te3 is chosen, GeTe or SnTe seem to be promising candidates for a Dirac semimetal, while SiTe or PbTe do not. It should be noted that even though both PbTe and Bi2S3 are not topological insulators, their combination resulted in the formation of Dirac cone at the Γ point. The situation dramatically changed upon inclusion of the DFT-D correction as shown in Figure 4 and S4b. It should be noted that all Dirac semimetal like band structures disappeared and became either insulators or metals when the structure was relaxed using DFT-D. The effect of the DFT-D correction seems to be more significant for Dirac cone-type band structures, such as GeTe/Sb2Te3 or GeTe/Bi2Te3, as shown in Figure 4, while such large changes were not observed in heterostructures exhibiting metallic band structures like SiTe/Sb2Se3 or SnTe/Bi2Se3. The electronic structure of a heterostructure consisting of a topological insulator and a normal insulator has been discussed previously.9,10 When hybridization across the two interfaces of the topological insulator layer are larger than that of the normal insulator, the heterostructure becomes a normal insulator as a result of the cancellation of the two interfaces by each other. On the other hand, an opposite magnitude correlation makes the system a topological insulator due to the existence of non-trivial outermost surfaces. In between these two conditions, there is an intermediate condition in which the same magnitude of hybridization is present across both layers resulting in the closing of the band gap and the formation of Dirac cone.25 Therefore, it can be suggested that since the magnitude of hybridization strongly depends on the choice of compound, a variety of bulk band structures can be obtained using different combinations of two compounds as shown in Figure 4 and Figure S4. Furthermore, since the DFT-D correction significantly affects the vdW gap distance in the vdW heterostructure, a change in the bond length will also alter the magnitude of hybridization between the two compounds possibly


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resulting in a gap opening as shown in Figure 4. These results suggest that the band gap of such heterostructures can be tuned via an external stimulus e.g. by application of a pressure or stress.

Figure 4. Effects of DFT-D correction on band structures for several IVTe/V2 VI3 heterostructures. Upper panels show the results of without DFTD and lower panels with DFT-D. The stress dependence of the GeTe/Sb2Te3 heterostructure band structure is summarized in Figure 5 for two different functionals. It was found that a Dirac cone appeared again for the GeTe/Sb2Te3 heterostructure with a tensile stress of -1.0 GPa using a GGA functional. This result is reasonable because the DFT-D correction tends to reduce the vdW gap distance, which is overestimated in a standard (GGA) DFT simulation, and when negative stress is applied, the vdW gap increases and finally reaches a value similar to that obtained in a simulation carried out without inclusion of the DFT-D correction. On the other hand, the system appears to become


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metallic and the valence band maximum is no longer at the gamma point when a compressive stress is applied. In order to examine the band structure more accurately, we performed additional simulations using the modified Becke-Johnson (MBJ) exchange potential.41,42 The MBJ local density approximation (MBJLDA) functional is known to produce more accurate band gaps than the standard LDA or GGA functional, which always underestimate the band gap, and is computationally less costly than use of a hybrid functional or GW methods. When the MBJLDA functional was used for band structure simulations, the band gap was found to open for an applied stress of -1.0 GPa, where a Dirac cone is present in the GGA simulation. Furthermore, the Dirac cone appears in the MBJLDA simulation when slightly weaker stress (ca. -0.38 GPa) is applied. This result is contrary to the general trend of the band gap becoming larger when the MBJLDA is used as compared to LDA or GGA simulations. It has been reported that standard DFT can sometimes yield incorrect band ordering especially in band inverted systems, i.e. topological insulators, and that using MBJLDA can help determine the correct band structure.43,44 Therefore, a reduction of the band gap in the MBJLDA simulation may indirectly imply the heterostructure is of a topologically non-trivial nature. Application of compressive stress seems to result in gap widening in MBJLDA simulations.

Figure 5. Effects of stress on band structures for GeTe/Sb 2 Te 3 heterostructure. Upper panels show the results of GGA-PBE functional and lower panels MBJLDA.


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The obtained band gaps from the two different functional are plotted as a function of applied stress in Figure 6a. A Dirac cone is formed at -1.0 GPa in the GGA simulation indicating a zero band gap. The gap increases up to 0.25 eV with decreasing tensile stress and then monotonically decreases even after the direction of the stress is inverted. These MBJLDA results can be seen as an inversion of the GGA results, namely, the Dirac cone is formed at a stress for which the GGA yields the maximum value of the band gap (ca. -0.38 GPa), and the gap increases in either stress direction. In reality, the chalcogenide heterostructure is grown on a substrate that leads to residual stress inside the film. For example, according to our previous experimental structural analysis of Sb2Te3 and GeTe/Sb2Te3 films carried out using X-ray diffraction (XRD), the diffraction peak positions of the heterostructure film occur at lower scattering angles in a surface normal scan than for the Sb2Te3 film indicating a residual tensile stress in the heterostructure film.45,46 This may be due to the difference in the thermal expansion coefficient of the constituent films, which leads to different residual stresses. Therefore, it may be possible to tune the internal stress in the heterostructure film in experimental thin film samples by selecting an appropriate substrate material. Based on these results, one possible application using this GeTe/Sb2Te3 heterostructure is proposed. Figure 6a suggests that application of an external strain may switch on and off the topological nature of the heterostructure resulting in tuning of the band gap. Figure 6b schematically illustrates a proposed switching device fabricated from a chalcogenide heterostructure film and a piezoelectric transducer. The device has source and drain electrodes and a piezoelectric gate layer in-between them. In fact, the residual stress of the thin films of a typical phase change material, Ge-Sb-Te, was reported to be around 0.3 GPa when the asdeposited amorphous film was crystallized by annealing, a value reasonably close to our simulated stress amplitude.47 Therefore, application of negative pressure may be achieved by


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utilizing residual stress in the film. If such residual stress can be induced by the proper choice of substrate and growth conditions, with no external field, a large current will flow between the source and drain electrodes due to the existence of a Dirac cone at the Γ point and its concomitant high mobility, while the current can be suppressed by application of a gate voltage that produces compressive strain in the chalcogenide heterostructure layer, resulting in the opening of the band gap as predicted by the simulation results. One of the expected advantages of this device is its extremely high mobility thanks to the almost linear band dispersion at the Γ point. Such strain induced gap control has also been reported for the black phosphorus/MoS2 heterostructures,48 III-V compounds,49 and phosphorene.50 Moreover, it has been reported recently that strain plays a very important role in the switching behavior of GeTe/Sb2Te3 superlattice memory.51,52 Recently, extensive experimental studies have revealed that the GeTe/Sb2Te3 superlattice exhibits intermixing during growth by molecular beam epitaxy (MBE)53 as well as sputtering,45,46 forming a Ge-Sb-Te ternary compound layer. Even though this may lead to the formation of more complicated band structures, we believe that since the concept of alternate stacking of a topological insulator Sb2Te3 layer and a normal insulator GeSb-Te layer still survives, this systematic study of the simplest heterostructures will provide important insights for the realization of a novel electronic device using artificially constructed van der Waals chalcogenide heterostructures.


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Figure 6. (a) Stress dependence of the energy band gap for different functionals for a GeTe/Sb 2 Te 3 heterostructure. (b) Proposed s witching device us ing GeTe/Sb 2 Te 3 heterostructure film.

CONCLUSIONS A systematic study of a variety of crystal structures and their corresponding electronic band structures were carried out for van der Waals chalcogenide heterostructure using density functional theory simulations. It was found that the band structure strongly depended on the choice of the constituent elements and crystal structures. Furthermore, the band structures were also found to exhibit a strong dependence not only on the composition but also on the functional used. Use of the more accurate MBJLDA functional demonstrated that a Dirac cone is formed when tensile stress is applied to the GeTe/Sb2Te3 heterostructure and the band gap can be increased by tuning the stress. Based on these simulation results, a novel switching device was proposed using a GeTe/Sb2Te3 heterostructure, where a piezoelectric layer induced strain can


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control the band gap opening and closing of the heterostructure film resulting in two different resistance states. The tunability of the Dirac cone (band gap) makes topological insulators more promising for use as novel electronic devices in the future. Since ideally Dirac electrons can flow without dissipation, such a switching device may possess an extremely large ON-OFF ratio that may enable ultrafast operation. Recent rapid improvement of fabrication techniques for van der Waals heterostructure will enable the realization of such new functional devices.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the website. Convergence of total energy and Fermi energy as a function of k points; detailed information of lattice constants and bond lengths of all simulated structures; all simulated band structures. (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Yuta Saito)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT


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This study was supported by JST CREST No. JPMJCR14F1 and by JSPS KAKENHI Grant No. 26886015 and 16K04896, Japan.

REFERENCES (1) Hasan, M. Z.; Kane, C. L. Colloquium : Topological Insulators. Rev. Mod. Phys. 2010, 82, 3045-3067. (2) Kane, C. L.; Mele, E. J. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett. 2005, 95, 226801-1-4. (3) König, M.; Wiedmann, S.; Brüne, C.; Roth, A.; Buhmann, H.; Molenkamp, L. W.; Qi, X.L.; Zhang, S.-C. Quantum Spin Hall Insulator State in HgTe Quantum Wells. Science 2007, 318, 766-770. (4) Hsieh, D.; Qian, D.; Wray, L.; Xia, Y.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z. A Topological Dirac Insulator in a Quantum Spin Hall Phase. Nature (London, U. K.) 2008, 452, 970-974. (5) Xia, Y.; Qian, D.; Hsieh, D.; Wray, L.; Pal, A.; Lin, H.; Bansil, A.; Grauer, D.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z. Observation of a Large-Gap Topological-Insulator Class with a Single Dirac Cone on the Surface. Nat. Phys. 2009, 5, 398-402. (6) Zhang, X.; Wang, J.; Zhang, S.-C. Topological Insulators for High-Performance Terahertz to Infrared Applications. Phys. Rev. B 2010, 82, 245107-1-5.


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For Table of Contents Only


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Manipulating the Bulk Band Structure of Artificially Constructed van

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