Insights into the Charge-Transfer Stabilization of Heterostructure

Article pubs.acs.org/cm

Cite This: Chem. Mater. XXXX, XXX, XXX−XXX

Insights into the Charge-Transfer Stabilization of Heterostructure Components with Unstable Bulk Analogs Marco Esters,†,§ Richard G. Hennig,‡ and David C. Johnson*,† †

Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, United States Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611, United States

‡

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S Supporting Information *

ABSTRACT: Solid state chemists have yet to find a targeted approach based on simple rules to predict new materials with desired physical properties. Recent advances in computational highthroughput methods have led to the creation of large databases with predicted new compounds. While many of these compounds are unstable, some may be stabilized inside heterostructures. BiSe is an example for such a compound where the rock-salt structure is unstable in bulk but can be found in misfit layer compounds and ferecrystals. In some of these heterostructures, BiSe also exhibits antiphase boundaries (APBs), periodic Bi−Bi pairings that interrupt the alternating pattern of the rock-salt structure. Understanding the behavior of BiSe may aid in the discovery of new heterostructure components where no stable bulk analog exists. We used density functional theory (DFT) and crystal orbital Hamilton populations (COHPs) to explain the different stabilities of rock-salt structured BiSe. COHPs show that rock-salt structured BiSe has occupied antibonding states at the Fermi level, which destabilize the structure. In heterostructures, these states can be depopulated by donating electrons into an adjacent layer or by forming APBs to localize electrons into a Bi−Bi bond. The results suggest that the depopulation of antibonding states is crucial to stabilizing rock-salt structured BiSe, and that BiSe needs to be paired with a suitable electron acceptor. We predict that this is a general principle that can be applied to other compounds with unstable polytypes and suggest that COHPs should play a larger role in the discovery of new heterostructure components.

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INTRODUCTION Molecular chemists use simple rules to predict the structures of target molecules that are likely to be stable or metastable enough to be synthetically prepared. A similar set of simple rules, however, has not been discovered for extended inorganic compounds. This creates a significant challenge for materials chemists, who historically have relied on analogies such as isoelectronic substitutions, homologous structural series, intuition, or serendipity in their search for new materials. In an effort to overcome these challenges, computational highthroughput methods have been developed to predict the structure and composition of undiscovered compounds.1 This has led to the generation of large databases that contain a large number of compounds predicted to have negative formation energies.2,3 However, many of these new structures are not stable toward decomposition or may not be able to be prepared using traditional synthesis techniques, suggesting either that they are not the thermodynamically most stable atomic configuration or that kinetics prevent them from being formed.4 It might be possible, however, to stabilize some of these predicted compounds as ultrathin layers within heterostructures. Heterostructures consist of monolayer or few-layer thick stacks of components in specific sequences and are an area of intense research efforts because of their unique electrical © XXXX American Chemical Society

properties arising from the reduction of dimensionality and the interactions between the constituents.5,6 Many heterostructures are derived from compounds that have layered structures, such as graphene or transition-metal dichalcogenides (TMDs TX2 where T is an early transition metal and X = S, Se, Te), where all bonds are terminated inside each layer with only weak van der Waals interactions between layers.7−9 The number of layered structures, however, is limited,10 and the desired properties may not be available within this limited set of compounds. Many new heterostructures would be possible if we found a way to stabilize monolayers and thin layers of compounds with 3D bulk structures. These new heterostructures would have unterminated bonds in each layer, and the relaxation processes these layers would undergo to stabilize the dangling bonds could lead to new structures with interesting electrical and magnetic properties. Misfit layer compounds (MLCs) are examples of heterostructures containing 2D layers of a constituent that has a bulk 3D structure.11 MLCs have the formula [(MX)1+δ]m[TX2]n, where M = Sn, Pb, Bi, rare earth; T = transition metal; X = S, Se; m and n are integers representing the number of MX Received: April 16, 2018 Revised: June 23, 2018 Published: June 25, 2018 A

DOI: 10.1021/acs.chemmater.8b01594 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials bilayers and TX2 layers, respectively, and 0.08 ≤ δ ≤ 0.28. The bulk forms of PbX and SnX crystallize in the rock salt or a closely related structure. In the MLCs, the TX2 constituent has a layered structure while the MX constituent adopts a rocksalt-type structure with rectangular or square basal planes that has unterminated bonds. In-plane distortions in the MX and TX2 components occur to form a commensurate axis. Because of the unterminated bonds, significant out-of-plane distortions (“puckering”) occur in the MX constituent. Closely related to MLCs are ferecrystals where this distortion (and thus the lattice match) is not observed, and turbostratic disorder is found between the layers.12 BiX is an especially interesting constituent in MLCs and ferecrystals because its structure in these heterostructures is not related to its bulk structure. While BiS has not been synthesized in bulk, BiSe and BiTe crystallize in a trigonal structure (P3̅m1, no. 164, Figure 1a) where Bi bilayers are

typical for a rock-salt structure is periodically interrupted by Bi−Bi pairings called antiphase boundaries (APBs).17 In this paper, we will denote the number of Bi atoms between APBs with ν as shown in Figure 1d. Electrical transport data suggest that there is no additional charge transfer to the TMD layers in these BiX-containing compounds compared to MLCs containing PbX and SnX.11,23 With CrX2, BiX does not form APBs, but no electrical transport properties have been reported.28 In ferecrystals, the structure and electrical properties of BiX also depend on the thickness of the TMD layers. Mitchson et al. found that in [(BiSe)1+δ]1[NbSe2]n, the concentration of APBs in the BiSe layer and the number of electrons donated from the BiSe to the NbSe2 block decreases with increasing TMD thickness. X-ray photoelectron spectroscopy (XPS) measurements on [(BiSe)1+δ]1[NbSe2]n show an additional peak at lower binding energy that was assigned to adjacent Bi atoms inside the antiphase boundaries. It was hypothesized that charge is localized in the APBs and that these APBs help stabilize the rock-salt structure.34 Ferecrystals with thicker BiSe layers are metastable and have been synthesized as [(BiSe)1+δ]2[TiSe2]2 and [(BiSe)1+δ]3[TiSe2]3. However, they rearrange into [(BiSe)1+δ]1[TiSe2]1 at about 250 °C.35 There are no reports of MLCs with thicker BiSe layers to date. This work explains the structural behavior found in BiSe layers and describes two mechanisms of stabilization. We chose to investigate BiSe because it is the only bismuth chalcogenide that is found both as a stable bulk solid and as a constituent in MLCs and ferecrystals, albeit with different structures. We found that the bulk and monolayers use different stabilization mechanisms resulting in different bulk and monolayer structures. In MLCs and ferecrystals, electrons can be donated into empty states of TMDs to remove electrons in antibonding orbitals or APBs are used to stabilize the rock-salt structure by localizing electrons inside bonding Bi−Bi orbitals. The formation of APBs depends on the number of states available in the TMD, which may stabilize an unstable TMD polytype if that polytype has more acceptor states available than the stable one. In the end, we discuss how these results may be used to find new two-dimensional materials and heterostructure components.

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Figure 1. (a) Structure of bulk BiSe as viewed along the [010] direction. The values in parentheses are the thicknesses of each layer. (b, c) Top-down view of the structure along with representative values for the in-plane lattice parameters of a single bilayer of BiSe (b) as found in misfit layer compounds and (c) as proposed for ferecrystals. The basal planes can have square or rectangular geometry. (d) BiSe structure including antiphase boundaries (APBs) as viewed along the [010] direction. ν indicates the number of Bi atoms between APBs. Bi atoms are light purple and Se atoms are dark orange.

COMPUTATIONAL METHODS

Density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP).36−38 We employ the generalized gradient approximation (GGA) exchange-correlation functional by Perdew, Burke, and Ernzerhof (PBE).39 For bulk BiSe in its trigonal structure, van der Waals interactions were introduced using the DFT-D3 method with Becke-Johnson damping40,41 because it gave the best agreement with experimental structures (see Table S1 in the Supporting Information).13−15 Monolayers of the transition-metal dichalcogenides TiSe2, NbSe2, and MoSe2 were calculated using the HSE06 hybrid functional of Heyd, Scuseria, and Ernzerhof with the standard exchange-mixing parameter α = 0.25.42 Projector augmented wave (PAW) potentials were employed to describe the interactions between core and valence electrons.43,44 In calculations on BiSe layers, the 5d106s26p3 and 4s24p4 electrons were considered as valence electrons for Bi and Se, respectively. For the transition metals Nb and Mo, the electrons in the 4d shell along with the 4p65s2 electrons were considered as valence electrons, and for Ti, the electron configuration 3p63d24s2 was used. Self-consistency was achieved with an energy convergence of 10−7 eV. Atomic positions and lattice parameters were allowed to relax until the forces on the ions were below 0.0025 eV Å−1. For isolated layers, a vacuum spacing of at least 20 Å was used to minimize interactions between periodic images. A cutoff energy of 500 eV and

sandwiched between Bi2X3 quintuple layers.13−16 In MLCs and ferecrystals, BiS and BiSe adopt a rectangular or square NaCllike structure (Figure 1b,c).17−34 Thus, BiX is a good model system to investigate under which conditions an unstable bulk compound can form inside a stable heterostructure. The structure and electrical properties of MLCs and ferecrystals containing BiX depend on the TMD layer. In MLCs containing TiX2, BiX adopts a rectangular rock-salt-type structure, and the electrical properties are consistent with BiX donating one electron to the TiX2 unit.26,27,30 In MLCs containing NbX2 and TaX2, the alternating Bi−X pattern B


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Chemistry of Materials

Figure 2. (a) Band structures and crystal orbital Hamilton populations (COHPs) of bulk BiSe in its trigonal structure (space group P3̅m1). The Fermi level is set to 0 and indicated with a dashed line. (b) Trigonal BiSe structure as viewed along the [010] direction. The Bi−Se bonds are colored according to the legend in (a). Bi atoms are light purple and Se atoms are dark orange. (c) Band structure and crystal orbital Hamilton populations (COHPs) of rock-salt structured bulk BiSe. The Fermi level is set to 0 and indicated with a dashed line. Γ-centered k-point grids with a density of at least 50 k-points per Å−1 were used for all calculations.45 Spin−orbit coupling was introduced in all calculations except in bonding analyses where spin−orbit interactions are not implemented yet. It is not expected that this changes the results significantly. Bonding analysis was conducted by calculating crystal orbital Hamilton populations (COHPs).46 COHPs were calculated using the Local-Orbital Basis Suite Towards Electronic-Structure Reconstruction (LOBSTER) code using the pbeVaspFit2015 basis set.47−50 The results were cross-checked with the linear muffin-tin orbital atomic sphere approximation (LMTO-ASA) as implemented in the Stuttgart LMTO-ASA code51,52 in the local density approximation with nonlocal corrections by Langreth, Mehl, and Hu.53,54 Only bonds shorter than 4 Å were considered. COHP curves and band structures were plotted using PYMATGEN.55

trigonal structure while the Bi−Se bonds considered in the trigonal structure are presented in Figure 2b. The lengths of each of those bonds are shown in Table 1. The COHP curves Table 1. Bond Lengths in Bulk BiSe in the Trigonal Structurea

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RESULTS AND DISCUSSION Stability of Rock-Salt Structured BiSe. The electronic structures of bulk BiSe were calculated for the experimentally observed trigonal structure (space group P3̅m1, no. 164) and a hypothetical rock-salt structure (space group Fm3̅m, no. 225). Our DFT calculations show that the trigonal structure is more stable than the rock-salt structure with cohesive energies of −3.01 and −2.96 eV, respectively. Figure 2a shows the band structures for the trigonal structure. BiSe in its trigonal structure is a small band gap insulator with a band gap of 52 meV. The existence of the band gap is the result of spin−orbit interactions.15,56 The results are consistent with prior calculations with a predicted band gap of 42 meV, which is well within the error of GGA. However, the calculations found in the literature did not include van der Waals interactions, but instead fixed the c-axis lattice parameter to an experimental value. Figure 2a also shows the crystal orbital Hamilton populations (COHPs) calculated with LOBSTER for the

bond

bond length (Å)

Bi1−Se1 Bi1−Se2 Bi2−Se2 Bi2−Se3 Bi3−Se3 Bi−Bi Bi−Se (rock salt)

2.88 3.10 3.05 2.92 3.38 3.07 3.06

a

The Bi−Se bond length for the rock-salt structure was added for comparison.

are consistent with the curves calculated using the LMTO-ASA approach (see Figure S1 in the Supporting Information), and the charge spilling values are all well below 2% (see Table S2 in the Supporting Information). The Bi−Bi interactions are strongly bonding with an integrated COHP value of −2.39 eV at the Fermi level. These interactions lead to no antibonding interactions being present at the Fermi level. These findings are consistent with extended Hückel calculations by Gaudin et al.13 In the rock-salt structure, BiSe is metallic as the band structure in Figure 2c shows. The bands crossing the Fermi level are mostly of Bi p and Se s and p character, indicating hybridization between these orbitals (see the density of states in Figure S2 in the Supporting Information). This suggests that BiSe is not fully ionic and that there are at least partially covalent bonds between Bi and Se atoms. The rock-salt C


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Chemistry of Materials structure has occupied antibonding states at the Fermi level (see Figure 2c), which stem primarily from antibonding Bi 6p−Se 4p interactions. The integrated COHP values for Bi−Bi bonds in this structure type are nearly 0 (−0.05 eV), and thus, there are no stabilizing Bi−Bi bonds in this structure type. This is why bulk BiSe crystallizes in the trigonal structure and not in the rock-salt structure. Such a rearrangement of bonds from antibonding heteroatomic bonds to bonding homoatomic bonds has also been observed in bulk phase-change materials such as Ge4Se3Te where bonding Ge−Ge bonds are formed to avoid the formation of antibonding Ge−chalcogenide bonds.57 Another mechanism that phase-change materials exhibit to remove antibonding states is to introduce cation defects such as in Ge2−xSb2Te4.58 There is, however, no experimental evidence that BiSe exhibits such cation defects. More accurate structure determination is required to determine conclusively whether cation defects play a role in the stabilization of bulk BiSe. Since the local structure around the atoms in rock-salt structured bulk BiSe and the rock-salt type BiSe layers found in MLCs and ferecrystals is similar, it is expected that the interactions in the layers are similar to those in the bulk structure. This raises the question why in MLCs and ferecrystals the rock-salt structure can be stabilized and why it has not been possible yet to make MLCs or ferecrystals with more than one BiSe bilayer. To investigate this phenomenon, we performed DFT calculations on isolated BiSe layers in the rock-salt structure with one (1L), two (2L), and three (3L) BiSe bilayers. Each structure converged to a square lattice with in-plane lattice parameters of 4.36 Å in the primitive unit cell (6.17 Å in the conventional unit cell), which is similar to reported in-plane lattice parameters in MLCs and ferecrystals.30−34 With 3.0 Å, the layer thickness in 1L BiSe is similar to those found in ferecrystals.31−34 For 2L and 3L BiSe, the layers form bilayers where interplane distances within the bilayer are up to 0.16 Å shorter than that between bilayers. This phenomenon is known experimentally in ferecrystals containing PbSe, which also crystallizes in the rock-salt structure.59 There are additional out-of-plane distortions where the Bi atoms are distorted into the vacuum and into the space between bilayers by approximately 0.1 Å. This so-called “puckering” has been observed in all MLCs and ferecrystals containing rock-salt structured constituents. The magnitude of the calculated puckering is smaller than the experimental data for BiSe in ferecrystals containing TiSe2, VSe2, and NbSe2.31−34 Figure 3 shows the COHP curves for the isolated layers. As with rock-salt structured bulk BiSe, there are occupied antibonding states at the Fermi level, predominantly from out-of-plane Bi 6pz−Se 4pz and Bi 6pz−Se 4s interactions (see Figure S3 in the Supporting Information). Adding additional layers does not significantly change the electronic structure. The additional interactions due to Bi−Se bonds between the bilayers are mostly nonbonding because of the larger distances between the Bi and Se atoms. Thus, none of the layers should be stable in their pristine states. To become more stable, the BiSe layers would have to lose one electron per formula unit (f.u.) to depopulate the antibonding states. In MLCs and ferecrystals, the TMD layers may act as an acceptor for these electrons so that BiSe can be stabilized in the rock-salt structure. This is consistent with electrical properties measured in MLCs containing BiX and TiX2 layers where BiX donates one additional electron into TiX2.26,27,30 MLCs containing SnX and PbX layers, which also

Figure 3. Averaged crystal orbital Hamilton populations (COHPs) for Bi−Se bonds in isolated 1L, 2L, and 3L BiSe. Bonds denoted with xy and z are located inside and outside the xy plane, respectively. “intra” and “inter” are the Bi−Se bonds along the z-axis within a bilayer and between bilayers, respectively. The Fermi energy is set to 0 and indicated with a dashed line. The structures of the layers are shown next to the plots. Bi atoms are light purple and Se atoms are dark orange.

crystallize in the rock-salt structure, have one less valence electron compared to BiX, so the Fermi level (assuming a rigid band model) does not lie inside antibonding states. PbX and SnX layers are thus stable without needing to donate additional electrons. While this explains the stability of 1L BiSe when paired with TiSe2 in a heterostructure, it does not explain why 2L and 3L BiSe have not been stabilized in MLCs and ferecrystals yet. While each BiSe structure needs to donate one electron per f.u., the resulting [(BiSe) 1 + δ ] 2 [TiSe 2 ] 2 and [(BiSe)1+δ]3[TiSe2]3 MLCs or ferecrystals would have layers with larger opposite charges. If the charges are located at the interfaces, this would result in stronger Coulomb interactions and thus in a stronger ionic bond with increasing charge. On the other hand, if the charges are evenly distributed (one electron per f.u. in each TiSe2 layer and one hole per f.u. in each BiSe bilayer), there would also be repulsive Coulomb D


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electrons less than the others, which points to a homogeneous charge distribution. We thus hypothesize that the decreasing stability of the BiSe layer with increasing thickness can be attributed to increasingly repulsive Coulomb interactions. Consequently, any heterostructure component that needs to donate one or more electrons can form only a limited number of layers. Examples of such components could be most rareearth-metal chalcogenides, which prefer a 3+ oxidation state, or SbX. On the other hand, constituents that do not need to donate additional charge, such as PbSe and SnSe, can crystallize in any number of bilayers. The bonding properties of the isolated layers should thus play a significant role in the design of new heterostructures. Properties of Antiphase Boundaries. So far, the results were able to explain the stabilities of bulk BiSe and 1L BiSe without antiphase boundaries (APBs). However, there are several MLCs and ferecrystals that contain APBs. Understanding the properties of APBs in BiSe could provide critical insights into the stability of BiSe in heterostructures. We performed calculations on APB structures with various concentrations by increasing the number of Bi atoms between two APBs ν (see Figure 1d for examples). Figure 5a shows the difference of the total energy per f.u. of 1L BiSe with and without APBs as a function of ν. The structures with APBs are more stable at ν = 2 (50% APBs), suggesting that APBs stabilize the rock-salt structure. As expected, the total energy converges toward the energy of 1L BiSe without APBs as ν increases, that is, as the concentration of APBs decreases. However, with 20 meV/f.u. at ν = 8 (20% APBs), the stabilization is still significant even at lower concentrations. The stabilizing properties of the APBs correlate well with the Bi−Bi distance as shown in Figure 5b. The APB structure becomes more stable when the Bi−Bi distances are close to the Bi−Bi distances in elemental bismuth, which is the case for ν ≥ 3. This is consistent with experiments, which found that the

interactions between the BiSe bilayers and between the TiSe2 layers. This scenario is shown schematically in Figure 4. In

Figure 4. Schematic depiction of the decomposition mechanism for [(BiSe1+δ)]m[TiSe2]m (m = 2, 3). The charge transfer from the BiSe double layers (dark purple) to the TiSe2 layers (light blue) lead to charged layers that exert attractive (blue double arrows) and repulsive (red double arrows) Coulomb forces. To minimize repulsive interactions, they react to [(BiSe1+δ)]1[TiSe2]1 at 250 °C.

[(BiSe)1+δ]1[TiSe2]1, there would be only attractive interlayer Coulomb interactions, but in [(BiSe)1+δ]2[TiSe2]2, there would be one repulsive interlayer Coulomb interaction for each attractive interaction, and in [(BiSe)1+δ]3[TiSe2]3, there would be more repulsive than attractive interlayer interactions. The repulsive interactions could be minimized by rearranging into [(BiSe)1+δ]1[TiSe2]1. Since [(BiSe)1+δ]3[TiSe2]3 would have stronger repulsive interactions than [(BiSe)1+δ]2[TiSe2]2, it would also be expected to be less stable than [(BiSe)1+δ]1[TiSe2]1, which is observed in experiments.35 A Bader charge analysis60−62 reveals that, in the pristine BiSe layers, the Bi atoms adjacent to the vacuum have only 0.1

Figure 5. (a) Energy difference ΔE1L per formula unit (f.u.) between BiSe structures with antiphase boundaries (APBs) and without APBs as a function of ν, the number of Bi atoms between APBs. Negative values indicate that the structure with APBs is more stable. (b) Bi−Bi distances dBi−Bi inside an APB. The dashed line indicates the Bi−Bi distances in metallic bismuth. (c, d) Crystal orbital Hamilton populations (COHPs) for BiSe antiphase boundary (APB) structures with (c) ν = 3 and (d) ν = 5. Bonds denoted with “in” and “out” are inside and outside the APB, and xy and z denote bonds inside and outside the xy plane, respectively. The Fermi level is set to 0 and indicated with a dashed line. E


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Figures 5c,d shows the COHP curves for selected APB structures. The COHP curves for all APB structures are shown in Figure S4 in the Supporting Information. As with bulk BiSe, Bi−Bi pairs introduce bonding interactions in the APB structures, which leads to less populated antibonding Bi−Se bonds. This explains the stability of the APB structures compared to that of 1L BiSe without APBs. However, there are still antibonding states occupied at the Fermi level. With increasing ν, the Fermi level gets moved up further into the antibonding regime and more electrons need to be donated to depopulate the antibonding states as shown in Table 2. However, the number of electrons that need to be donated is smaller than that for 1L BiSe without APBs, which explains why even for ν = 8, the APB structure is still significantly more stable. According to the Coulomb repulsion argument that we used to explain the stability of rock-salt structured BiSe layers, BiSe layers containing APBs should also become less stable with increasing thickness. However, since APB structures need to donate less charge to depopulate antibonding states, the thicker layers will also be charged less. Consequently, these layers should be more stable at higher temperatures than layers without APBs, and it might be possible to synthesize [(BiSe)1+δ]m[TSe2]m where m > 1 and T is a transition metal with which BiSe forms APBs in a MLC. It is interesting, however, that thicker layers do not form with antiphase boundaries in [(BiSe)1+δ]n[TiSe2]n but instead interdiffuse with the TMD layers to form [(BiSe)1+δ]1[TiSe2]1. Other heterostructure components may also be able to form APBs to reduce the number of electrons that need to be donated to the adjacent TMD layer. SbS is known to form APBs in MLCs with NbS2 and TaS2,11 and we expect SbSe to behave similarly. However, APBs are not known to form in MLCs with rare-earth metal chalcogenides even though rareearth metals are trivalent and would thus have to donate or localize an additional electron.11 Along with our results for BiSe, this suggests that the cation needs to be able to form at least partially covalent bonds to be able to form APBs. Charge-Transfer Stabilization. The question that remains to be answered is under which circumstances BiSe forms APBs. In MLCs with NbSe2 and TaSe2, BiSe forms APB structures whereas in MLCs with TiSe2 and CrSe2, no APBs have been reported.18,21,22,27,28 In ferecrystals, on the other hand, APBs have been found with TiSe2 as well, albeit in smaller concentrations than with NbSe2.31,32,34 As elaborated in the sections before, BiSe without APBs needs to donate one electron per f.u. to be stable. However, these electrons need to find acceptor states. Figure 6 shows the density of states (DOS) of select TMD monolayers and a band alignment diagram for these TMDs and 1L BiSe without APBs. TiSe2 crystallizes in the 1T polytype where Ti atoms are coordinated by Se atoms in near-octahedral geometry. Above the Fermi level, TiSe2 has many states available to accept electrons so BiSe can be stabilized by donating electrons, which is why there are no APBs in MLCs and only few APBs in ferecrystals with TiSe2. The differences between MLCs and ferecrystals are likely due to the synthesis conditions: MLCs are synthesized using vapor transport methods whereas ferecrystal synthesis uses a kinetic approach, which gives atoms less time and energy to rearrange.65 The same mechanism can be used to explain why BiSe and CrSe2 form a stable compound without APBs. In CrSe2, Cr has a formal oxidation state of +4. Cr4+, however, is unstable and metastable CrSe2 has so far only been synthesized

Bi−Bi distances in APBs are approximately the same length as the Bi−Bi distances in bismuth metal.17,34 The shape of the energy difference curve is thus determined by two factors. For ν < 3, the structure becomes more stabilized compared to 1L BiSe without APBs as the Bi−Bi distances approach the distances in elemental bismuth. For ν > 3, the structure increases in energy relative to 1L BiSe without APBs as the concentration of APBs decreases. We calculated binding energy shifts of the Bi atoms in each compound to compare our results with XPS measurements by Mitchson et al. on [(BiSe)1+δ][NbSe2]n (n = 1, 2), which showed that the Bi 5d peaks have two contributions.34 These contributions were attributed to Bi atoms outside and inside the APBs, where the latter is shifted to lower binding energy by 0.51 eV. It was hypothesized that this is due to charge localization in the APBs where Bi has an oxidation state of 0 whereas outside the APBs, the oxidation state of Bi was +3. Transmission electron microscopy images have shown APBs with ν = 5 in the BiSe layers. Table 2 shows the binding energy Table 2. XPS Binding Energy Shift ΔEbind 5d between Bi Atoms inside and outside an APB, Average Charges of Bi Atoms outside and inside an APB and of All Se Atoms Obtained from Bader Analyses, and the Number of Electrons (e−) per Formula Unit (f.u.) That Need To Be Donated To Depopulate the Antibonding States as a Function of νa ν no APB 0 1 2 3 4 5 6 7 8

ΔEbind 5d (eV)

charge Bi outside APB

charge Bi inside APB

+0.70

−0.31 −0.61 −0.61(4) −0.57(4) −0.54(4) −0.51(7) −0.50(7) −0.46(8)

+0.85 +0.91 +0.85(1) +0.81(3) +0.78(4) +0.77(3) +0.75(5) +0.76(4)

+0.54 +0.44 +0.35 +0.33(1) +0.31 +0.31(1) +0.31(2) +0.32(1) +0.32(1)

charge Se

e−/f.u. to donate

−0.69

1.0

−0.54 −0.57(2) −0.62(6) −0.64(6) −0.64(6) −0.64(5) −0.65(6) −0.65(5) −0.66(6)

0.00 0.20 0.33 0.43 0.50 0.56 0.60

a

Standard deviations are given in parentheses where available. BiSe without APBs does not contain atoms inside an APB and BiSe with ν = 0 does not contain atoms outside an APB. For ν = 0 and 1, it is not possible to depopulate all antibonding states. Neutral Bi and Se atoms have absolute Bader charges of 15.0 and 6.0, respectively, which correspond to the number of valence electrons in the PAW pseudopotentials.

shift for the Bi 5d core level between Bi atoms inside and outside APBs calculated using DFT and the initial state approximation.63 The calculated values agree very well with the experimental values, suggesting that our relaxed APB structures are reasonable approximations to BiSe layers found in MLCs and ferecrystals. Bader charge analysis60−62 shows that the Bi atoms inside an APB have approximately 0.5 electrons more than the Bi atoms outside the APBs. This means that one electron is localized in each APB, confirming the hypothesis by Mitchson et al. that APBs localize charge. The magnitude of the Bader charges, on the other hand, suggests that the charges on Bi and Se are not +3 and −2, respectively. This is not surprising because both Bi and Se have relatively small electronegativity differences.64 Furthermore, as mentioned in the discussion on rock-salt structured bulk BiSe, there is significant hybridization between Bi p and Se s and p orbitals. F


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correct, this series should be more stable than the analogous series with TiSe2, before rearranging into [(BiSe)1+δ]1[NbSe2]1 at higher temperatures. These calculations explain why rock-salt structured BiSe is unstable in bulk but is stabilized by charge transfer in heterostructures such as misfit layer compounds and ferecrystals. The idea of using charge transfer to stabilize structural units to make new structures was put forth by Cario et al.68 Cario suggested that the lattices of the constituents should match and that the constituents should have complementary donor and acceptor properties. An example is BaFZnP which contains the donor building block [Ba2F2] and the acceptor building block [Zn2P2]. On the basis of the most stable oxidation states of the elements, the blocks prefer to be charged [Ba2F2]2+ and [Zn2P2]2− and are thus complementary. This design principle, however, is more universal since the lattices need not match as in ferecrystals or MLCs. The results obtained with BiSe suggest that charge-transfer stabilization does not explicitly depend on lattice match but instead depends only on the electronic structure of the individual constituents. Removing lattice match constraints would greatly expand the number of heterostructures that could be synthesized. It was proposed in the past that heterostructure constituents with structures not found in equilibrium phase diagrams, for example, rock-salt structured BiSe and 1T-CrSe2, can be stabilized by charge transfer.11 Our results also indicate that the structure of the building blocks themselves are stabilized by charge transfer by removing electrons that would occupy antibonding states in the bulk structure, and that the only requirement for the other constituent is that it has enough empty states available to accept the electrons. By extension, adding electrons to a layer might also change its structure.69 For example, a monolayer of MoSe2 is more stable with Mo in a trigonal prismatic environment (2H polytype) than in an octahedral environment (the 1T polytype). However, the 1T polytype can be stabilized by Li intercalation where Li acts as an electron donor.70,71 As the band alignment in Figure 6 shows, 1T-MoSe2 has states available above the Fermi level that can be occupied by electrons, for example, from Li or from a BiSe layer. The next available empty states in 2H-MoSe2 on the other hand are in its conduction bands, which are higher in energy than the Fermi level of 1L BiSe. BiSe can thus not donate electrons into 2H-MoSe2, which explains why MLCs containing BiSe and MoSe2 have not been successfully synthesized yet. Since the 1T polytype is successfully stabilized via Li intercalation into 2H-MoSe2, however, MoSe2 might be stabilized in its 1T form through charge transfer inside a heterostructure with BiSe. In these cases, using Cario’s principles, the BiSe layer would then represent a [BiSe]+ and the TMDs a [TSe2]− (T = Cr, Mo, Ti) building block whereas with NbSe2 and TaSe2, the building blocks would be [BiSe] and [TSe2]. Electronic structure calculations including COHP analysis can thus be used to determine which components can form suitable donor−acceptor pairs. These results provide a pathway to a more general procedure to find new heterostructure components with unstable bulk analogs using COHP analysis even when the bulk analog is not stable, as is the case with rock-salt structured BiSe. To find new heterostructure components, the COHPs of the compounds that are not on the convex hull should be determined, as they likely contain electrons occupying antibonding states at the

Figure 6. Density of states (DOS) for 1L BiSe and monolayers of 1TTiSe2, 2H-NbSe2, 1T-MoSe2, and 2H-MoSe2. The Fermi levels are set to 0 and indicated by dashed lines. Bottom: Band alignment of the monolayers with a single bilayer of BiSe without APBs. The Fermi levels of each compound are indicated with a dashed line. Solid colors represent occupied states. The Fermi level of BiSe is set to 0.

by oxidizing KxCrSe2 (0.9 < x < 1), where chromium is primarily Cr3+, with I2 in acetonitrile.66,67 When paired with BiSe, however, CrSe2 receives an electron from the BiSe layer so that the chromium ion reduces to the very stable Cr3+. This is why MLCs containing BiSe and CrSe2 are thermodynamically stable. NbSe2 on the other hand crystallizes in the 2H polytype, where Nb is coordinated by Se in a trigonal prismatic geometry. The DOS shows that there are less states available above the Fermi level before a gap without available states is reached. Since BiSe is not able to donate all the electrons required to depopulate the antibonding states into the NbSe2 layer, APBs need to be formed to localize electrons. With thicker NbSe2 layers, more states become available and less APBs need to be formed. This is why, in [(BiSe)1+δ]1[NbSe2]n, Mitchson et al. found a systematic decrease in APB concentration with increasing n, that is, with thicker NbSe2 layers.34 Since the concentration of APBs in ferecrystals with NbSe2 is fairly high, it would be interesting to synthesize a series of [(BiSe)1+δ]m[NbSe2]m compounds (m ≥ 2) and determine the structure as a function of temperature. If the charge localization and Coulomb repulsion hypotheses are G



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Fermi level. Our investigations on BiSe suggest that monolayers of these compounds can be stabilized by donating these electrons into another heterostructure component. This electron-accepting heterostructure component needs to have many unoccupied states above the Fermi level, and the Fermi level needs to be sufficiently below the Fermi level of the electron-donating constituent. While the examples provided in this work all use TMDs as electron acceptors, it is not a requirement that the electron acceptor is a TMD. Our results suggest that the heterostructure component with unstable bulk analog may be able to form a heterostructure with any compound that has enough empty states near the Fermi level to accept the electrons in the antibonding orbitals. These design principles rely only on simple and inexpensive electronic structure calculations and may thus be suitable for high-throughput applications. Other design principles based on COHPs were already proposed for magnetic metals by Dronskowski et al.72 New magnetic materials could be predicted based on antibonding states near the Fermi level, but spin-polarization instead of electron donation is the mechanism to depopulate the antibonding states. Our results present another strong case that bonding analysis should play a more prominent role in materials design. Another advantage of our approach is that the calculations do not require any heterostructure unit cells, which can be very large or even impossible to construct because of disorder between the layers. While this approach cannot provide accurate predictions of physical properties, it may give important insights to experimentalists about which heterostructures to synthesize.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b01594. Benchmarking of van der Waals functionals for bulk BiSe, COHPs for bulk BiSe calculated with the LMTOASA method, spilling values for all COHP calculations, orbital-resolved density of states for rock-salt structured bulk NaCl, orbital-resolved COHP for 1L BiSe, and COHPs for all APB structures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Marco Esters: 0000-0002-8793-2200 Richard G. Hennig: 0000-0003-4933-7686 David C. Johnson: 0000-0002-1118-0997 Present Address §

Center for Materials Genomics, Duke University, Durham, North Carolina 27708, United States. Author Contributions

The manuscript was written through contributions of all authors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation under grants DMR-1710214 (M.E. and D.C.J.) and DMR1440547 (R.G.H.). The authors acknowledge the University of Oregon ACISS cluster (National Science Foundation OCI0960354) and the University of Florida Research Computing system for computing resources.

CONCLUSIONS In this work, we used density functional theory and crystal orbital Hamilton population analysis to gain an in-depth understanding about the stability of rock-salt structured BiSe and the mechanisms that stabilize it in heterostructures. We have shown that bulk BiSe does not crystallize in the rock-salt structure because of occupied antibonding states at the Fermi level. Instead, it crystallizes in a trigonal structure because of bonding Bi−Bi interactions. In misfit layer compounds and ferecrystals, the rock-salt structure is stable because it can depopulate its antibonding states by donating electrons into the transition-metal dichalcogenide layer. While multilayer BiSe needs to donate the same number of electrons per formula unit, there are repulsive Coulomb interactions between the BiSe bilayers, making them less stable. If the transition-metal dichalcogenide does not have enough empty states available, BiSe forms antiphase boundaries. These antiphase boundaries contain bonding Bi−Bi interactions and localize charge, thus reducing the number of electrons that need to be donated to depopulate the antibonding states. The charge-transfer properties of BiSe can be used to stabilize compounds and polytypes that are not stable in the bulk such as CrSe2 or 1T-MoSe2. The results indicate a potential pathway to predict new heterostructure components by finding compounds with a small number of electrons that occupy antibonding states near the Fermi level along with a suitable acceptor layer with a large number of unoccupied states above the Fermi level. These principles are based only on simple electronic structure calculations without requiring large heterostructure unit cells, making them especially suitable for high-throughput materials discovery applications.

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REFERENCES

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