Indirect-To-Direct Band Gap Transition of One-Dimensional V2Se9: Theoretical Study with Dispersion Energy Correction.

Recently, we synthesized a one-dimensional (1D) structure of V2Se9. The 1D V2Se9 resembles another 1D material, Nb2Se9, which is expected to have a direct band gap. To determine the potential applications of this material, we calculated the band structures of 1D and bulk V2Se9 using density functional theory by varying the number of chains and comparing their band structures and electronic properties with those of Nb2Se9. The results showed that a small number of V2Se9 chains have a direct band gap, whereas bulk V2Se9 possesses an indirect band gap, like Nb2Se9. We expect that V2Se9 nanowires with diameters less than ∼20 Å would have direct band gaps. This indirect-to-direct band gap transition could lead to potential optoelectronic applications for this 1D material because materials with direct band gaps can absorb photons without being disturbed by phonons.

Introduction

The development of low-dimensional materials has launched different approaches to materials research for many promising applications.[1,2] Two-dimensional (2D) materials are composed of planar crystalline sheets stabilized by strong in-plane bonds and weak interlayer interactions. Because graphene was first separated from graphite, graphene-based applications in electronics, chemistry, and mechanics have been intensively studied due to graphene’s superior physical properties (e.g., high charge carrier mobility and mechanical strength). However, graphene does not have a band gap and so is difficult to develop with transistors.[3,4] If graphene is finely patterned with narrow widths, a band gap can be formed.[3] Unfortunately, as the width of graphene decreases, the band gap increases, and the electron mobility sharply decreases. Other 2D materials with appropriate band gaps, including transition-metal dichalcogenides (TMDCs) and black phosphorus, have been introduced.[5−11] Similar to graphene, a dramatic reduction in charge carrier mobility due to edge scattering is inevitable after device manufacture.[12] The reduction of dimensionality also can influence the charge transfer, the structure of the crystal, spin property, or the charge carrier mobility in the metal nanowire system.[13−19]

Other types of one-dimensional (1D) materials, such as Mo6S9–I, Sb2Se3, and VS4, have been studied by several researchers.[20−26] Because they are formed by periodically stacking single-chain atomic crystals (SCACs) that have strong intrachain bonds with weak van der Waals (vdW) interchain interactions, these 1D materials are prepared by isolating SCACs from bulk crystals (similar to 2D materials). The structural characteristics of 1D materials result in a surface free from dangling bonds which hinder application of 2D materials.[27,28] However, it is difficult to clearly determine the crystal structure of Mo6S9–I because the positions of the sulfur and iodine ions coordinated to the central molybdenum ions may vary, even at the same stoichiometric composition. In addition, the thermodynamic properties of the ternary system (Mo–S–I) are not well known, which makes it difficult to understand the physical properties of the Mo6S9–I material. In addition, Sb2Se3 and VS4 have not been reported experimentally as 1D atomic dispersions.

Very recently, other semiconducting 1D materials, such as Nb2Se9 and V2Se9, were reported to be successfully synthesized by solid-state reactions.[29,30] These materials can be separated as 1D nanowires up to a single-atomic chain size because of the weak vdW interactions between the selenium ions surrounding the inorganic chains. There are two approaches for preparing the nanowires: (i) mechanical exfoliation, which is similar to the conventional experimental set-ups used in 2D (e.g., graphene, boron nitride, and TMDCs) research,[31] and (ii) chemical exfoliation, which occurs by designing an appropriate solvent and dispersant.[32−34] Based on these two exfoliation methods, the bulk materials can be separated up to 1 nm in thickness [as experimentally confirmed by atomic force microscopy (AFM)]; the separated materials can be a single unit of the inorganic chain. In this report, we performed theoretical calculations to investigate the potential optoelectronic applications of V2Se9 chains after disintegration of bulk V2Se9 crystals into single V2Se9 chains.

The calculations showed that V2Se9 SCACs would have direct band gaps, whereas bulk V2Se9 would have an indirect band gap. As in Nb2Se9,[35] the band gap decreased by increasing the number of chains from 1.09 eV (single chain) to 0.54 eV (bulk). The band structures of single, double, triple, and septuple SCAC bundles were similar, but they were different from that of the bulk structure. We investigated the effects of vdW interchain interactions by adding the dispersion energy correction to the structural optimization. The dispersion energy decreased the band gaps but did not alter the indirect-to-direct band gap transition trend significantly, whereas the dispersion energy was important in predicting the direct band gap of the double-layer MoS2.[36]

Results and Discussion

Figure shows the calculated band structures of bulk and few-chain systems, from the high symmetry point M to point Γ. Full band structures can be found in Supporting Information Figures S1–S5. Unlike 2D materials, a collection of 1D materials can have various arrangements. The lowest energy arrangements of the double and triple chains were chosen for the band structure calculation. Triangular arrangement of triple-chain V2Se9 is more stable than linear V2Se9, which implies that aggregation stabilizes the energy of V2Se9 SCACs. Thus, we calculated the band structure of hexagonally stacked septuple-chain bundles for seven chains. As Figure a presents, bulk V2Se9 had an indirect band gap of 0.54 eV from point Γ to a point (0.419, 0, 0.419) near M (0.5, 0, 0.5), designated as T. However, all 1D few-chain systems had direct band gaps that increased as the number of chains decreased. The maximum band gap was 1.09 eV in a single chain. Direct band gaps appeared at point Γ, a local minimum point in the conduction bands of few-chain systems but a local maximum point of the bulk structure. Point Γ was a local energy maximum in the few-chain system, unlike in the bulk system. The band energies of the conduction band at point Γ decreased as the number of chains increased in the few-chain systems. However, the conduction band at point T increased with the number of few-chain systems, whereas the conduction band energy of T in the bulk was minimal. This implies that the stacking effect on the energy at point Γ in the bulk is different from that in the few-chain systems. The partial orbital analysis showed that point Γ had larger contributions to p and d orbitals than did T (Figure S6). The different aspects of the conduction band near point M is the reason that bulk V2Se9 has an indirect band gap while the few-chain V2Se9 shows direct band gaps. The difference between the valence bands of bulk and few-chain systems is much smaller than the difference between the conduction bands. The number of chains has little influence on the valence band of few-chain and bulk V2Se9. The band structures of V2Se9 without the DFT-D3 dispersion energy correction are similar to the band structures with the DFT-D3, but the band gaps increase (Table S1).

Figure 1

Part of band structures of (a) bulk, (b) 7-chain, (c) triple, (d) double, and (e) single SCAC(s) V2Se9 from point M to point Γ. The zero energy is shifted to the maximum energy of valence band. The structures are optimized by the Perdew–Burke–Ernzerhof (PBE) method with the DFT-D3 energy correction. Inset graphics represent the corresponding optimized structures of bulk and few-chain V2Se9.

We compared the band structures of V2Se9 with those of Nb2Se9. The band structures of Nb2Se9 with dispersion energy correction are shown in Figure S7. All few-chain systems have similar band structures in both V2Se9 and Nb2Se9. The valence bands of SCACs and bulk are also similar in both Nb2Se9 and in V2Se9. The contribution of selenium is greater than that of vanadium to the partial density of state both for the bulk and few-chain systems except the double chain (Figure S8). Screening of inner vanadium ions by outer selenium ions prevents the conduction band from being perturbed by other chains. The interactions between chains mainly change the characteristics related to selenium ions. However, the few V2Se9 chains have electronic bands with many valleys, whereas the few Nb2Se9 chains carry structureless bands.

All few-chain systems calculated previously have similar properties to a single chain. To determine the boundary between such few-chain systems and bulk systems, we plotted the changes in the band gap for a number of V2Se9 and Nb2Se9 chains, as in Figure . The band gap decreases as the number of chains increases, as does the change of the band gap. We expected that a decrease in the band gap (ΔE) by the number of chains (n) would approach the band gap in bulk V2Se9 at 0.54 eV and Nb2Se9 at 0.65 eV. We interpolated the tendency between ΔE and n as an exponential curve. From this interpolation, n satisfying |ΔE(n) – ΔEbulk| < 0.01 eV, where ΔEbulk is the band gap of the bulk system, is expected to be greater than 24 in V2Se9 and 20 in Nb2Se9. These numbers of chains can construct a triple-layer bundle with hexagonal stacking. The short interchain distance between two V2Se9 chains is 6.79 Å and the distance between two Nb2Se9 chains is 6.86 Å. Therefore, the shortest diameter of a triple-layer V2Se9 bundle is approximately 20.37 Å, and that of a triple-layer Nb2Se9 bundle is approximately 20.58 Å (supposing the cross-section of a bundle is an ellipse). The exponential function decays fast, and the number of chains enough to have a band gap similar to the bulk from exponential interpolation could be the lower bound. Thus, we believe that V2Se9 and Nb2Se9 SCACs thinner than about ∼20 Å would have the characteristics of single chains, such as a direct band gap. In the previous study of Nb2Se9 without dispersion correction, a value of 36 Å was suggested.[35]

Figure 2

Band gap (ΔE) changes by the number of chains (n) of V2Se9 and Nb2Se9. calc. and interpol. abbreviate calculation and interpolation, respectively. As n increases, ΔE decreases to the bulk band gap of 0.54 eV in V2Se9 and 0.65 eV in Nb2Se9, as represented by dashed lines. We interpolated the band gap changes to exponential curves such that ΔE = 0.60 e–0.17 + 0.54 for V2Se9 and ΔE = 0.70 e–0.21 + 0.65 for Nb2Se9.

The dispersion energy does not change the band gap transition trend in V2Se9 and Nb2Se9, although it is significant in 2D MoS2. The reason is that such 1D materials have remarkably different conduction bands than the bulk material. With MoS2, the 2D and 3D structures have a similar band structure to that of bulk MoS2. The dispersion energy changes the size of the indirect and direct band gaps, while the positions of the band gaps are maintained. However, 1D few-chain V2Se9 and Nb2Se9 have significantly different band structures compared to those of 3D bulk structures. Unlike 2D TMDC, the effect of dispersion energy in these 1D material changes the positions of the indirect and direct band gaps. We expect that there would be bundles of V2Se9 and Nb2Se9 whose band structures have intermediate shape between that of a single chain and that of the bulk material, with the number of chains in these bundles more than seven.

Table summarizes the characteristics of V2Se9 and Nb2Se9 calculated by PBE + DFT-D3. The band gap differences between the bulk and a single chain are similar in these materials. The size of the V2Se9 chain is 0.1 Å smaller than that of Nb2Se9, and the band gap of the bulk material and single chain of V2Se9 is 0.1 eV smaller than that of Nb2Se9. The physical properties related to the band gaps and the structures of chains in these two 1D materials are similar.

Table 1

Characteristics of V2Se9 and Nb2Se9 by PBE + DFT-D3 Theoretical Calculations

	V2Se9	Nb2Se9
crystal structure	C2/c	P1̅
a (bulk, Å)	12.68	8.19
b (bulk, Å)	12.54	8.37
c (bulk, Å)	14.05	13.10
α (bulk, deg)	90	58.7
β (bulk, deg)	104.96	56.8
γ (bulk, deg)	90	92.5
number of chains ina cell	4	1
short interchain distance (bulk, Å)	6.79	6.86
long interchain distance (bulk, Å)	7.13	7.25
band gap of bulk (eV)	0.54, indirect	0.65, indirect
band gap of single chain (eV)	1.09, direct	1.21, direct
difference of band gaps of bulk and single chain (eV)	0.55	0.56
number of chains that makes the band gap near to bulk	24	21
short diameter of the chain bundle that makes band gap near to bulk (Å)	20.37	20.58

Conclusions

Using density functional theory (DFT) calculations, we found that 1–7 V2Se9 SCAC structures would have direct band gaps, whereas bulk V2Se9 would have an indirect band gap, like Nb2Se9 SCACs.[35] By interpolation, we predicted that a 1D V2Se9 chain with a diameter less than ∼ 20 Å would have a direct band gap. Additionally, we investigated the effect of vdW interactions between chains on the DFT-D3 energy correction. DFT-D3 correction maintained the structures of V2Se9 bulk and SCAC roughly, but the interchain distances were reduced. Band gaps of few chain systems decrease as the number of chains increases, with and without DFT-D3 correction, and finally approach the band gaps of the bulk structure. The band structures of SCACs with 1–7 chains are similar, and DFT-D3 optimization retains the band structures of V2Se9 systems qualitatively; however, the band gaps were reduced by DFT-D3 correction. The optimized structures and band gaps for various numbers of chains of V2Se9 showed similar characteristics to those of Nb2Se9. The dispersion energy does not change the band structure of these 1D materials, nor does it affect the indirect-to-direct band gap transition, unlike in the 2D material MoS2.

This distinctive 1D material V2Se9 could be used in optoelectronic devices because it can absorb photon energy without being disturbed by phonons. The charge mobility calculation of 1D V2Se9 is needed to determine whether there are further applications for the field effect transistors that require a direct band gap and appropriately fast mobility, as with 2D MoS2.[37,38] The spin property of this 1D material is also needed to be analyzed in future research. The 1D materials have higher surface-to-volume ratios and no dangling bonds, unlike the 2D materials; therefore, the 1D material V2Se9 described in this study seems to be a promising material in nanoelectronics.

Structures and Computational Methods

Figure a shows the crystal structure of V2Se9, which is a periodic array of unit V2Se9 SCACs. Bulk V2Se9 crystals were prepared via the flux method using excess molten selenium as a solvent. When the V–Se liquid at 330 °C was cooled to room temperature, dark grey needles precipitated. Figure b shows a scanning electron microscopy (SEM) image of the V2Se9 needles prepared in this study. To demonstrate the characteristics of the chain-stacked structure of the V2Se9, the bulk V2Se9 crystal was cleaved using a conventional peeling method.[39]Figure c shows the AFM images of V2Se9 chains exfoliated from bulk V2Se9 crystals. The exfoliated chains had thicknesses of 1.1, 6.9, and 7.5 nm, indicating that single chains (1.1 nm) or bundles (6.9 and 7.5 nm) could be generated by mechanical exfoliation (Figure d). This result shows that weak vdW interactions among the chains in the bulk crystal results in V2Se9 crystals cleaved to V2Se9 chains, as in typical 2D materials.The bulk structure of V2Se9 has a monoclinic symmetry (C2/c). The unit of V2Se9 chain structures consists of four vanadium and 18 selenium ions, as in Nb2Se9. A V4Se18 chain structure is composed of two V2Se4 octahedrons connected by Se5; each octahedron faces the other octahedron (Figure a).[40] The relative coordinates of ions in the reference direct the chains to [1 0 1]. We rotated the lattice vectors to a set of ([1 0 1], [0 1 0], and [1 0 1̅]). Then, 1D structures consisting of the number of finite chains could be constructed by repeating k-points into the x-axis in computational chemistry software. This rotated unit cell has three whole chain units and two half-chain units (Figure b,c). To validate the rotated frame, we calculated the band structures for the original and rotated lattice vector choices and compared the band gaps (see Figure S9).

Figure 3

(a) Stick-and-ball crystal structure of V2Se9, where the red balls are vanadium and the yellow balls are selenium; (b) SEM images of the V2Se9 single crystal; (c) AFM image; and (d) height profiles of mechanically exfoliated V2Se9.

Figure 4

Views of V2Se9 single-lattice cells, which are rotated from the reference structure to direct the length of the chains to the [1 0 0] axis. (a) Two V4Se18 chain units are shown, consisting of V2Se4 octahedrons and Se5 connecting the octahedrons. The numbering of selenium and vanadium ions follows those of the reference.[40] An inclined view (b) and projected view (c) to the plane perpendicular to the length of chains are shown. A single cell has four chains. Two chains are stacked in the bottom of the unit cell as the first layer, and two chains are stacked on the top of the unit cell as the second layer. Two layers are shifted by a half-length between chains in each layer.

We constructed few-chain systems that have single, double, triple, and septuple chain(s) by repeating the rotated unit cell to obtain the target chain arrangements and by removing redundancies. After the formation of the initial few SCAC systems, we optimized the structures of SCACs and bulk V2Se9. The calculation was performed using the projected augmented wave method[41,42] in the Vienna Ab-Initio Package (VASP).[43−46] Computational details are presented in the Supporting Information.

A theoretical calculation predicted that Nb2Se9 SCACs would have direct band gaps, bulk Nb2Se9 would have an indirect band gap, and the band gaps would increase as the number of chains decreased.[35] These phenomena are mainly caused by vdW interchain interactions. Previous studies of metal chalcogenides used only the generalized gradient approximation method,[35,47,48] which cannot properly describe vdW effects; therefore, further calculations were performed to incorporate vdW interactions.[36,49] We chose the DFT-D3 method, which introduces the dispersion energy correction proportional to 1/r6.[50,51] To investigate the effects of vdW interactions, we optimized the structures with and without the DFT-D3 correction and then compared the atomic structures and band structures of SCACs and bulk V2Se9. Indeed, when the dispersion correction was applied, the structure further approached the experimental reference structure (Table S2). The dispersion energy correction decreases the interchain distances of bulk and all SCAC V2Se9 and Nb2Se9 (Tables S3–S5 and Figures S10 and S11).

By looking at the electron localization function of the single chain and bulk V2Se9, we identified the bonding characters: the two Se–Se bondings in V2Se4 octahedron and two Se–Se bondings in Se5 are covalent, and the Se–V bondings are ionic. Accordingly, we expect that the charge valence of V2Se9 would be (V5+)2(Se22–)4Se2–. It implies that the system would be diamagnetic because there is no unpaired electron.