Structures, Energetics, and Electronic Properties of Layered Materials

Nov 8, 2013 - The relative structural stability and electronic properties of ZB and WZ ..... This trend is in line with the degree of nonplanarity of ...
0 downloads 6 Views 2MB Size
Download PDF
Article pubs.acs.org/JPCC

Structures, Energetics, and Electronic Properties of Layered Materials and Nanotubes of Cadmium Chalcogenides Jia Zhou,*,† Jingsong Huang,†,‡ Bobby G. Sumpter,†,‡ Paul R. C. Kent,†,‡ Humberto Terrones,†,§ and Sean C. Smith*,† †

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Bethel Valley Road, Oak Ridge, Tennessee 37831-6493, United States ‡ Computer Science and Mathematics Division, Oak Ridge National Laboratory, Bethel Valley Road, Oak Ridge, Tennessee 37831-6367, United States S Supporting Information *

ABSTRACT: Geometric structures, energetics, and electronic properties of single-layer sheets, multilayer stacks, and single-walled nanotubes (SWNTs) of cadmium chalcogenides CdX (X = S, Se, Te) have been studied using ab initio density functional theory, along with spin−orbit coupling, van der Waals (vdW) interactions, and the GW approximation. Methodologies applied to the rationally designed materials have been validated through the experimental structural parameters and band gaps of 3D bulk zinc blende and wurtzite phases of CdX. The 2D single-layer sheet of CdS is found to be completely planar, while those of CdSe and CdTe are slightly corrugated, all showing a honeycomb lattice. The 2D sheets are destabilized with respect to the bulk zinc blende and wurtzite phases, but can be significantly stabilized by forming 3D multilayer stacks as a result of interlayer interactions. 1D (5,5) armchair and (9,0) zigzag SWNTs are also stabilized from their single-layer sheet counterparts. Both SWNTs consist of two concentric cylinders, with the Cd and X atoms in the inner and the outer cylinders, respectively, and with the intercylinder separations showing the same trend as the degree of nonplanarity in the singlelayer sheets. By analogy to quantum dots of CdX, we suggest quantum flakes as interesting targets for experimental synthesis due to the diverse band gaps complementary to those of the bulk phases, allowing a much wider wavelength range, from infrared, visible, to ultraviolet, to be utilized.

■

INTRODUCTION

tronics, thermoelectrics, topological insulators, and energy conversion and storage.6,10,13 Among diverse inorganic graphene analogues, silicene,14,15 germanene,16 SiC,17 h-BN,18−21 and AlN22 all bear a close resemblance to graphene in terms of their valence electron count. Graphene, silicene, germanene, and SiC are isoelectronic and could be denoted as group IV−IV materials due to the presence of two atoms in the unit cell, where the valence electron count is eight. Moving left and right by one column on the periodic table gives binary group III−V materials such as hBN and AlN, which also have eight valence electrons. In addition, experiments and theoretical studies indicate that, similar to graphene, all of these inorganic graphene analogues have a 2D honeycomb lattice of atoms, although some may adopt chairlike puckering distortions in hexagonal rings. These single-layer structures can be rolled into nanotubes, which in turn can be unzipped into nanoribbons. Nanotubes, categorized as single-walled nanotubes (SWNTs) and multiwalled nanotubes (MWNTs), have been in the spotlight of material science for two decades owing to their unusual properties. Unlike semimetallic graphene, carbon nanotubes could be metallic or semiconducting, depending on the chiral indices.23 BN

The discovery of graphene, a single atomic layer of graphite, has created enormous excitement in the past decade1,2 by revealing a wealth of novel physics including realization of a twodimensional gas of massless Dirac fermions, ambipolar electric field effect, room-temperature quantum Hall effect, breakdown of the Born−Oppenheimer approximation, and quantum capacitance, to name a few.1−5 It also triggered a boom for two-dimensional (2D) layered materials beyond graphene such as hexagonal boron nitride (h-BN), transition metal dichalcogenides (e.g., MoS2, NbSe2), and group V metal chalcogenides (e.g., Sb2Te3 and Bi2Se3).6 Similar to graphite, the bulk structures of these materials are characterized by strong intralayer covalent bonds and weak interlayer van der Waals (vdW) interactions and thus are given the name of vdW solids. Their 2D layered materials can be made by direct mechanical cleavage,7 or liquid-phase exfoliation of their vdW solids,8,9 in addition to other chemical routes.8,10 Similar to graphene, these 2D materials may display distinct properties from their bulk 3D counterparts. For instance, the indirect band gap of bulk transition metal dichalcogenides becomes direct in single-layer materials,11,12 which has important implications for optoelectronics. The quantum confinement-enabled unusual properties of graphene and its various inorganic analogues may find a wide range of applications in field-effect transistors, spin- or valley© 2013 American Chemical Society

Received: October 1, 2013 Revised: November 5, 2013 Published: November 8, 2013 25817

dx.doi.org/10.1021/jp409772r | J. Phys. Chem. C 2013, 117, 25817−25825

The Journal of Physical Chemistry C

Article

nanotubes were fixed at 20 Å to ensure the periodic images are well separated while other lattice vectors were fully relaxed. All atoms were also relaxed until the Hellmann−Feynman forces were smaller than 0.001 eV/Å. The k-point grids, the kinetic energy cutoff, and the vacuum regions employed were based on a set of systematic convergence studies on the 3D ZB/WZ phases and 2D single-layer sheets for CdSe, where the k-point grids range from 8 × 8 × 8, 16 × 16 × 16, to 32 × 32 × 32 (or from 8 × 8 × 1, 16 × 16 × 1, to 32 × 32 × 1 for 2D single-layer sheets), the cutoffs from 300 through 600 eV, and the vacuum regions from 10 through 40 Å, showing that energy differences are converged to ≤0.5 meV per formula unit of CdX. To examine spin−orbit (SO) effects on the structures and energies, SO coupling calculations were performed using the PBE functional. Since vdW interactions are expected to be significant in some cases, especially in layered structures, the DFT-D2 method of Grimme43 was applied using the original semiempirical dispersion potential parameters optimized for Cd, S, Se, and Te. Hereafter, it is referred to as PBE-D2 due to the use of PBE functional. For comparison, we also performed calculations for 3D ZB and WZ phases using the recently developed self-consistent vdW-DF2 method of Langreth and Ludqvist.44,45 Note that the exchange functional in vdW-DF2 is rPW86 instead of PBE, while the correlation functional is based on local density approximation (LDA). Finally, it is known that the DFT band gaps are often significantly underestimated for semiconductors and insulators. For more accurate band gaps, herein we performed quasiparticle GW0 calculations,46−49 in which the eigenvalues are updated in the Green’s function only. For reasons of computational cost, we reduced the energy cutoff for the response function to 150 eV and used sufficiently large k-point grids of 8 × 8 × 8 or 8 × 8 × 1 for the GW0 calculations48,50 of 3D bulk and 2D single-layer sheets, respectively.

nanotubes, first synthesized in 1995, have a larger thermal stability and a wider band gap than carbon nanotubes.24 SiC nanotubes, on the other hand, are always a semiconductor regardless of the helicity.25,26 Moving left and right on the periodic table by one more column from the binary group III−V materials gives binary II− VI materials such as cadmium chalcogenides CdX (X = S, Se, Te). Leaving out the d10 electrons in the valence configuration of Cd, it may be considered that the valence electron counts of these II−VI materials are similar to those of the IV−IV and III−V materials. Group IV−IV, III−V, and II−VI materials are all known to have bulk zinc blende (or cubic diamond for C) and wurtzite (or hexagonal diamond for C) structures that have a tetrahedral coordination for each atom. However, only IV−IV and III−V materials have vdW solids with layered structures from which single-layer graphene and its analogues are derived. For CdX, quantum confinement effects have been demonstrated for 0D quantum dots and 1D quantum rods/wires or nanoribbons, which are particularly significant for photovoltaic, light emitting diode, and photodetector applications.27−30 In recent years, 2D nanosheets of CdX with one through a few atomic layers have been synthesized from solvothermal and colloidal techniques.31−33 This experimental progress prompts one to envision the synthesis of free-standing single-layer sheets of CdX in the near future. Thus, it is interesting to find out whether a single-layer sheet of CdX will adopt a graphene-like honeycomb lattice although their vdW solids have still not been realized. With this motivation, herein we aim to explore the layered and nanotube structures of CdX. We systematically study the geometric structures, relative energies, and electronic properties of single-layer sheets, multilayer stacks, and singlewalled nanotube structures of CdX based on DFT, with or without spin−orbit coupling and vdW interactions, further coupled with the quasiparticle GW approximation, a widely used method for accurate band gap predictions. By comparison with the existing ZB and WZ bulk phases, we discuss the relative stabilities of the new structures and their diverse band gaps, which allow a wide range of wavelength, from infrared, visible, to ultraviolet, to be utilized.

■

RESULTS AND DISCUSSION 3D Bulk ZB and WZ Structures. Cadmium chalcogenides CdX (X = S, Se, Te) are known to crystallize in both cubic ZB and hexagonal WZ structures. Despite the difference in their space groups, these structures are in fact very similar to each other in terms of the tetrahedral coordination of each atom and the stacked “layers” along the [111] direction of ZB and the [0001] direction of WZ. Note that their difference with other layered vdW solids such as graphite, hexagonal boron nitride, transition metal dichalcogenides, etc., is that the Cd and X atoms are covalently bonded between neighboring “layers”. The main difference between ZB and WZ phases manifests in the stacking sequences, lateral displacements, and the interlayer rotation. ZB adopts an ABC sequence with lateral displacements of (1/3a′, 1/3a′) and (2/3a′, 2/3a′), where a′ is the lattice constant of the primitive cell. In comparison, WZ adopts an AB sequence with an interlayer lateral displacement of (1/ 3a, 1/3a), where a is the lattice constant in the (110) plane, followed by an interlayer rotation of 60 degree. Consequently, the ZB phase displays a staggered conformation if viewed along the [111] direction, whereas the WZ phase displays an eclipsed conformation if viewed along the lattice vector c. The relative structural stability and electronic properties of ZB and WZ have been widely studied both experimentally and theoretically.51−58 Here we revisit their structures, relative energies, and electronic properties in order to gauge the performance of the theoretical methods to be applied to other rationally designed new materials.

■

METHODOLOGY First-principles calculations were carried out using the Vienna ab initio simulation package (VASP) version 5.2.12.34−37 The Kohn−Sham equations were solved using the projectoraugmented wave (PAW) method.38,39 Standard PAW potentials were employed for the elemental constituents, with valence configurations of 4d105s2 for Cd, 3s23p4 for S, 4s24p4 for Se, and 5s25p4 for Te. The exchange and correlation interactions of valence electrons are described by the Perdew−Burke− Ernzerhof (PBE) functional40,41 within the generalized gradient approximation (GGA). Three types of structures were investigated including 3D bulk phases of zinc blende (ZB) and wurtzite (WZ), 2D single-layer sheets and 3D multilayer stacks, and 1D single-walled armchair and zigzag nanotubes. The Brillouin-zone integrations were performed on a dense Γcentered 16 × 16 × 16 k-point grid42 for 3D bulk structures (ZB, WZ, and multilayer stacks), a 16 × 16 × 1 grid for 2D single-layer sheets, and on a 16 × 1 × 1 grid for 1D nanotubes. The kinetic energy cutoff for plane waves was set to 500 eV, and the “accurate” precision setting was adopted to avoid wrap around errors. The convergence criterion for the electronic selfconsistent loop was set to 10−6 eV. During the structure optimizations, the vacuum regions for single-layer sheets and 25818

dx.doi.org/10.1021/jp409772r | J. Phys. Chem. C 2013, 117, 25817−25825

The Journal of Physical Chemistry C

Article

Table 1. Structure Parameters (a and c in Å), Total Energy Per Formula (E in eV/2 Atom), and Band Gap (Eg in eV) for the 3D Bulk ZB and WZ Phases of CdX (X = S, Se, Te) CdS

CdSe

properties

PBE

PBE-SO

PBE-D2

exp.

PBE

a_ZB a_WZ c_WZ E_ZB E_WZ

5.941 4.206 6.845 −6.321 −6.323

5.940 4.206 6.843 −6.349 −6.352

5.848 4.147 6.719 −6.772 −6.777

5.818a 4.136a 6.714a -

6.211 4.394 7.173 −5.658 −5.656

GW0[D2]

exp.

PBE-SO

6.211 6.113 4.393 4.329 7.173 7.043 −5.707 −6.117 −5.705 −6.117 CdSe

CdS band gap Eg_ZB Eg_WZ a

PBE 1.05 1.11

GW0[PBE] 2.23 2.26

2.36 2.42

c

2.55 2.58c

PBE

CdTe

PBE-D2

GW0[PBE]

0.51 0.56

1.45 1.48

GW0[D2] 1.60 1.65

exp.

PBE

6.052a 4.300a 7.011a -

6.629 4.682 7.677 −4.981 −4.973

exp. c

1.90 1.83c

PBE-SO

PBE-D2

6.632 6.520 4.684 4.606 7.683 7.545 −5.110 −5.470 −5.102 −5.465 CdTe

exp. 6.482a 4.58b 7.50b -

PBE

GW0[PBE]

GW0[D2]

exp.

0.59 0.62

1.40 1.51

1.60 1.70

1.60c 1.60c

Reference 51. bReference 56. cReference 57.

especially the GW0[D2] results are in much better agreement with the experimental results.57 The experimental band gaps decrease monotonically from CdS, to CdSe, and to CdTe for both ZB and WZ phases. However, the theoretical band gaps are comparable between CdSe and CdTe, probably because the CdTe band gaps are overestimated. Unlike other GW0[D2] band gaps, which are slightly underestimated compared to the experimental values by ca. 0.2 eV, the GW0[D2] band gaps of CdTe are nearly identical to or even slightly larger than the experimental values. Nevertheless, the GW0 calculation, and especially that based on the PBE-D2 geometries, provides much better predictions for Eg values than DFT. On the basis of these benchmark calculations, it can be expected that the PBE-D2 method in combination with GW0 serves to provide a good reference for the rest of the new materials, where experimental values are not available. The band structure and density of states (DOS) for each structure are documented in the Supporting Information (Figure S1). Single-Layer (SL) Sheets and Multilayer (ML) Stacks. The experimental realization of SL structures such as graphene1,2,61 and silicene14,15 offers the opportunity to exploit their unique electronic and optical properties in advanced optoelectronic devices. Both graphene and silicene are 2D materials of C or Si atoms arranged in a honeycomb lattice. However, graphene is a planar structure, while silicene is not, featuring chairlike puckering distortions in each hexagonal ring. This is mainly because carbon favors sp2 hybridization, while silicon favors sp3 hybridization.62 Considering the similar valence electron count, it is possible that CdX may adopt layered honeycomb lattice structures. Motivated by the SL structures of graphene and silicene, here we investigated the structures, energetics, and electronic properties of the SL sheets of CdX. The structural relaxations of the SL structures were started from two initial geometries, one completely planar, as in graphene, and the other from a sheet excised from the (111) plane of the ZB phase or the (0001) plane of the WZ structure. For CdS, both optimizations ended up with a completely planar honeycomb lattice (Figures 1a,b). However, the CdSe and CdTe SL sheets excised from the 3D bulk structures do not fully relax to completely planar structures, but instead to corrugated sheet structures similar to that of silicene (Figures 1c,d). The corrugated sheets are more stable than their planar counterparts by 5 and 21 meV for CdSe and CdTe, respectively, indicating that the ground states are nonplanar. To rationalize these differences, we scanned the potential

Structure optimizations for the bulk ZB and WZ phases start with the available experimental X-ray structures. Note that the calculations for the ZB phase are performed for the primitive cell instead of its cubic cell structure. The lattice parameters, total energy normalized per formula unit, and band gaps are listed in Table 1. The lattice parameters obtained from PBE only and in combination with SO effect are comparable, with root-mean-square deviations (RMSDs) of 13.4 and 13.5 pm from the experimental values. Since in the following we will study rationally designed layered materials that are expected to experience significant vdW interactions, it is essential to test the vdW-corrected DFTs using the experimental data of the bulk materials. Both the semiempirical vdW-corrected PBE-D2 and the first-principles vdW-DF2 methods tested yield an improved comparison over the PBE results, showing an appreciable vdW effect even for these 3D bulk materials. It has been shown that vdW interactions can give significant contributions to the structural and cohesive properties not only for layered materials, but also for 3D bulk materials including ionic solids.59,60 Among these two vdW methods tested, the PBE-D2 results are in excellent agreement with the experimental results, with an RMSD of only 3.5 pm. In comparison, the vdW-DF2 results have an RMSD of 13.1 pm (see Supporting Information, Table S1). For relative stability of ZB and WZ phases, as can be seen from Table 1, CdS is slightly more stable in the WZ than the ZB phase by 2 meV, while CdSe and CdTe are more stable in the ZB than the WZ phase by 2 and 8 meV, respectively, consistent with the trend in previously published results.52,53 SO effects have also been examined, showing no effect on the relative stability for each case. In comparison, at the level of PBE-D2, the WZ phase is stabilized by ca. 2−3 meV with respect to the ZB phase for all three species. Consequently, CdS is now more stable in the WZ phase by 5 meV, CdSe becomes comparable in energy in ZB and WZ phases, and CdTe is more stable in the ZB phase by only 5 meV. Experimental energy differences are not available to compare with. The small energy differences imply that the actual structures of the CdX series to exist depend sensitively on their growth conditions such as substrate orientation, growth temperature, and history of annealing.52 Band gaps, Eg, are calculated with both DFT and GW0 methods. The GW0[PBE] results are based on the PBEoptimized geometries, while the GW0[D2] results are based on the PBE-D2-optimized geometries. As expected, the PBE band gaps are significantly underestimated, while the GW0[PBE] and 25819

dx.doi.org/10.1021/jp409772r | J. Phys. Chem. C 2013, 117, 25817−25825

The Journal of Physical Chemistry C

Article

lattice parameters for all three species are elongated with respect to their bulk WZ phase, because the spread-out SL sheets are completely planar for CdS and become less corrugated for CdSe and CdTe than the corresponding “layers” in their bulk structures. The percentage of elongation shows a trend in good agreement with the degree of nonplanarity in terms of δ. Based on the PBE and PBE-D2 calculations, the SL sheets are less stable than the ZB or WZ phases by ca. 0.5 eV without and ca. 0.8 eV with vdW corrections. The band gaps from GW0[D2] calculations are 4.27, 3.53, and 3.26 eV for CdS, CdSe, and CdTe, respectively, showing a monotonic trend with increasing atomic number. All of these band gaps are direct at the Γ point, and are greater than those of the bulk materials, falling into the ultraviolet range. Thus, these SL sheets would have no absorption in the visible range and represent yet another set of examples of “white graphene”, similar to the SL boron nitride sheets.19 It is worth noting that in some single-layer transition metal dichalcogenide materials, GW0 was found to largely overestimate the band gaps, whereas the results from DFT calculations are better.63 Improved agreement with experiments can often be obtained by solving the Bethe−Salpeter equation (BSE), highlighting the critical role of an excitonic effect in single-layer 2D semiconductors. For the 2D SL sheets proposed in this work, the best results we could obtain are from the GW0 calculations. Whether one must resort to the BSE to address possible excitonic effects will ultimately require experimental data. Given the large energy differences between the SL sheets and the ground-state bulk ZB and WZ phases, it is important to study ML stacks to find out whether interlayer interactions may significantly stabilize the ML stacks with respect to the SL sheets and particularly to the bulk ZB and WZ phases. A separate set of calculations indicates that graphite is lower in energy than graphene by 0.11 eV per 2 atoms at the PBE-D2 level of theory. It should be noted that because of the essential interlayer vdW interactions, PBE-D2 is capable of reproducing the experimental interlayer separation of graphite, while pure PBE cannot. Prompted by the AB stacking motif of hexagonal graphite, next we investigated the ML structures of CdX, constructed by stacking single layers together in an AB fashion. The ML stacks have three possible structures, labeled as α, β, and γ, with different interlayer registries. As can be seen in Figure 3, Cd atoms are registered directly on X atoms in the α structure, whereas the same atoms are registered on top of one another in the β and γ structures. As a result of the ionic character of the CdX series, the α structures with a Cd-X registry are strongly distorted into nonplanar sheets compared to the β and γ structures. Due to their staggered conformation, it is impossible for these ML stacks, especially the α structure, to collapse to the WZ phase that has an eclipsed conformation. In addition, due to their AB stacking motif, these ML stacks have two atoms per cell registered on the center of the hexagonal rings of neighboring layers. Therefore, it is also impossible for the ML stacks to collapse to the ZB phase, which has three layers in the ABC stacking, causing an alternating atom−atom registry that is different from the atom−ring-center registry found in the ML stacks. Thus the ML stacks represent a new phase of the CdX series that is different from the ZB or WZ structures. The lattice parameters, energies, and band gaps for the ML stacks are also listed in Table 2. The lattice parameters within the layers (a_ML) are similar at the PBE and PBE-D2 levels, as in the SL sheets. In comparison, the interlayer distances, as

Figure 1. Optimized single layer sheets of CdX (X = S, Se, Te): (a) planar CdS (top view), (b) planar CdS (side view), (c) corrugated CdSe (side view), and (d) corrugated CdTe (side view). Top views of CdSe/CdTe are similar to that of CdS. The colors of atoms are kept consistent hereafter.

energy surface (PES) as a function of the deviation δ between the Cd plane and the X (X = S, Se, and Te) plane. As can be seen in Figure 2, the minimum for CdS on the PES is located at

Figure 2. PBE calculated potential energy surface of single-layer sheets of CdX (X = S, Se, Te) as a function of the relative deviation δ (Å) of the Cd plane and the X plane.

δ = 0 Å, explaining its complete planar honeycomb lattice. In comparison, for CdSe and CdTe, the planar structures with δ = 0 Å are flanked by two symmetrical corrugated structures with δ = 32.1 and 48.9 pm, respectively. Therefore, the planar structures of CdSe and CdTe correspond to a first-order saddle point and the ground state structure should be one of the two degenerate minima on the PES. Inclusion of SO coupling and vdW corrections does not change these observations. The lattice parameters, total energy normalized per formula unit, and the band gaps of the SL sheets are listed in Table 2. PBE and PBE-D2 provide nearly identical geometries, with differences less than 5 pm. Similar to the bulk phases, SO coupling (not shown) has negligible effect on geometries. The 25820

dx.doi.org/10.1021/jp409772r | J. Phys. Chem. C 2013, 117, 25817−25825

The Journal of Physical Chemistry C

Article

Table 2. Structure Parameters (a and c in Å), Total Energy Per Formula (E in eV/2 Atom), and Band Gap (Eg in eV) for the SL Sheets and the ML Stacks of CdX (X = S, Se, Te) CdS

CdSe

CdTe

properties

PBE

PBE-D2

PBE

PBE-D2

PBE

PBE-D2

a_SL a_MLα c_MLα a_MLβ c_MLβ a_MLγ c_MLγ E_SL E_MLα E_MLβ E_MLγ

4.262 4.093 6.671 4.262 9.528 4.261 10.345 −5.817 −6.117 −5.821 −5.819

4.236 4.018 6.560 4.229 6.842 4.144 7.632 −5.980 −6.662 −6.222 −6.142

4.442 4.281 6.972 4.438 9.185 4.441 10.892 −5.138 −5.453 −5.143 −5.140

4.402 4.212 6.849 4.413 6.850 4.280 7.836 −5.306 −6.017 −5.611 −5.556

4.726 4.588 7.470 4.713 8.758 4.723 11.078 −4.485 −4.745 −4.498 −4.489

4.679 4.518 7.317 4.725 6.943 4.510 8.310 −4.669 −5.364 −5.044 −4.973

CdS

CdSe

CdTe

band gap

PBE[D2]

GW0[D2]

PBE[D2]

GW0[D2]

PBE[D2]

GW0[D2]

Eg_SL Eg_MLα Eg_MLβ Eg_MLγ

1.68 0.92 0.72 0.70

4.27 1.97 1.89 1.79

1.32 0.45 −0.10 0.31

3.53 1.23 0.67 1.06

1.31 0.57 −0.26 0.23

3.26 1.16 0.19 0.82

Figure 3. PBE-D2 optimized multilayer stacks of CdX (X = S, Se, Te): (a) CdS (from left to right are MLα, MLβ, and MLγ), (b) CdSe (from left to right are MLα, MLβ, and MLγ), and (c) CdTe (from left to right are MLα, MLβ, and MLγ).

0.1−0.2 Å from its PBE values. In comparison, the significant reduction of the lattice parameter c_ML in the β and γ structures by 2−3 Å with PBE-D2 functional indicate that their interlayer interactions are mainly vdW interactions. Among the three structures for each species, α is the most stable at the PBE-D2 level, followed by β and γ. In addition, the energy difference between the α and β (or γ) structures at the PBE-D2 level decreases monotonically with increasing atomic number. This trend agrees well with earlier theoretical findings that CdS has the greatest ionic character while CdSe and CdTe are more covalent.53 Comparing the most stable α-ML stacks with the SL sheets, the energies of the ML stacks are lowered by ca. 0.7 eV per 2 atoms at the PBE-D2 level due to the interlayer interactions including mainly bonding interactions plus addi-

reflected by half of c_ML, show greater difference between PBE and PBE-D2, especially for the β and γ structures. PBE, which lacks vdW interactions, probably fails to provide correct interlayer distances. It is expected that PBE-D2 should give more reasonable interlayer distances. In fact, the lattice parameters c_ML obtained from PBE-D2 are comparable to that in graphite at the same level, 6.437 Å. The observation that the c_ML parameter is shortened by different amounts for the three ML stacks should be ascribed to the difference in their interlayer registries. Due to the ionic character of the CdX series, the α structures with a Cd-X registry are strongly distorted into nonplanar sheets and their corresponding interlayer distances are the shortest. The application of PBED2 functional only reduced the lattice parameter c_ML by 25821

dx.doi.org/10.1021/jp409772r | J. Phys. Chem. C 2013, 117, 25817−25825

The Journal of Physical Chemistry C

Article

Figure 4. Optimized single-walled nanotube structures of CdX (X = S, Se, Te): (a) (5,5) armchair nanotube (top is a side view of CdS, and below are front views of CdS, CdSe, and CdTe from left to right), and (b) (9,0) zigzag nanotube (top is a side view of CdS, and below are front views of CdS, CdSe, and CdTe from left to right).

Table 3. Structure Parameters (Diameter in Å), Total Energy Per Formula (E in eV/2 Atom), and Band Gap (Eg in eV) for a (5,5) NTA and a (9,0) NTZ of CdX (X = S, Se, Te) CdS

a

CdSe

properties

PBE

PBE-D2

PBE

d_NTAa d_NTZa E_NTA E_NTZ

11.384/12.286 11.917/12.802 −5.870 −5.869

11.193/12.220 11.732/12.745 −6.067 −6.064 CdS

11.758/12.925 12.315/13.469 −5.245 −5.242

CdTe PBE-D2

11.556/12.844 11.945/13.399 −5.445 −5.441 CdSe

PBE

PBE-D2

12.489/13.817 13.048/14.399 −4.607 −4.603

12.256/13.734 12.665/14.316 −4.815 −4.810 CdTe

band gap

PBE

PBE-D2

PBE

PBE-D2

PBE

PBE-D2

Eg_NTA Eg_NTZ

1.84 1.84

1.90 1.90

1.57 1.58

1.64 1.65

1.55 1.57

1.64 1.67

Inner cylinder (Cd)/outer cylinder (X).

present studies only focused on the infinite ML stacks, but as can be seen from the large difference of the band gaps between SL sheets and ML stacks, one may expect that the ML stacks with a finite number of layers may have band gaps that fall somewhere between those of SL sheets and ML stacks. Similar to the band gap engineering using quantum dots (QDs) of CdX, the preparation of finite-size ML stacks can foster quantum flakes (QFs) with size-dependent band gaps finetuned by the dimension of QFs for various applications including solar cells. Armchair and Zigzag Single-Walled Nanotubes (SWNTs). Following the studies on 3D and 2D materials, next we turn to 1D SWNTs. Similar to the case of carbon nanotubes, an SL sheet of CdX can be wrapped into two different SWNT structures, i.e., armchair NT (NTA) and zigzag NT (NTZ). Chiral SWNTs and nanoribbons could be of interest but are out of the scope of this work. A (5,5) NTA and a (9,0) NTZ for each species were constructed, and their optimized structures are shown in Figure 4. For both NTAs and NTZs, the Cd atoms are in the inner cylinder, while the S, Se and Te are in the outer cylinder. The separation between the concentric cylinders is the smallest at 0.5 Å for CdS and the largest at 0.7 Å for CdTe. This trend is in line with the degree of nonplanarity of the SL sheets shown previously. The structure parameters, total energy normalized to formula unit, and band gaps are listed in Table 3. The average diameters of NTZs are slightly larger than those of NTAs, and both increase with increasing atomic number for chalcogen X. NTA and NTZ are close in energy, and both are stabilized from their SL sheet

tional vdW forces. However, ML structures are still less stable than the ground-state WZ or ZB phases, by ca. 0.1 eV per 2 atoms for the most stable α structure. These energy differences, although sizable, should not be used to preclude the possible syntheses of these metastable ML stacks. The stabilizations of ML stacks with respect to the SL sheets as a result of the interlayer interactions also suggest that the free-standing SL sheets can be stabilized by growing epitaxial films of CdX on proper substrates. Since PBE-D2 calculated structures are more reliable and the α structure is the most stable ML stack, GW0[D2] band gaps are discussed for the α structure only. The band gaps of ML stacks range from 2.0 down to 1.2 eV, showing again a monotonic trend with increasing atomic number. The band gaps are indirect for CdS and CdSe and direct for CdTe, showing a gradual transition with increasing atomic number for chalcogens in terms of the difference between direct and indirect band gaps for each species. These values overlap with the band gap range of the ZB and WZ bulk phases at the lower end but extend the lower limit down to the infrared region of the electromagnetic spectrum, indicating that these materials are capable of absorbing long wavelength radiations. It is also interesting that the SL sheets are white for lack of absorption in the visible range, whereas the ML stacks, especially those of CdSe and CdTe, could be black because the band gaps are even smaller than the lower end of 1.6 eV for the visible range. These materials are thus complementary to the bulk ZB and WZ materials in that a much wider wavelength range on the spectrum can be now utilized. It is worth pointing out that the 25822

dx.doi.org/10.1021/jp409772r | J. Phys. Chem. C 2013, 117, 25817−25825

The Journal of Physical Chemistry C

Article

counterparts by ca. 50−120 meV at the PBE level. Due to the wall-to-wall interactions, vdW interactions can also be important for SWNTs. At the PBE-D2 level, both NTAs and NTZs are stabilized from their SL sheet counterparts by ca. 80−140 meV, and their diameters are slightly reduced from the PBE results. The stabilization of ML stacks with respect to SL sheets by the interlayer interactions suggests that the singlewalled NTAs and NTZs may be further stabilized by forming multiwalled NTs. Growth of SWNTs into a bundle or on a proper substrate may also lead to additional stabilization. Compared to the bulk phases, the SL sheets, and the ML stacks studied above, the number of atoms in the unit cell increases significantly to 20 for the (5,5) NTA and to 36 for the (9,0) NTZ, thus prohibiting their GW0 calculations. Hence only the DFT calculated values are listed in Table 3. The band gaps of 1D SWNTs are all direct at the Γ point, as can be seen in Figure S1. Given that the DFT calculated band gaps of NT structures are larger than those of SL structures by 0.21−0.35 eV, one may anticipate that the GW0 band gaps of SWNTs are at least as large as, if not larger than, the GW0 band gaps of SL structures. These SWNT structures should thus be considered good insulators.

These rationally designed new materials are complementary to the 3D bulk ZB and WZ materials in that a much wider wavelength range on the electromagnetic spectrum can be now utilized. On one hand, the band gaps of 2D SL sheets (and possibly 1D SWNTs as well) are found to fall into the ultraviolet region, making them yet another set of “white graphene” materials for lack of absorption in the visible range. On the other hand, the band gaps of 3D ML stacks overlap with the band gap range of the bulk phases at the lower end but extend the lower limit down to the infrared region. The visible color of the ML stacks of CdSe and CdTe could be black because the band gaps are even smaller than the lower end of 1.6 eV for the visible range. The large differences in band gaps between the SL sheets and the infinite ML stacks suggest that, similar to the band gap engineering using quantum dots (QDs), the preparation of finite-size ML stacks of CdX can foster quantum flakes (QFs) with size-dependent band gaps finetuned by the dimension of QFs for various applications including solar cells.

■

ASSOCIATED CONTENT

S Supporting Information *

■

Comparison of PBE, PBE-D2, and vdW-DF2 results for the 3D bulk ZB and WZ phases; band structures and DOS for all materials studied; complete author lists for refs 6, 8, 9, 18, 32, and 61. This material is available free of charge via the Internet at http://pubs.acs.org.

CONCLUSIONS In summary, we have studied the geometric structures, relative energies, and electronic properties of 3D ML stacks, 2D SL sheets, and 1D SWNT structures of cadmium chalcogenides CdX (X = S, Se, Te) using ab initio DFT theory, supplemented with SO coupling, vdW interactions, and the GW approximation. The rational design of these new structures was motivated by the prototypical single layer structures of graphene, BN, SiC, and their nanotubes, which are characterized by a similar valence electron count. On the basis of the benchmark calculations for the 3D bulk ZB and WZ phases, whose experimental lattice parameters and band gaps are available, proper theoretical methodologies have been identified, allowing trustworthy results to be derived for rationally designing new materials. We have found that the 2D SL sheet structure of CdS is completely planar while those of CdSe and CdTe are slightly corrugated, all showing a honeycomb lattice. These SL sheets are destabilized with respect to their corresponding bulk ZB and WZ phases but can be significantly stabilized by forming 3D ML stacks in an AB stacking motif as a result of interlayer interactions including bonding interactions and/or vdW interactions. Out of the three possible 3D ML stacks, the most stable α structures with a Cd-X interlayer atomic registry show a strong distortion into nonplanar sheets, as a result of the ionic character of the CdX series. 1D (5,5) armchair and (9,0) zigzag SWNTs are also found to be stabilized from their SL sheet counterparts. Both SWNTs consist of two concentric cylinders, with the Cd atoms in the inner cylinder and the chalcogenide atoms in the outer cylinder, and with the intercylinder separations showing the same trend as the degree of nonplanarity in the SL sheets. The interlayer interactions demonstrated for ML stacks suggest that all these new materials may be interesting targets for experimental synthesis despite their higher energies per stoichiometric formula relative to the bulk phases, since the free-standing SL sheets can be stabilized by growing epitaxial films of CdX on proper substrates and the SWNTs may be stabilized by forming MWNTs or growing on a proper substrate or into a bundle.

■

AUTHOR INFORMATION

Corresponding Authors

*Phone +1-865-574-7192; e-mail [email protected]. *Phone +1-865-574-5081; e-mail [email protected]. Present Address §

Department of Physics, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802−6300, United States. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work used computational resources of the National Center for Computational Sciences at Oak Ridge National laboratory and of the National Energy Research Scientific Computing Center, which are supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0500OR22750 and DE-AC02-05CH11231, respectively. We also acknowledge the support from the Center for Nanophase Materials Sciences, which is sponsored at ORNL by the Scientific User Facilities Division, U.S. Department of Energy.

■

REFERENCES

(1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666−669. (2) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. TwoDimensional Gas of Massless Dirac Fermions in Graphene. Nature 2005, 438, 197−200. (3) Zhang, Y.; Tan, Y.-W.; Stormer, H. L.; Kim, P. Experimental Observation of the Quantum Hall Effect and Berry’s Phase in Graphene. Nature 2005, 438, 201−204. (4) Pisana, S.; Lazzeri, M.; Casiraghi, C.; Novoselov, K. S.; Geim, A. K.; Ferrari, A. C.; Mauri, F. Breakdown of the Adiabatic Born-

25823

dx.doi.org/10.1021/jp409772r | J. Phys. Chem. C 2013, 117, 25817−25825

The Journal of Physical Chemistry C

Article

Oppenheimer Approximation in Graphene. Nat. Mater. 2007, 6, 198− 201. (5) Xia, J.; Chen, F.; Li, J.; Tao, N. Measurement of the Quantum Capacitance of Graphene. Nat. Nanotechnol. 2009, 4, 505−509. (6) Butler, S. Z.; Hollen, S. M.; Cao, L.; Cui, Y.; Gupta, J. A.; Gutiérrez, H. R.; Heinz, T. F.; Hong, S. S.; Huang, J.; Ismach, A. F.; et al. Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene. ACS Nano 2013, 7, 2898−2926. (7) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Two-Dimensional Atomic Crystals. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10451−10453. (8) Hernandez, Y.; Nicolosi, V.; Lotya, M.; Blighe, F. M.; Sun, Z.; De, S.; McGovern, I. T.; Holland, B.; Byrne, M.; Gun’Ko, Y. K.; et al. Highyield Production of Graphene by Liquid-phase Exfoliation of Graphite. Nat. Nanotechnol. 2008, 3, 563−568. (9) Coleman, J. N.; Lotya, M.; O’Neill, A.; Bergin, S. D.; King, P. J.; Khan, U.; Young, K.; Gaucher, A.; De, S.; Smith, R. J.; et al. TwoDimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials. Science 2011, 331, 568−571. (10) Rao, C. N. R.; Nag, A. Inorganic Analogues of Graphene. Eur. J. Inorg. Chem. 2010, 4244−4250. (11) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010, 105, 136805. (12) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.-Y.; Galli, G.; Wang, F. Emerging Photoluminescence in Monolayer MoS2. Nano Lett. 2010, 10, 1271−1275. (13) Zhou, K.-G.; Mao, N.-N.; Wang, H.-X.; Peng, Y.; Zhang, H.-L. A Mixed-Solvent Strategy for Efficient Exfoliation of Inorganic Graphene Analogues. Angew. Chem., Int. Ed. 2011, 50, 10839−10842. (14) Aufray, B.; Kara, A.; Vizzini, S.; Oughaddou, H.; Leandri, C.; Ealet, B.; Lay, G. L. Graphene-like Silicon Nanoribbons on Ag(110): A Possible Formation of Silicene. Appl. Phys. Lett. 2010, 96, 183102. (15) Lalmi, B.; Oughaddou, H.; Enriquez, H.; Kara, A.; Vizzini, S.; Ealet, B.; Aufray, B. Epitaxial Growth of a Silicene Sheet. Appl. Phys. Lett. 2010, 97, 223109. (16) Bianco, E.; Butler, S.; Jiang, S.; Restrepo, O. D.; Windl, W.; Goldberger, J. E. Stability and Exfoliation of Germanane: A Germanium Graphane Analogue. ACS Nano 2013, 7, 4414−4421. (17) Sun, L.; Li, Y.; Li, Z.; Li, Q.; Zhou, Z.; Chen, Z.; Yang, J.; Hou, J. G. Electronic Structures of SiC Nanoribbons. J. Chem. Phys. 2008, 129, 174114. (18) Shi, Y.; Hamsen, C.; Jia, X.; Kim, K. K.; Reina, A.; Hofmann, M.; Hsu, A. L.; Zhang, K.; Li, H.; Juang, Z.-Y.; et al. Synthesis of Few-Layer Hexagonal Boron Nitride Thin Film by Chemical Vapor Deposition. Nano Lett. 2010, 10, 4134−4139. (19) Zeng, H.; Zhi, C.; Zhang, Z.; Wei, X.; Wang, X.; Guo, W.; Bando, Y.; Golberg, D. “White Graphenes”: Boron Nitride Nanoribbons via Boron Nitride Nanotube Unwrapping. Nano Lett. 2010, 10, 5049−5055. (20) Lopez-Bezanilla, A.; Huang, J.; Terrones, H.; Sumpter, B. G. Boron Nitride Nanoribbons Become Metallic. Nano Lett. 2011, 11, 3267−3273. (21) Lopez-Bezanilla, A.; Huang, J.; Terrones, H.; Sumpter, B. G. Structure and Electronic Properties of Edge-Functionalized Armchair Boron Nitride Nanoribbons. J. Phys. Chem. C 2012, 116, 15675− 15681. (22) Xie, T.; Lin, Y.; Wu, G.; Yuan, X.; Jiang, Z.; Ye, C.; Meng, G.; Zhang, L. AlN Serrated Nanoribbons Synthesized by Chloride Assisted Vapor−Solid Route. Inorg. Chem. Commun. 2004, 7, 545−547. (23) Lu, X.; Chen, Z. Curved Pi-Conjugation, Aromaticity, and the Related Chemistry of Small Fullerenes (