Article pubs.acs.org/JPCC
Theoretical Predictions of Freestanding Honeycomb Sheets of Cadmium Chalcogenides Jia Zhou,*,† Jingsong Huang,†,‡ Bobby G. Sumpter,†,‡ Paul R. C. Kent,†,‡ Yu Xie,† 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: Two-dimensional (2D) nanocrystals of CdX (X = S, Se, Te) typically grown by colloidal synthesis are coated with organic ligands. Recent experimental work on ZnSe showed that the organic ligands can be removed at elevated temperature, giving a freestanding 2D sheet of ZnSe. In this theoretical work, freestanding single- to few-layer sheets of CdX, each possessing a pseudo honeycomb lattice, are considered by cutting along all possible lattice planes of the bulk zinc blende (ZB) and wurtzite (WZ) phases. Using density functional theory, we have systematically studied their geometric structures, energetics, and electronic properties. A strong surface distortion is found to occur for all of the layered sheets, and yet all of the pseudo honeycomb lattices are preserved, giving unique types of surface corrugations and different electronic properties. The energetics, in combination with phonon mode calculations and molecular dynamics simulations, indicate that the syntheses of these freestanding 2D sheets could be selective, with the single- to few-layer WZ110, WZ100, and ZB110 sheets being favored. Through the GW approximation, it is found that all single-layer sheets have large band gaps falling into the ultraviolet range, while thicker sheets in general have reduced band gaps in the visible and ultraviolet range. On the basis of the present work and the experimental studies on freestanding double-layer sheets of ZnSe, we envision that the freestanding 2D layered sheets of CdX predicted herein are potential synthesis targets, which may offer tunable band gaps depending on their structural features including surface corrugations, stacking motifs, and number of layers.
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INTRODUCTION Semiconducting II−VI binary cadmium chalcogenides CdX (X = S, Se, Te) have been drawing tremendous interest for broad applications, owing to their outstanding electronic and optical properties.1−5 Three-dimensional (3D) bulk structures of CdX in zinc blende (ZB) and wurtzite (WZ) phases are close in structural stability.6,7 Experimental advances in the last two decades have shown that the manipulation of physical dimensions provides an efficient way to tune the electronic and optical properties of CdX. For instance, quantum confinement effects have been demonstrated for dimensionally reduced nanocrystals of CdX including 0D quantum dots,8−11 and 1D quantum rods, wires, ribbons, and belts,12−19 allowing them to be employed in photovoltaic, light-emitting diode, biological imaging, and photodetector applications.10,12,13,18,20−23 In a similar vein, 2D colloidal nanodisks and nanoplatelets of few-layer CdX have recently been developed,24−27 displaying thickness-dependent absorption and emission spectra.28 Nanocrystals typically grown by colloidal synthesis are coated with organic ligands (or surfactants), which passivate the surface electronic states, stabilize the nanocrystals, and control their size and shape.10,29,30 © 2014 American Chemical Society
The II−VI CdX materials may be considered isovalent with the IV−IV and III−V materials if one leaves out the closed-shell 4d10 electrons of Cd. This prompts one to wonder whether freestanding 2D layered honeycomb structures of CdX without ligands can be made, similar to graphene and its inorganic analogues, such as silicene, h-BN, etc.31 2D graphene analogues have attracted great attention in various disciplines from the standpoints of both fundamental science and technology,32−34 ever since single-layer graphene was fabricated by micromechanical cleavage.35,36 Many 2D layered materials are prepared simply by the mechanical or liquid-phase exfoliation of their layered solids, such as graphite, BN, MoS2, Bi2Te3, etc.37−39 The exfoliation is facilitated by the weak interlayer van der Waals (vdW) forces.33 In comparison, the 3D bulk structures of CdX are characterized by “layers” of six-membered rings with alternating Cd and X atoms, but they are different from layered vdW solids in that neighboring “layers” are covalently bonded, thus making it challenging to prepare their freestanding 2D sheets directly by exfoliation. This could be the Received: May 1, 2014 Revised: May 16, 2014 Published: May 19, 2014 16236
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exchange and correlation interactions of valence electrons are described by the Perdew−Burke−Ernzerhof (PBE) functional.53,54 The DFT-D2 method of Grimme55 was tested for the CdSe series. The DFT-D2 results turned out to be qualitatively similar to those of DFT (see Supporting Information (SI) Table S1 for details), and thus are omitted in the text. The Brillouin-zone integrations were performed on a dense Γ-centered 16 × 16 × 1 k-point grid.56 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 electronic self-consistency was set to 10−6 eV. During the structure optimizations, the vacuum regions were 30 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 adopted computational methodology for geometry and energy calculations has been validated in our previous work.31 To test the stability of the structures found, we also calculated their phonon modes by using Density Functional Perturbation Theory (DFPT) in Quantum Espresso.57 The PAW potentials (Cd.pbe-dnkjpaw_psl.0.2.UPF and Se.pbe-n-kjpaw_psl.0.2.UPF) provided within Quantum Espresso and PBE functional were adopted, together with a kinetic energy cutoff for plane waves of 55 Ry (ca. 750 eV) and a k-mesh of 6 × 6 × 1 (higher energy cutoff for plane waves at 80 Ry together with increased FFT grids gave similar results). To explore the possibility of interconversion between singlelayer sheets with different corrugations, ab initio molecular dynamics (MD) simulations were performed with VASP using the PAW potentials and the PBE functional given above for geometries and energies. Simulations using an NVT ensemble at 300 and 500 K with a time step of 1 fs were carried out for 20 ps on 3 × 3 or 4 × 4 supercell geometries, which are constructed from the optimized geometries of primitive cells. Following a set of systematic convergence tests, the k-mesh was set to the Γ point only, the kinetic energy cutoff for plane waves was reduced to the default 274.3 eV, and the “normal” precision setting was adopted. The convergence criterion for electronic self-consistency was set to 10−5 eV. Finally, for accurate band gap calculations, quasiparticle GW0 calculations58−61 were performed. The GW0 calculations are partially self-consistent, since the eigenvalues (excluding orbitals) are updated in the Green’s function only, while the screened potential is fixed to the initial W0 from the DFT calculations. However, with the update of eigenvalues, these calculations give more accurate results than the computationally cheaper nonself-consistent G0W0 calculations. For reasons of computational cost, we reduced the energy cutoff for the response function to 150 eV and used sparser but sufficiently large k-point grids of 8 × 8 × 1 for the GW0 calculations.60,62 Compared to the well underestimated band gaps at a pure DFT level, our previous calculations using the GW0 approach yield much better agreements with experimental band gap values for bulk CdX.31
reason that freestanding 2D layered sheets of CdX have not yet been seriously considered, except for a couple of theoretical explorations of their single-layer sheets.31,40 During the past decade, various 2D lamellar inorganic− organic hybrid structures [CdnXn(L)m] (where X = S, Se, or Te, L = alkylamine ligand, n = 1−3, and m = 0.5 or 1 depending on L) have been synthesized by solvothermal and soft colloidal template techniques.24,41−44 These lamellar structures may be viewed as being obtained by “breaking” the 3D CdX lattice45 with organic alkylamines into separate inorganic honeycomb slabs, with the number of layers in each CdX slab depending on the reactants and reaction temperatures. Similar to other layered vdW solids, these 2D lamellar structures can be exfoliated by sonication in appropriate organic solvents into isolated 2D nanosheets, with each CdX slab coated by alkylamine ligands.24 Similar 2D single- and double-layer hybrid structures of ZnX have also been reported.41,43,45 Recently, a genuine freestanding double-layer honeycomb lattice of ZnSe has been synthesized by exfoliating its lamellar hybrid intermediate followed by removing the alkylamine ligand with heating.46 The freestanding 2D sheet of ZnSe has been tested for photoelectrochemical solar water splitting, exhibiting a photocurrent density 4−10 times higher than those of its ligand-coated hybrid layers, 8 times higher than quantum dots, and nearly 200 times higher than that of its 3D bulk.46 This simple two-step procedure opens an avenue for the systematic fabrication of freestanding 2D sheets of ZnX from their lamellar intermediates. Given the similarity between ZnX and CdX, one can envision the synthesis of freestanding 2D sheets of CdX, which may offer a novel set of 2D layered materials for a wealth of innovative applications. Experimentally, lamellar CdX and ZnX are found to consist of ligand-coated ZB or WZ sheets encased by the (100) or (110) facets.24,28,41,43,45 Except for the ZB sheet with (100) facets, the rest of the sheets possess pseudo honeycomb lattices with unique types of surface corrugations. The single-layer 2D sheets of CdX explored previously are equivalent to a cut along the (111) plane of the ZB phase or equivalently the (001) plane of the WZ phase, which are found to relax to planar graphenelike honeycomb lattices.31,40 These differences prompt the following questions: What are all of the possible ways to form a pseudo honeycomb lattice? Are the surface corrugations persistent when the organic ligands are removed? And how do the structures, energies, and properties of the freestanding 2D sheets of CdX depend on their surface corrugations and layer thicknesses? It is essential to address these fundamental questions in light of the great likelihood that freestanding 2D honeycomb structures of CdX will be made in the near future. With this motivation, herein we systematically investigate the single- to few-layer honeycomb structures of CdX derived from all possible lattice planes of the parent bulk phases. We determine their geometric structures, energetics, and electronic properties by using density functional theory (DFT) and the quasiparticle GW approximation.
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METHODOLOGY First-principles calculations for geometrical structures and energetics were carried out using the Vienna ab initio simulation package (VASP).47−50 The Kohn−Sham equations were solved using the projector-augmented wave (PAW) method.51,52 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
RESULTS AND DISCUSSION We start with the ZB and WZ bulk phases instead of the lamellar hybrid structures to construct the initial structures of the freestanding single- to few-layer sheets. The simplification, mainly due to the lack of all X-ray structures of the lamellar hybrids, is justified by the fact that the inorganic slabs in the lamellar hybrid structures are close to their bulk structures.24 16237
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On the basis of a thorough search, Scheme 1 unveils all of the possible lattice planes of the ZB and WZ phases along which Scheme 1. All of the Possible Single-Layer (SL) and DoubleLayer (DL) Sheets with a Pseudo Honeycomb Lattice Cut along Different Lattice Planes (in red) of the ZB (a) and WZ (b) Bulk Structuresa
Figure 1. Optimized SL sheets of CdSe: (a) ZB111/WZ001 (side view), (b) ZB111/WZ001 (top view), (c) ZB110/WZ100 (side view), (d) ZB110/WZ100 (top view), (e) WZ110 (side view), and (f) WZ110 (top view). The colors of atoms are kept consistent hereafter.
a
only three distinct structures. (Note that the structures of CdS and CdTe are similar to CdSe, and therefore are not shown.) The ZB111 or WZ001 SL sheets for all CdX (X = S, Se, Te), although cut from different bulk structures, the final optimized structures are the same. As can be seen from Figure 1a,b, the ZB111/WZ001 SL sheet of CdSe is relaxed to a nearly planar structure, with a nonplanarity of 0.3 Å as determined by the separation between the Cd plane and the Se plane. In comparison, the corresponding SL sheet of CdS is completely planar, while that of CdTe is slightly less planar than CdSe due to its larger separation of 0.5 Å between the Cd plane and the Te plane.31 Regardless of the degree of nonplanarity, all of these SL sheets of CdX are arranged in a honeycomb lattice, similar to graphene. This appears to be a natural outcome of the 4d105s2 valence configuration of Cd. If one leaves out the closed-shell 4d10 electrons, then CdX may be considered isovalent with other graphene analogues such as silicene, germanene, SiC, h-BN, etc.31 Figure 1c,d shows the optimized ZB110 or the WZ100 SL sheet of CdSe (both reach the same accordion fold structure following full optimizations), while Figure 1e,f shows the optimized WZ110 SL sheet of CdSe displaying a different corrugation. Unlike the ZB111/WZ001 SL sheet, where the Cd and Se atoms are on separate Cd and Se planes in either the initial or the optimized structures, the Cd and Se atoms are coplanar (either top or bottom) in the initial ZB110/WZ100 and WZ110 SL sheets (Scheme 1). With relaxation, the Cd atoms move to inner planes while the Se atoms remain on the outer surfaces, forming four-atom-layer structures. In spite of the relaxations, these two SL sheets bear strong corrugations, similar to their corresponding unrelaxed crystal cuts. Due to the strong corrugations, the thickness of the ZB110/WZ100 and WZ110 SL sheets are 2.63 and 2.69 Å, respectively (not including vdW atomic radii), much thicker than the nearly planar ZB111/WZ001 SL sheets (SI Table S2). Comparing the three SL sheets shown in Figure 1, it is surprising that, given the same geometrical connectivity between the Cd and Se atoms,
Few-layer sheets (not labelled) are constructed similarly.
one may derive the desired 2D sheets possessing a pseudo honeycomb lattice. With the 2D sheets excised out of the bulk, the planes shown in Scheme 1 also correspond to the facets encasing the 2D sheets. For the ZB bulk phase, only the (111) and (110) planes meet the requirement, while for the WZ bulk phase, three different planes including (001), (100), and (110) are possible, thus giving a total of five scenarios, which are labeled as ZB111, ZB110, WZ001, WZ100, and WZ110 to indicate the corresponding bulk structures and the facets of the 2D sheets. Although colloidal few-layer nanodisks and nanoplatelets of CdX with ligand-coated ZB100 sheets have also been made experimentally,27,28 their inorganic slabs do not have honeycomb lattices, and the ZB100 facet has higher calculated surface energy than the ZB111 and ZB110 facets.46 Therefore, the ZB100 sheets are not studied in this work. In the following, we discuss the optimized structures, energetics, and electronic properties of the 2D single- to few-layer sheets encased by all of these five facets. Single-Layer (SL) Sheets. Figure 1 shows the side and top views of the optimized SL sheets of CdSe. The geometry optimizations were performed for all of the five facets, yielding 16238
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are currently performing calculations using very large supercells with long-range ripples, which will also be subject to phonon calculations. As will be seen in the following section, a doublelayer sheet stacked from the ZB111/WZ001 SL sheet still shows imaginary frequencies while those stacked from the ZB110/WZ100 and WZ110 SL sheets have only real frequencies, indicating that they are stable. To explore the possibility of interconversion between the three SL sheets, ab initio MD simulations were performed for 20 ps for the 4 × 4 supercell of the ZB111/WZ001 sheet, and the 3 × 3 supercells of the ZB110/WZ100 and WZ110 sheets. It is found that the nearly planar geometry of the ZB111/ WZ001 sheet is strongly distorted to a nonplanar structure during the 20 ps run at 500 K (SI Figure S1), which displays local corrugation features from the more stable ZB110/WZ100 and WZ110 sheets. The same observation is obtained with the temperature lowered to 300 K. In comparison, the ZB110/ WZ100 sheet maintains its accordion fold geometry after 20 ps run at 300 K, although it may adopt some local corrugation features of the most stable WZ110 sheet if the temperature is raised to 500 K. Raising the temperature may provide sufficient kinetic energy to overcome the local barrier to reach a different corrugation. However, for the WZ110 sheet, simulations at both 300 and 500 K did not change its corrugation. In addition, it is noteworthy that for the latter two SL sheets, long-range ripples were observed during the 20 ps simulations along the b lattice vector for the 3 × 3 supercell of the ZB110/WZ100 sheet and along the a lattice vector for the 3 × 3 supercell of the WZ110 sheet (SI Figure S1), implying a tendency for these two sheets to undergo long-range rippling on top of local corrugations. Nevertheless, the observations from the MD simulations for the three SL sheets are consistent with their order of stabilities. It is expected that the WZ110 SL sheet would be the easiest to access, closely followed by the ZB110/ WZ100 SL sheets, both of which may display long-range ripples on top of local corrugations, while the most-planar, graphenelike ZB111/WZ001 SL sheets would be the most difficult to synthesize due to the tendency to distort to the more stable WZ110 and ZB110/WZ100 structures. Double-Layer (DL) Sheets. Figure 3 shows the side and top views of all possible optimized DL sheets of CdSe that can be obtained from the five different facets of the ZB or WZ phase. (The optimized DL sheet structures of CdS and CdTe are similar and therefore not shown.) From the top views, the honeycomb lattices are clearly visible. Unlike the SL sheets shown in Figure 1, the DL sheets encased by the ZB111 (Figure 3a,b) and WZ001 (Figure 3e,f) facets are no longer the same, nor are the DL sheets encased by the ZB110 (Figure 3c,d) and WZ100 (Figure 3g,h) facets. Both of the ZB111 and WZ001 DL sheets have AB stacking but with different interlayer offsets: each Cd/Se atom on one layer is registered directly on the top of a Se/Cd atom of the other layer in the WZ001 DL sheet, while there are half of Cd/Se atoms sitting above/below the centers of CdSe hexagons in the ZB111 DL sheets. The WZ100 DL sheet also shows an AB stacking, but with a lateral offset by 1/2 b of the bulk structure. The rest ZB110 and WZ110 DL sheets both have a pseudo AA stacking motif, as can be seen from the top view of Figure 3, that maximizes the hexagonal overlap. As in the SL case, the Cd atoms tend to move inward during optimizations while the chalcogenide atoms prefer to remain on the outer surfaces. As can be seen from the phonon dispersions (SI Figure S2), both of the ZB111 and WZ001 DL sheets have imaginary
the SL sheets can adopt dramatically different types of corrugation, accompanied by different energies and properties. To our best knowledge, this behavior has not been reported for other freestanding 2D layered materials. Energetically, the WZ110 SL sheet of CdSe is the most stable among the three structures. The ZB110/WZ100 and ZB111/ WZ001 counterparts are higher in energy by 13 and 173 meV per formula unit, respectively. (A similar trend is found for CdS and CdTe.) A different and yet relevant class of 2D lamellar inorganic−organic hybrid structures with SL sheets of ZnTe and CdSe has been synthesized via solvothermal route.41,43,45 The inorganic slabs in these hybrid structures are encased by the ZB110, WZ100, or WZ110 facets, but not by the ZB111 or WZ001 facets. Hoffmann and co-workers have examined these different SL sheets of CdSe and ZnSe with methylamine CH3NH2 as the ligand model, and found that the WZ110 structure is the most stable, the ZB110 and WZ100 structures are slightly less stable by
