Home
Search
Collections
Journals
About
Contact us
My IOPscience
Geometric and electronic structures of mono- and di-vacancies in phosphorene
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 065705 (http://iopscience.iop.org/0957-4484/26/6/065705) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.203.227.61 This content was downloaded on 25/01/2015 at 16:23
Please note that terms and conditions apply.
Nanotechnology Nanotechnology 26 (2015) 065705 (9pp)
doi:10.1088/0957-4484/26/6/065705
Geometric and electronic structures of mono- and di-vacancies in phosphorene Ting Hu and Jinming Dong Group of Computational Condensed Matter Physics, National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China E-mail: [email protected] Received 21 November 2014, revised 29 December 2014 Accepted for publication 2 January 2015 Published 19 January 2015 Abstract
The geometric structures, stabilities and diffusions of the monovacancy (MV) and divacancy (DV) in two-dimensional phosphorene, as well as their influences on their vibrational and electronic properties have been studied by first-principles calculations. Two possible MVs and 14 possible DVs have been found in phosphorene, in which the MV-(5|9) with a pair of pentagon–nonagon is the ground state of MVs, and the DV-(5|8|5) with a pentagon–octagon– pentagon structure is the most stable DV. All 14 DVs could be divided into four basic types based upon their topological structures and transform between different configurations via bond rotations. The diffusion of MV-(5|9) is found to exhibit an anisotropic character, preferring to migrate along the zigzag direction in the same half-layer. The introduction of MV and DV in phosphorene influences its vibrational properties, inducing the localized defect modes, which could be used to distinguish different vacancy structures. The MVs and DVs also have a significant influence on the electronic properties of phosphorene. It is found that the phosphorene with MV-(5|9) is a ferromagnetic semiconductor with the magnetic moment of 1.0 μB and a band gap of about 0.211 eV, while the DV induces a direct-indirect band gap transition. Our calculation results on the MV and DV in phosphorene are important for the promising application of the phosphorene in the nanoelectronics. Keywords: vacancy, phosphorene, stability (Some figures may appear in colour only in the online journal) 1. Introduction
Unlike zero-gap semimetal graphene, the phosphorene exhibits a direct band gap, which can be modified from 1.51 eV of a monolayer to 0.59 eV of a five-layer [12]. Moreover, it is reported that the phosphorene has a high carrier mobility up to 1000 cm2 V–1 s–1 [8] and an appreciably high on/off ratio up to 104 when it is used in a transistor [9], making this material of great interest for future nanoelectronic applications. Furthermore, the phosphorene has a characteristic puckered structure, leading to a substantial anisotropy of its mechanical behavior, electric conductance and optical responses [9, 13–15], which distinguishes it from many other isotropic 2D crystals. Various investigations have shown that the atomic-scale defects and vacancies, generated usually by ion or electron irradiations [16, 17], can strongly influence electronic and mechanical properties of these 2D materials [18, 19]. Therefore, understanding possible formation and diffusion
The two-dimensional (2D) hexagonal nanosheets, such as graphene [1, 2], silicene [3], germanene [4], boron-nitride (hBN) [5], and the transition metal dichalcogenides [6, 7] have been intensively investigated in recent years because of their distinctive electronic structures and promising applications in the nanoelectronics and spintronics. Most recently, another 2D nanomaterial, i.e., the few-layer black phosphorus (phosphorene), has been successfully fabricated and immediately attracted considerable attention [8–11]. The black phosphorus is a three-dimensional layered material, in which individual atomic layers are stacked together by Van der Waals interactions. And its 2D derivative, phosphorene, is another 2D stable elemental material that can be mechanically exfoliated [8] in addition to the graphene. 0957-4484/15/065705+09$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
Nanotechnology 26 (2015) 065705
T Hu and J Dong
and a 4 × 4 supercell is adopted to model the MVs in phosphorene. In addition, we have also adopted the larger 5 × 5 supercells to check if the 4 × 4 supercell is large enough, both of which are found to present essentially the same results. All calculations in this work were performed by the spin polarized density functional theory (DFT) in the generalized gradient approximation, implemented by the VASP code [30, 31], in which the Perdew–Burke–Ernzerhof [32] exchange-correlation functional and the projector augmented wave formalism [33] are employed. The layered structures are placed in the xy plane and a large vacuum region is added in z direction, making the closest distance between two adjacent nanosheets to be 15 Å. The geometry structure optimization was performed using the conjugated- gradient minimization scheme until the maximum residual force on each atom was less than 0.001 eV Å−1. A plane-wave cutoff of 350 eV for phosphorene was used in our numerical calculations and the energies were converged to 10−5 eV/atom. The Brillouin-zone integration of the supercell is sampled with 5 × 5 × 1 Monkhorst– Pack grid. The climbing image nudged elastic band (CI-NEB) method [34] was used for determining the MV’s migration paths and diffusion energy barrier.
mechanisms of these intrinsic vacancies as well as their effects on the system’s electronic and vibrational properties is of fundamental interest. For example, the geometric structures of vacancies and their diffusions in graphene and silicene have been investigated by a number of experimental [20–22] and theoretical studies [23–27]. The imaging with 80 keV electrons has shown that several point defects could be excited in pristine graphene [21], whose diffusion can be directly followed by the scanning transmission microscope operated at 60 kV [22]. It has been reported theoretically that the ground-state structure of monovacancy (MV) in graphene has a C1h nonplanar structure with a closed five- and ninemembered (5-9) pair of rings, which is induced by the symmetry-breaking Jahn–Teller distortion [23–25], and has a magnetic moment of about 1.12–1.53 μB, depending on the MV concentrations [26]. In the low-buckled silicene, however, recent first-principles calculations [27, 28] found a new type nonmagnetic MV with a plane-like sp3-hybridization at its defect core is more stable than the MV (5-9). Theoretical calculations have also indicated that formation energies of divacancies (DVs) in graphene and silicene are lower in energy than that of two isolated MVs, making the MVs tend to coalesce into a DV [23, 27]. Compared with a large amount of experimental and theoretical studies on the MVs and DVs in graphene and silicene, very little is known about them in monolayer phosphorene [29]. In this paper, we have performed the firstprinciples calculations to study the geometric structures and formation energies of MVs and DVs in 2D phosphorene, as well as diffusion barriers of the MVs and their influences on their electronic and magnetic properties. It has been found that the MV-(5|9) is the ground state MV structure in phosphorene and there exist 14 possible DVs, which could be divided into four basic types based upon their topological structures. Introduction of the MVs and DVs induce the localized defect modes (LDM) in phosphorene, influencing its vibrational properties, which could be used to distinguish different vacancy structures. These vacancies also have a significant influence on the electronic properties of phosphorene. The obtained results present a primitive knowledge of the possible MVs and DVs in phosphorene, which would be helpful for observing them in future experiments and their possible applications. The remainder of this paper is organized as follows. In section 2, the geometric structures and computational details are described. In section 3, the main numerical results and some discussions are given. Finally, in section 4, a conclusion is presented.
3. Results and discussions 3.1. Structure and stability of MVs in phosphorene
The optimized geometric structure of pristine phosphorene is found to have a puckered honeycomb-like lattice structure with its pucker distance d of about 2.104 Å, as shown in figure 1(a), which can be essentially regarded as a combination of the upper and lower half-layer structures. We can define a phosphorene plane, lying at the pucker’s middle, as indicated by the blue dashed line in figure 1(a). The relaxed lattice constants of the monolayer phosphorene are a1 = 4.619 Å and a2 = 3.298 Å, which are in good agreement with other theoretical calculations [35]. There are two inequivalent P–P bonds in the structure, which are l1 = 2.22 Å and l2 = 2.26 Å, respectively. In order to produce a MV in the phosphorene, one P atom, labeled as P0 and denoted by a dashed circle in figure 1(a), is removed from the monolayer phosphorene. In our calculations, in fact, we have constructed several possible MV configurations by adjusting manually the P atoms around the vacancy site, which include those found previously in the graphene and silicene. And then subsequent geometric structure relaxations have been made to get finally the optimized MV structures. It is found from our DFT calculations that two possible MV reconstructions can exist in the monolayer phosphorene, which are called as MV-(55|66) and MV-(5|9), as shown in figures 1(b) and (c), respectively. For inducing the MV-(55|66) with a pair of pentagon– hexagons, once the P0 atom in the upper half-layer is removed, the neighboring P7 atom in the lower half-layer moves up toward the central phosphorene plane, forming two new P–P bonds with both the P2 and P3 atoms, lying on the
2. Model and method Unlike flat plane structure of graphene, the phosphorene has a characteristic puckered honeycomb lattice, buckling alternately by zigzag lines, as shown in figure 1(a), which is also quite different from that of silicene where the A and B sublattices sit in two vertically separated planes [28]. There are four P atoms in one basic unit cell of monolayer phosphorene 2
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 1. The top and side views for the optimized geometric structures of (a) pristine phosphorene with one phosphorus atom ejected, which is denoted by a dashed circle, labeled as P0; (b) MV-(55|66) and (c) MV-(5|9). The atoms near the ejected P0 are marked as P1–P13, respectively. The a1 × a2 unit cell of pristine phosphorene is outlined by black dashed lines, while the phosphorene plane is represented by the blue dashed lines in (a). In order to identify phosphorus atoms in two half-layers of the phosphorene, they are denoted by different colors: blue (purple) for those on the upper (lower) half-layer.
diffusions, which is dominated by the diffusion barrier. Thus it is also important to investigate the MV’s migration in phosphorene. The MV’s diffusion barrier is calculated by employing the climb nudged elastic bond method to search the transition states. As the MV-(55|66) is an unstable structure, we only discuss the diffusion behavior of MV-(5|9). Due to the characteristic anisotropic structure of phosphorene, we have calculated two possible migration paths along zigzag and armchair direction respectively. Figures 2(a)–(c) illustrate the structural evolutions for the MV’s diffusion in the zigzag direction, where the P2 atom, labeled by a green circle, moves to the MV’s center, breaking the P1–P2 bond to form a new bond with the P3 atom. The final and initial structures in figures 2(a) and (c) are topologically equivalent, which are related by a rotation of 180° perpendicular to the plane and a translation of a2/2 along the zigzag direction. The energy barrier of this diffusion process is found to be about 0.182 eV, in contrast to the big barrier value of about 1.0 eV for the MV-(5|9) diffusion in graphene [23], indicating that the MV-(5|9) is much more easier to diffuse in phosphorene because of the weak P–P bonds. The 2nd possible MV-(5|9) diffusion path is that along the armchair direction, as presented in figures 2(a), (d) and (e). As shown in figure 2(a), the P7 atom lying in the lower half-layer moves upward to form a new bond with P3, inducing thus a transient MV-(55|66), which then much easily decays into a new MV-(5|9) by breaking the old P7–P8 bond because it is unstable, as said above. In this process, the final and initial structures in figures 2(a) and (e) are also topologically equivalent, both of which are related by a rotation of 180° about y axis and a translation of a1/4 along the armchair direction. The diffusion barrier for this process is found to be about 0.395 eV, which is 0.213 eV higher than that along the zigzag direction, as indicated in figure 2(f). Thus our calculated results indicate clearly that the MV-(5|9) of phosphorene exhibits an anisotropic diffusion character, preferring to migrate along the zigzag direction, rather than along the armchair one.
same upper half-layer as the P0 atom. It is found that the bond lengths of two new P7–P2 and P7–P3 bonds are about 2.47 Å, while those of the two old P7–P6 and P7–P8 bonds are elongated to be 2.33 Å. This type MV is similar to the stable MV1 reconstruction found recently in silicene [27], which but does not exist in the graphene. On the other hand, as shown in figure 1(c), for inducing the MV-(5|9), after the P0 atom in the upper half-layer is removed, the P7 atom should remain in the lower half-layer, but the P2 atom moves down to form a new bond with the P7 atom, forming a pentagon–nonagon (5|9) pair ring. The P2–P7 bond length is found to be about 2.36 Å. In order to investigate the MV’s stabilities in phosphorene, we have first calculated their formation energy Ef, defined as Ef = Evac − NiEP. Here, the Evac and Ni are the total energy and number of phosphorus atoms in a 4 × 4 supercell of the defective phosphorene, respectively. And EP is the energy of one phosphorus atom in a perfect phosphorene sheet. All the energies are evaluated by the spin-polarized calculations. The calculated formation energy of MV-(55|66) is about 1.971 eV, which is about 0.378 eV higher than that of MV-(5|9), indicating that the MV-(5|9) is a preferred ground state MV reconstruction in phosphorene. The formation energies of MVs in phosphorene is much lower than those in graphene (∼7.9 eV) and those in silicene (∼2.7 eV) [28]. Next, we need to further examine the stabilities of two MVs at finite temperatures. The first-principles finite temperature molecular dynamics (MD) simulations with a Nose– Hoover thermostat have been performed. It is found that the MV-(5|9) can be stable at the room temperatures of 300 K and even 500 K in the simulation time of 10 ps, while the MV-(55| 66) will quickly transform into the MV-(5|9) within 1 ps even at a very low temperature of 3 K. The MD simulations indicate that the MV-(5|9) is a thermo-dynamically stable configuration at room temperatures, which would be observed possibly in future experiment. In contrary, the MV-(55|66) is unstable, which is much different from the situation of silicene [27]. It is supposed that at finite temperatures, the MV defects may aggregate, or transform between each other via atom’s 3
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 2. Transient structural configurations of a MV-(5|9) along different diffusion paths in phosphorene: (a) the initial MV-(5|9), (b) transient diffusion state along the zigzag direction in the same half-layer (path 1), (c) final image along path 1, (d) transient diffusion state along the armchair direction in different half-layers (path 2), where the lower part is the side view of the defective phosphorene. (e) Final image along path 2. (f) Energy evolution of the MV-(5|9) along the different migration paths.
same half-layers are first removed. And then their four surrounding atoms (P1, P3, P7 and P11) would have four dangling bonds, which prefer in pairs to form two new P–P bonds (P1– P11, P3–P7), inducing a pentagon–octagon–pentagon (5-8-5) structure. While for DV-1-2, two nearest-neighbor P atoms (P0 and P7), but lying in the different half-layers are removed. After that an evolution process is similar to the above case of getting DV-1-1, by forming another two new P–P bonds (P2– P3, P6–P8). Other basic types of the DV-2, DV-3 and their different variants can be obtained by one bond rotation from the DV-1 structures, realized through rotating different P–P bonds by about 90°. Firstly, the DV-2-1 and DV-2-2 can be created by rotating the P1–P5 and P5–P6 in the DV-1-2 and DV-1-1, respectively. Secondly, the DV-3-1 (DV-3-2) is obtained from the DV-1-1 by a clockwise (counterclockwise) rotation of the hetero-layer P1–P5 bond, respectively. And the DV-3-3 could be obtained from DV-1-2 by rotating the homo-layer bond P3–P4. These Stone–Wales type transformations also often happen in graphene, leading to the defect transformation and migration [22, 23]. Moreover, the DV-4 structures can be obtained by one bond rotation from DV-2 structures. Thus in order to get a DV-4 from DV-1 types, we need to do at least two bond rotations. It can be found from figure 3 that the DV-4-1 (DV4-2) can be obtained from DV-2-1 by a 90° counterclockwise (clockwise) rotation of the hetero-layer P4–P9 bond. Similarly, the DV-4-3 (DV-4-4) can be obtained by a
3.2. Structure and stability of DVs in phosphorene
Now, let us study the possible DVs in phosphorene. Considering the unique puckered structure of phosphorene and weak P–P bonds in it, there possibly exist many different DV configurations in phosphorene. We have indeed found 14 optimized DV structures in phosphorene, as shown in figure 3, which could be divided into four basic types based upon their topological structures, denoted simply as DV-1, DV-2, DV-3 and DV-4, respectively. For example, as shown obviously in figure 3, DV-1 has a pentagon–octagon–pentagon (5|8|5) structure, DV-2 has three pairs of pentagon and heptagon (555|777), DV-3 has a pentagon–heptagon–heptagon–pentagon (5|7|7|5), and DV-4 has four pairs of pentagon and heptagon around a hexagon (5555|6|7777). Each basic DV type has also a lot of different variants, as indicated clearly in table 1 and figure 3. In the following, we will use the symbols DV-x-y to denote the different types and variants of a DV, in which the number x denotes the basic types of a DV with different topological configuration, while y is the serial number of the different variants in the same basic type of each DV. It is very interesting to know how we can get so many different types and variants of DVs. A detailed analysis of the DV’s geometrical structures gives their formation mechanism. The two different DV-1s can be obtained from the initial MV structure shown in figure 1(a) by removing one more P atom nearest to the vacancy site. For example, in order to get DV-11, two nearest-neighbor P atoms (P0 and P2), lying in the 4
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 3. (a)–(n) The optimized geometric structures of the 14 different DV configurations in phosphorene. Table 1. Formation energies (in eV) of 14 different DV configurations in phosphorene.
DV-1 (5|8|5)
DV-2 (555|777)
DV-3 (5|7|7|5)
DV-4 (5555|6|7777)
Variant
Ef
Variant
Ef
Variant
Ef
Variant
Ef
Variant
Ef
DV-1-1 DV-1-2
1.316 3.077
DV-2-1 DV-2-2
2.075 2.297
DV-3-1 DV-3-2 DV-3-3
1.701 1.797 4.280
DV-4-1 DV-4-2 DV-4-3 DV-4-4
1.374 1.452 1.628 1.731
DV-4-5 DV-4-6 DV-4-7
3.191 3.265 3.641
5
Nanotechnology 26 (2015) 065705
T Hu and J Dong
counterclockwise (clockwise) rotation of the hetero-layer bond P16–P17 in DV-2-2. And rotation of the homo-layer bond P14–P15 in DV-2-1 will lead to the DV-4-6 configuration, while the DV-4-5 and DV-4-7 are achieved by a clockwise rotation of the homo-layer bond P18–P19 and P20– P21 in DV-2-2, respectively. The calculated formation energies of these DVs are given in table 1. Due to the miscellaneous variants of DV structures, we firstly picked out the most stable one in each basic type and then consider the rest as the ‘excited states’ of each type. It can be found from table 1 that the most stable configurations in each type are the DV-1-1, DV-4-1, DV-3-1 and DV2-1 with their formation energies of 1.316, 1.374, 1.701 and 2.075 eV, which obviously follow an energy order of Ef (DV1) < Ef (DV-4) < Ef (DV-3) < Ef (DV-2). Therefore, the DV-11 is the most stable DV configuration in all the four basic types and 14 variants of the DVs. By comparing the formation energies of MVs and DVs in phosphorene, it is also noticed that the formation energy of the DV-1-1 is lower than those of two isolate MVs by 1.870 eV. Such a remarkable energy reduction will drive the two MVs to coalesce into a DV-1-1 by thermo-active diffusion. As a comparison, we have also studied the stabilities of three typical DVs in graphene: DV-(5|8|5), DV-(555|777) and DV-(5555|6|7777), denoted as C-DV-1, C-DV-2 and C-DV-4 in the following, whose formation energies are 8.071, 7.165 and 7.637 eV respectively, following an energy order of Ef (C-DV-2) < Ef (C-DV-4) < Ef (C-DV-1). It is known that the formation energy of C-DV-2 in graphene is lower than that of C-DV-1 by about 0.9 eV [23], which is verified by our DFT calculations too. Besides, the formation energy of 57-75 defect (here’s DV-3 type) in graphene is even higher than that of C-DV-1 and is quite unstable. From the above calculated results, it can be found that the DV’s stabilities in phosphorene and graphene are greatly different, showing an almost opposite formation energy order. In phoshporene, the DV-(5|8|5) configuration is the most stable DV type, while the DV-(555|777) one is the most unstable one, in contrast to that the C-DV(555-777) being the most stable one in graphene. We have given an energy spectra and the transforming relationship of the 14 DVs in figure 4 in order to present a more clearly visualized picture for them. It is noticed that although the DV-1-2 has relatively higher formation energy, however, it can transform into a more energetically favored DV-2-1 (1.002 eV lower in formation energy) simply through a bond rotation. The DV-2-1 then further reconstructs into a more stable DV-4-1 or DV-4-2, which has the lower formation energy by 0.701 or 0.623 eV, respectively, than DV-2-1. It is noticed that the DV-4-1 is the 2nd most stable DV configuration in phosphorene. Since the DVs can transform between their different configurations by bond rotations, thus it is also important to consider the energy barrier associated with the bond rotation in phosphorene. We have simulated several transformation processes by employing the c-NEB method and the obtained energy barriers for bond rotations lie in a range of 0.57–1.27 eV, which is much lower than that in graphene
Figure 4. The energy spectra and the transformation relationship of
the 14 different DV configurations in phosphorene. The red and green arrows represent the transformation processes from DV-1-1 and DV-1-2, respectively.
(∼5 eV) [23] and comparable with that in silicene (∼1.2 eV) [27]. To further confirm the DV’s dynamic stability, we have also performed the first-principles finite temperature molecular dynamics simulations on the lowest energy DV configurations in each basic type at 300 K. After 10 ps, we have found that all the four basic type DVs in their corresponding lowest energy variant configurations are still stable, indicating that all of them are thermo-dynamically stable configurations even at room temperatures, which could be observed possibly in future experiment. 3.3. Vibrational properties of MVs and DVs in phosphorene
It is known that the vibrational properties are closely related to the geometric structures of the materials with the defects and their Raman spectra could be an efficient experimental method to identify the specific vacancy structures. Thus, the detailed vibrational properties of MVs and DVs in phosphorene, as well as the pristine phoshporene have been studied in order to identify them easily. The vibrational frequencies and eigenvectors for the phonons at Γ point (k = 0) are obtained by the ab initio force constant method. According to the point group theory, the monolayer phosphorene belongs to the D2h space group, in which the Ag, B1g, B2g and B3g modes are the Raman-active modes while B1u and B3u are infrared active. The calculated Raman-active vibrational modes of monolayer phosphorene are illustrated in figure 5(a), which is in well consistent with previous studies [36]. However, due to existence of vacancies in phosphorene, some new vibrational modes would emerge, which are closely related to the different vacancy structures and could be useful for identifying them. Since there are miscellaneous vacancy structures, here we only consider the MV-(5|9) and the most stable variants in each type of DVs: DV-1-1, DV-2-1, DV-3-1 and DV-4-1 as examples. By checking their vibrational modes, we have found that some new topological defect modes have been induced, which are mainly localized at the 6
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 5. The vibrational vectors of (a) Raman-active modes of monolayer phosphorene and the localized defect modes of phosphorene with (b) MV-(5|9), (c) DV-1-1, (d) DV-2-1, (e) DV-3-1 and (f) DV-4-1.
vacancy sites and are denoted as LDM here. Their vibrational vectors are shown in figures 5(b)–(f), from which it is noticed that the MV-(5|9) induces two LDMs at 282.3 and 326.7 cm−1. In contrast, the three DVs, DV-1-1, DV-2-1 and DV-4-1, have low frequency LDMs around 110 cm−1, while the DV-3-1 has a typical high frequency LDM at about 488.8 cm−1. These typical LDMs could be used to distinguish the different DV structures in phosphoreene.
e.g., inducing the localized electronic states and even magnetic moment in the system. Thus it is important to investigate the electronic and magnetic properties of the typical vacancies in phosphorene. Figure 6(a) gives the band structure of the pristine phosphorene, showing a semiconducting behavior with a direct band gap of about 0.91 eV at Γ point, which is consistent with the previous calculations [9, 13, 34]. Then, both spin polarized and unpolarized DFT calculations have been performed for the defective phosphorene with the ground state MV-(5|9). The spin unpolarized DFT calculation result is given in figure 6(b). It is clearly seen from figure 6(b) that a nearly flat band, labeled as a, exists around the Fermi level. In order to
3.4. Electronic and magnetic properties of vacancies in phosphorene
It is known that existence of local defects can affect greatly the electronic and magnetic properties of the 2D material [37], 7
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 6. (a) The band structure of pristine phosphorene in a 4 × 4 supercell. (b) The spin unpolarized and (c) spin polarized band structures of the defective phosphorene with MV-(5|9). In (b), the pDOS of P3 atom and some other P atoms around the vacancy site in the energy range of −0.25 eV to 0.25 eV is shown on the right-hand side of the band structure. (d) The spin polarized charge density (ρup − ρdown) of phosphorene with MV-(5|9) with isosurface value of 4 × 10−4 e Å−3. Here, the ρup and ρdown denote the spin-up and spin-down electron densities, represented by the yellow and cyan colors, respectively. The black and red lines in the band structures denote the spin-up and spin-down states, respectively.
see what orbitals contribute the flat band, we have calculated the projected densities of states (pDOS) of P3 atom and some other P atoms around the vacancy site in the energy range of −0.25 eV to 0.25 eV around the Fermi level, which is given on the right side of the band structure in figure 6(b). Detailed analysis of pDOS indicates that the flat band is contributed mainly by the px and py orbitals and minor amount of s and pz orbitals of the above mentioned P atoms. The MV-induced localized state makes the system to be a metallic one. However, the spin polarized calculation indicates that the flat band split into two bands, opening a band gap of about 0.211 eV, as shown in figure 6(c), which lowers the system’s energy by 0.079 eV, compared with that of the nonmagnetic state. The corresponding spin polarized charge densities, shown in figure 6(d), indicate that the induced magnetic moments are mainly localized around the vacancy site. The total magnetic moment of the MV-(5|9) is found to be about 1.0 μB. The local spin moment can be calculated by using the Bader method [38], which is found to be about 0.50 μB at the P3 atom and 0.02–0.04 μB for other atoms around the vacancy. We have also calculated the band structures of DVs in phosphorene. Taking the most stable DV of DV-1-1 in a 4 × 4 supercell and the second-most stable one of DV-4-1 in a 4 × 5 supercell as examples, the calculated band structures of them are shown in figures 7(a) and (b), respectively. Both the DVs give rise to two defect states near the Fermi level, labeled as 1
Figure 7. The electronic band structures (left) and partial charge
densities (right) of divacancy band 1 and 2 of the defective phosphorene with (a) DV-1-1 in a 4 × 4 supercell and (b) DV-4-1 in a 4 × 5 supercell. Here, the isosurface is 1 × 10−4 e Å−3. 8
Nanotechnology 26 (2015) 065705
T Hu and J Dong
References
and 2, whose partial charge densities are given at the right side of figure 7. Both of their band structures indicate that introduction of DVs induces a transition from the original direct band gap into indirect one, increasing the band gap of pristine phosphorene to now 1.053 eV and 1.102 eV for the DV-1-1 and DV-4-1, respectively. Other DV configurations also exhibit similar semiconducting character.
[1] Novoselov K, Geim A, Morozov S, Jiang D, Zhang Y, Dubonos S, Grigorieva I and Firsov A 2004 Science 306 666–9 [2] Zhang Y, Tan Y, Stormer H and Kim P 2005 Nature 438 201–4 [3] Cahangirov S, Topsakal M, Akturk E, Sahin H and Ciraci S 2009 Phys. Rev. Lett. 102 236804 [4] Houssa M, Pourtois G, Afanas’ev V V and Stesmans A 2010 Appl. Phys. Lett. 96 082111 [5] Topsakal M, Akturk E and Ciraci S 2009 Phys. Rev. B 79 115442 [6] Mak K F, Lee C, Hone J, Shan J and Heinz T F 2010 Phys. Rev. Lett. 105 136805 [7] Splendiani A, Sun L, Zhang Y, Li T, Kim J, Chim C, Galli G and Wang F 2010 Nano Lett. 10 1271–5 [8] Li L, Yu Y, Ye G-J, Ge Q, Ou X, Wu H, Feng D, Chen X-H and Zhang Y 2014 Nat. Nanotechnology 9 372–7 [9] Liu H, Neal A T, Zhu Z, Tomanek D and Ye P D 2014 ACS Nano 8 4033–41 [10] Xia F, Wang H and Jia Y 2014 Nat. Commun. 5 4458 [11] Reich E S 2014 Nature 506 19 [12] Qiao J, Kong X, Hu Z-X, Yang F and Ji W 2014 Nat. Commun. 5 4475 [13] Tran V, Soklaski R, Liang Y and Yang L 2014 Phys. Rev. B 89 235319 [14] Jiang J-W and Park H S 2014 Nat. Commun. 5 4727 [15] Fei R and Yang L 2014 Nano Lett. 14 2884 [16] Kotakoski J, Jin C H, Lehtinen O, Suenaga K and Krasheninnikov A V 2010 Phys. Rev. B 82 113404 [17] Komsa H-P, Kotakoski J, Kurasch S, Lehtinen O, Kaiser U and Krasheninnikov A V 2012 Phys. Rev. Lett. 109 035503 [18] Palacios J J, Fernandez-Rossier J and Brey L 2008 Phys. Rev. B 77 195428 [19] Attaccalite C, Bockstedte M, Marini A, Rubio A and Wirtz L 2011 Phys. Rev. B 83 144115 [20] Girit Ç Ö et al 2009 Science 323 1705 [21] Meyer J C, Kisielowski C, Erni R, Rossell M D, Crommie M F and Zettl A 2008 Nano Lett. 8 3582–6 [22] Kotakoski J, Mangler C and Meyer J C 2014 Nat. Commun. 5 3991 [23] Lee G-D, Wang C Z, Yoon E, Hwang N-M, Kim D-Y and Ho K M 2005 Phys. Rev. Lett. 95 205501 [24] Yamashita K, Saito M and Oda T 2006 JJAP 45 6534 [25] El-Barbary A A, Telling R H, Ewels C P, Heggie M I and Briddon P R 2003 Phys. Rev. B 68 144107 [26] Yazyev O V and Helm L 2007 Phys. Rev. B 75 125408 [27] Gao J, Zhang J, Liu H, Zhang Q and Zhao J 2013 Nanoscale 5 9785 [28] Li R, Han Y, Hu T, Dong J and Kawazoe Y 2014 Phys. Rev. B 90 045425 [29] Hu W and Yang J 2014 Defect in phosphorene (arXiv:1411.6986.v2) [30] Kresse G and Hafner J 1993 Phys. Rev. B 48 13115 [31] Kresse G and Furthmüller J 1996 Comput. Mater. Sci. 6 15 [32] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 [33] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758–75 [34] Henkelman G, Uberuaga B P and Jónsson H 2000 J. Chem. Phys. 113 9901 [35] Peng X, Wei Q and Copple A 2014 Phys. Rev. B 90 085402 [36] Fei R and Yang L 2014 Appl. Phys. Lett. 105 083120 [37] Ugeda M M, Brihuega I, Hiebel F, Mallet P, Veuillen J-Y, Gómez-Rodríguez J M and Ynduráin F 2012 Phys. Rev. B 85 121402 [38] Tang W, Sanville E and Henkelman G 2009 J. Phys.: Condens. Matter 21 084204
4. Conclusions We have performed spin-polarized DFT calculations on the geometric structures, and stabilities of both the MVs and DVs in 2D phosphorene as well as MV’s diffusions. Further, the influences of these vacancies on the vibrational and electronic properties of the defective phosphorenes have been studied. It is found that two possible MVs, MV-(5|9) and MV-(55|66), exist in the phosphorene, among which the MV-(5|9) is the ground state MV with its formation energy lower than that of MV-(55|66) by about 0.378 eV. The diffusion of MV-(5|9) exhibits an anisotropic character, preferring to migrate along the zigzag direction in the same half-layer. In addition, the 14 possible DVs in phosphorene have been found, which could be divided into four basic types based upon their topological structures and can transform between their different variants via bond rotations. The four lowest energy DV configurations in each basic types follow an energy order of Ef (DV-1) < Ef (DV-4) < Ef (DV-3) < Ef (DV-2). And the DV-1-1 with the (5| 8|5) topological defects is the most stable DV in all the 14 variants of DVs in phosphorene, which is quite different from those in graphene, where the C-DV(555|777) is the most stable. The introduction of vacancies in phosphorene also influences the vibrational properties, inducing the LDM, which could be used to distinguish different vacancy structures. The MVs and DVs also have a significant influence on the electronic properties of phosphorene. Phosphorene with MV-(5|9) is a magnetic semiconductor with the magnetic moment of 1.0 μB and a band gap of about 0.211 eV, while the DV-1-1 and DV-4-1 induce a direct-indirect band gap transition and increase the band gap of pristine phosphorene to 1.053 eV and 1.102 eV, respectively. Our DFT calculations on the fundamental vacancy properties in 2D materials are important for the research and application of the low dimentional materials in nanoscience.
Acknowledgments This work is supported by the State Key Program for Basic Research of China through the Grant No 2011CB922100Q. Our numerical calculations are performed in the High Performance Computing Center of Nanjing University.
9
Search
Collections
Journals
About
Contact us
My IOPscience
Geometric and electronic structures of mono- and di-vacancies in phosphorene
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 065705 (http://iopscience.iop.org/0957-4484/26/6/065705) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.203.227.61 This content was downloaded on 25/01/2015 at 16:23
Please note that terms and conditions apply.
Nanotechnology Nanotechnology 26 (2015) 065705 (9pp)
doi:10.1088/0957-4484/26/6/065705
Geometric and electronic structures of mono- and di-vacancies in phosphorene Ting Hu and Jinming Dong Group of Computational Condensed Matter Physics, National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China E-mail: [email protected] Received 21 November 2014, revised 29 December 2014 Accepted for publication 2 January 2015 Published 19 January 2015 Abstract
The geometric structures, stabilities and diffusions of the monovacancy (MV) and divacancy (DV) in two-dimensional phosphorene, as well as their influences on their vibrational and electronic properties have been studied by first-principles calculations. Two possible MVs and 14 possible DVs have been found in phosphorene, in which the MV-(5|9) with a pair of pentagon–nonagon is the ground state of MVs, and the DV-(5|8|5) with a pentagon–octagon– pentagon structure is the most stable DV. All 14 DVs could be divided into four basic types based upon their topological structures and transform between different configurations via bond rotations. The diffusion of MV-(5|9) is found to exhibit an anisotropic character, preferring to migrate along the zigzag direction in the same half-layer. The introduction of MV and DV in phosphorene influences its vibrational properties, inducing the localized defect modes, which could be used to distinguish different vacancy structures. The MVs and DVs also have a significant influence on the electronic properties of phosphorene. It is found that the phosphorene with MV-(5|9) is a ferromagnetic semiconductor with the magnetic moment of 1.0 μB and a band gap of about 0.211 eV, while the DV induces a direct-indirect band gap transition. Our calculation results on the MV and DV in phosphorene are important for the promising application of the phosphorene in the nanoelectronics. Keywords: vacancy, phosphorene, stability (Some figures may appear in colour only in the online journal) 1. Introduction
Unlike zero-gap semimetal graphene, the phosphorene exhibits a direct band gap, which can be modified from 1.51 eV of a monolayer to 0.59 eV of a five-layer [12]. Moreover, it is reported that the phosphorene has a high carrier mobility up to 1000 cm2 V–1 s–1 [8] and an appreciably high on/off ratio up to 104 when it is used in a transistor [9], making this material of great interest for future nanoelectronic applications. Furthermore, the phosphorene has a characteristic puckered structure, leading to a substantial anisotropy of its mechanical behavior, electric conductance and optical responses [9, 13–15], which distinguishes it from many other isotropic 2D crystals. Various investigations have shown that the atomic-scale defects and vacancies, generated usually by ion or electron irradiations [16, 17], can strongly influence electronic and mechanical properties of these 2D materials [18, 19]. Therefore, understanding possible formation and diffusion
The two-dimensional (2D) hexagonal nanosheets, such as graphene [1, 2], silicene [3], germanene [4], boron-nitride (hBN) [5], and the transition metal dichalcogenides [6, 7] have been intensively investigated in recent years because of their distinctive electronic structures and promising applications in the nanoelectronics and spintronics. Most recently, another 2D nanomaterial, i.e., the few-layer black phosphorus (phosphorene), has been successfully fabricated and immediately attracted considerable attention [8–11]. The black phosphorus is a three-dimensional layered material, in which individual atomic layers are stacked together by Van der Waals interactions. And its 2D derivative, phosphorene, is another 2D stable elemental material that can be mechanically exfoliated [8] in addition to the graphene. 0957-4484/15/065705+09$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
Nanotechnology 26 (2015) 065705
T Hu and J Dong
and a 4 × 4 supercell is adopted to model the MVs in phosphorene. In addition, we have also adopted the larger 5 × 5 supercells to check if the 4 × 4 supercell is large enough, both of which are found to present essentially the same results. All calculations in this work were performed by the spin polarized density functional theory (DFT) in the generalized gradient approximation, implemented by the VASP code [30, 31], in which the Perdew–Burke–Ernzerhof [32] exchange-correlation functional and the projector augmented wave formalism [33] are employed. The layered structures are placed in the xy plane and a large vacuum region is added in z direction, making the closest distance between two adjacent nanosheets to be 15 Å. The geometry structure optimization was performed using the conjugated- gradient minimization scheme until the maximum residual force on each atom was less than 0.001 eV Å−1. A plane-wave cutoff of 350 eV for phosphorene was used in our numerical calculations and the energies were converged to 10−5 eV/atom. The Brillouin-zone integration of the supercell is sampled with 5 × 5 × 1 Monkhorst– Pack grid. The climbing image nudged elastic band (CI-NEB) method [34] was used for determining the MV’s migration paths and diffusion energy barrier.
mechanisms of these intrinsic vacancies as well as their effects on the system’s electronic and vibrational properties is of fundamental interest. For example, the geometric structures of vacancies and their diffusions in graphene and silicene have been investigated by a number of experimental [20–22] and theoretical studies [23–27]. The imaging with 80 keV electrons has shown that several point defects could be excited in pristine graphene [21], whose diffusion can be directly followed by the scanning transmission microscope operated at 60 kV [22]. It has been reported theoretically that the ground-state structure of monovacancy (MV) in graphene has a C1h nonplanar structure with a closed five- and ninemembered (5-9) pair of rings, which is induced by the symmetry-breaking Jahn–Teller distortion [23–25], and has a magnetic moment of about 1.12–1.53 μB, depending on the MV concentrations [26]. In the low-buckled silicene, however, recent first-principles calculations [27, 28] found a new type nonmagnetic MV with a plane-like sp3-hybridization at its defect core is more stable than the MV (5-9). Theoretical calculations have also indicated that formation energies of divacancies (DVs) in graphene and silicene are lower in energy than that of two isolated MVs, making the MVs tend to coalesce into a DV [23, 27]. Compared with a large amount of experimental and theoretical studies on the MVs and DVs in graphene and silicene, very little is known about them in monolayer phosphorene [29]. In this paper, we have performed the firstprinciples calculations to study the geometric structures and formation energies of MVs and DVs in 2D phosphorene, as well as diffusion barriers of the MVs and their influences on their electronic and magnetic properties. It has been found that the MV-(5|9) is the ground state MV structure in phosphorene and there exist 14 possible DVs, which could be divided into four basic types based upon their topological structures. Introduction of the MVs and DVs induce the localized defect modes (LDM) in phosphorene, influencing its vibrational properties, which could be used to distinguish different vacancy structures. These vacancies also have a significant influence on the electronic properties of phosphorene. The obtained results present a primitive knowledge of the possible MVs and DVs in phosphorene, which would be helpful for observing them in future experiments and their possible applications. The remainder of this paper is organized as follows. In section 2, the geometric structures and computational details are described. In section 3, the main numerical results and some discussions are given. Finally, in section 4, a conclusion is presented.
3. Results and discussions 3.1. Structure and stability of MVs in phosphorene
The optimized geometric structure of pristine phosphorene is found to have a puckered honeycomb-like lattice structure with its pucker distance d of about 2.104 Å, as shown in figure 1(a), which can be essentially regarded as a combination of the upper and lower half-layer structures. We can define a phosphorene plane, lying at the pucker’s middle, as indicated by the blue dashed line in figure 1(a). The relaxed lattice constants of the monolayer phosphorene are a1 = 4.619 Å and a2 = 3.298 Å, which are in good agreement with other theoretical calculations [35]. There are two inequivalent P–P bonds in the structure, which are l1 = 2.22 Å and l2 = 2.26 Å, respectively. In order to produce a MV in the phosphorene, one P atom, labeled as P0 and denoted by a dashed circle in figure 1(a), is removed from the monolayer phosphorene. In our calculations, in fact, we have constructed several possible MV configurations by adjusting manually the P atoms around the vacancy site, which include those found previously in the graphene and silicene. And then subsequent geometric structure relaxations have been made to get finally the optimized MV structures. It is found from our DFT calculations that two possible MV reconstructions can exist in the monolayer phosphorene, which are called as MV-(55|66) and MV-(5|9), as shown in figures 1(b) and (c), respectively. For inducing the MV-(55|66) with a pair of pentagon– hexagons, once the P0 atom in the upper half-layer is removed, the neighboring P7 atom in the lower half-layer moves up toward the central phosphorene plane, forming two new P–P bonds with both the P2 and P3 atoms, lying on the
2. Model and method Unlike flat plane structure of graphene, the phosphorene has a characteristic puckered honeycomb lattice, buckling alternately by zigzag lines, as shown in figure 1(a), which is also quite different from that of silicene where the A and B sublattices sit in two vertically separated planes [28]. There are four P atoms in one basic unit cell of monolayer phosphorene 2
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 1. The top and side views for the optimized geometric structures of (a) pristine phosphorene with one phosphorus atom ejected, which is denoted by a dashed circle, labeled as P0; (b) MV-(55|66) and (c) MV-(5|9). The atoms near the ejected P0 are marked as P1–P13, respectively. The a1 × a2 unit cell of pristine phosphorene is outlined by black dashed lines, while the phosphorene plane is represented by the blue dashed lines in (a). In order to identify phosphorus atoms in two half-layers of the phosphorene, they are denoted by different colors: blue (purple) for those on the upper (lower) half-layer.
diffusions, which is dominated by the diffusion barrier. Thus it is also important to investigate the MV’s migration in phosphorene. The MV’s diffusion barrier is calculated by employing the climb nudged elastic bond method to search the transition states. As the MV-(55|66) is an unstable structure, we only discuss the diffusion behavior of MV-(5|9). Due to the characteristic anisotropic structure of phosphorene, we have calculated two possible migration paths along zigzag and armchair direction respectively. Figures 2(a)–(c) illustrate the structural evolutions for the MV’s diffusion in the zigzag direction, where the P2 atom, labeled by a green circle, moves to the MV’s center, breaking the P1–P2 bond to form a new bond with the P3 atom. The final and initial structures in figures 2(a) and (c) are topologically equivalent, which are related by a rotation of 180° perpendicular to the plane and a translation of a2/2 along the zigzag direction. The energy barrier of this diffusion process is found to be about 0.182 eV, in contrast to the big barrier value of about 1.0 eV for the MV-(5|9) diffusion in graphene [23], indicating that the MV-(5|9) is much more easier to diffuse in phosphorene because of the weak P–P bonds. The 2nd possible MV-(5|9) diffusion path is that along the armchair direction, as presented in figures 2(a), (d) and (e). As shown in figure 2(a), the P7 atom lying in the lower half-layer moves upward to form a new bond with P3, inducing thus a transient MV-(55|66), which then much easily decays into a new MV-(5|9) by breaking the old P7–P8 bond because it is unstable, as said above. In this process, the final and initial structures in figures 2(a) and (e) are also topologically equivalent, both of which are related by a rotation of 180° about y axis and a translation of a1/4 along the armchair direction. The diffusion barrier for this process is found to be about 0.395 eV, which is 0.213 eV higher than that along the zigzag direction, as indicated in figure 2(f). Thus our calculated results indicate clearly that the MV-(5|9) of phosphorene exhibits an anisotropic diffusion character, preferring to migrate along the zigzag direction, rather than along the armchair one.
same upper half-layer as the P0 atom. It is found that the bond lengths of two new P7–P2 and P7–P3 bonds are about 2.47 Å, while those of the two old P7–P6 and P7–P8 bonds are elongated to be 2.33 Å. This type MV is similar to the stable MV1 reconstruction found recently in silicene [27], which but does not exist in the graphene. On the other hand, as shown in figure 1(c), for inducing the MV-(5|9), after the P0 atom in the upper half-layer is removed, the P7 atom should remain in the lower half-layer, but the P2 atom moves down to form a new bond with the P7 atom, forming a pentagon–nonagon (5|9) pair ring. The P2–P7 bond length is found to be about 2.36 Å. In order to investigate the MV’s stabilities in phosphorene, we have first calculated their formation energy Ef, defined as Ef = Evac − NiEP. Here, the Evac and Ni are the total energy and number of phosphorus atoms in a 4 × 4 supercell of the defective phosphorene, respectively. And EP is the energy of one phosphorus atom in a perfect phosphorene sheet. All the energies are evaluated by the spin-polarized calculations. The calculated formation energy of MV-(55|66) is about 1.971 eV, which is about 0.378 eV higher than that of MV-(5|9), indicating that the MV-(5|9) is a preferred ground state MV reconstruction in phosphorene. The formation energies of MVs in phosphorene is much lower than those in graphene (∼7.9 eV) and those in silicene (∼2.7 eV) [28]. Next, we need to further examine the stabilities of two MVs at finite temperatures. The first-principles finite temperature molecular dynamics (MD) simulations with a Nose– Hoover thermostat have been performed. It is found that the MV-(5|9) can be stable at the room temperatures of 300 K and even 500 K in the simulation time of 10 ps, while the MV-(55| 66) will quickly transform into the MV-(5|9) within 1 ps even at a very low temperature of 3 K. The MD simulations indicate that the MV-(5|9) is a thermo-dynamically stable configuration at room temperatures, which would be observed possibly in future experiment. In contrary, the MV-(55|66) is unstable, which is much different from the situation of silicene [27]. It is supposed that at finite temperatures, the MV defects may aggregate, or transform between each other via atom’s 3
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 2. Transient structural configurations of a MV-(5|9) along different diffusion paths in phosphorene: (a) the initial MV-(5|9), (b) transient diffusion state along the zigzag direction in the same half-layer (path 1), (c) final image along path 1, (d) transient diffusion state along the armchair direction in different half-layers (path 2), where the lower part is the side view of the defective phosphorene. (e) Final image along path 2. (f) Energy evolution of the MV-(5|9) along the different migration paths.
same half-layers are first removed. And then their four surrounding atoms (P1, P3, P7 and P11) would have four dangling bonds, which prefer in pairs to form two new P–P bonds (P1– P11, P3–P7), inducing a pentagon–octagon–pentagon (5-8-5) structure. While for DV-1-2, two nearest-neighbor P atoms (P0 and P7), but lying in the different half-layers are removed. After that an evolution process is similar to the above case of getting DV-1-1, by forming another two new P–P bonds (P2– P3, P6–P8). Other basic types of the DV-2, DV-3 and their different variants can be obtained by one bond rotation from the DV-1 structures, realized through rotating different P–P bonds by about 90°. Firstly, the DV-2-1 and DV-2-2 can be created by rotating the P1–P5 and P5–P6 in the DV-1-2 and DV-1-1, respectively. Secondly, the DV-3-1 (DV-3-2) is obtained from the DV-1-1 by a clockwise (counterclockwise) rotation of the hetero-layer P1–P5 bond, respectively. And the DV-3-3 could be obtained from DV-1-2 by rotating the homo-layer bond P3–P4. These Stone–Wales type transformations also often happen in graphene, leading to the defect transformation and migration [22, 23]. Moreover, the DV-4 structures can be obtained by one bond rotation from DV-2 structures. Thus in order to get a DV-4 from DV-1 types, we need to do at least two bond rotations. It can be found from figure 3 that the DV-4-1 (DV4-2) can be obtained from DV-2-1 by a 90° counterclockwise (clockwise) rotation of the hetero-layer P4–P9 bond. Similarly, the DV-4-3 (DV-4-4) can be obtained by a
3.2. Structure and stability of DVs in phosphorene
Now, let us study the possible DVs in phosphorene. Considering the unique puckered structure of phosphorene and weak P–P bonds in it, there possibly exist many different DV configurations in phosphorene. We have indeed found 14 optimized DV structures in phosphorene, as shown in figure 3, which could be divided into four basic types based upon their topological structures, denoted simply as DV-1, DV-2, DV-3 and DV-4, respectively. For example, as shown obviously in figure 3, DV-1 has a pentagon–octagon–pentagon (5|8|5) structure, DV-2 has three pairs of pentagon and heptagon (555|777), DV-3 has a pentagon–heptagon–heptagon–pentagon (5|7|7|5), and DV-4 has four pairs of pentagon and heptagon around a hexagon (5555|6|7777). Each basic DV type has also a lot of different variants, as indicated clearly in table 1 and figure 3. In the following, we will use the symbols DV-x-y to denote the different types and variants of a DV, in which the number x denotes the basic types of a DV with different topological configuration, while y is the serial number of the different variants in the same basic type of each DV. It is very interesting to know how we can get so many different types and variants of DVs. A detailed analysis of the DV’s geometrical structures gives their formation mechanism. The two different DV-1s can be obtained from the initial MV structure shown in figure 1(a) by removing one more P atom nearest to the vacancy site. For example, in order to get DV-11, two nearest-neighbor P atoms (P0 and P2), lying in the 4
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 3. (a)–(n) The optimized geometric structures of the 14 different DV configurations in phosphorene. Table 1. Formation energies (in eV) of 14 different DV configurations in phosphorene.
DV-1 (5|8|5)
DV-2 (555|777)
DV-3 (5|7|7|5)
DV-4 (5555|6|7777)
Variant
Ef
Variant
Ef
Variant
Ef
Variant
Ef
Variant
Ef
DV-1-1 DV-1-2
1.316 3.077
DV-2-1 DV-2-2
2.075 2.297
DV-3-1 DV-3-2 DV-3-3
1.701 1.797 4.280
DV-4-1 DV-4-2 DV-4-3 DV-4-4
1.374 1.452 1.628 1.731
DV-4-5 DV-4-6 DV-4-7
3.191 3.265 3.641
5
Nanotechnology 26 (2015) 065705
T Hu and J Dong
counterclockwise (clockwise) rotation of the hetero-layer bond P16–P17 in DV-2-2. And rotation of the homo-layer bond P14–P15 in DV-2-1 will lead to the DV-4-6 configuration, while the DV-4-5 and DV-4-7 are achieved by a clockwise rotation of the homo-layer bond P18–P19 and P20– P21 in DV-2-2, respectively. The calculated formation energies of these DVs are given in table 1. Due to the miscellaneous variants of DV structures, we firstly picked out the most stable one in each basic type and then consider the rest as the ‘excited states’ of each type. It can be found from table 1 that the most stable configurations in each type are the DV-1-1, DV-4-1, DV-3-1 and DV2-1 with their formation energies of 1.316, 1.374, 1.701 and 2.075 eV, which obviously follow an energy order of Ef (DV1) < Ef (DV-4) < Ef (DV-3) < Ef (DV-2). Therefore, the DV-11 is the most stable DV configuration in all the four basic types and 14 variants of the DVs. By comparing the formation energies of MVs and DVs in phosphorene, it is also noticed that the formation energy of the DV-1-1 is lower than those of two isolate MVs by 1.870 eV. Such a remarkable energy reduction will drive the two MVs to coalesce into a DV-1-1 by thermo-active diffusion. As a comparison, we have also studied the stabilities of three typical DVs in graphene: DV-(5|8|5), DV-(555|777) and DV-(5555|6|7777), denoted as C-DV-1, C-DV-2 and C-DV-4 in the following, whose formation energies are 8.071, 7.165 and 7.637 eV respectively, following an energy order of Ef (C-DV-2) < Ef (C-DV-4) < Ef (C-DV-1). It is known that the formation energy of C-DV-2 in graphene is lower than that of C-DV-1 by about 0.9 eV [23], which is verified by our DFT calculations too. Besides, the formation energy of 57-75 defect (here’s DV-3 type) in graphene is even higher than that of C-DV-1 and is quite unstable. From the above calculated results, it can be found that the DV’s stabilities in phosphorene and graphene are greatly different, showing an almost opposite formation energy order. In phoshporene, the DV-(5|8|5) configuration is the most stable DV type, while the DV-(555|777) one is the most unstable one, in contrast to that the C-DV(555-777) being the most stable one in graphene. We have given an energy spectra and the transforming relationship of the 14 DVs in figure 4 in order to present a more clearly visualized picture for them. It is noticed that although the DV-1-2 has relatively higher formation energy, however, it can transform into a more energetically favored DV-2-1 (1.002 eV lower in formation energy) simply through a bond rotation. The DV-2-1 then further reconstructs into a more stable DV-4-1 or DV-4-2, which has the lower formation energy by 0.701 or 0.623 eV, respectively, than DV-2-1. It is noticed that the DV-4-1 is the 2nd most stable DV configuration in phosphorene. Since the DVs can transform between their different configurations by bond rotations, thus it is also important to consider the energy barrier associated with the bond rotation in phosphorene. We have simulated several transformation processes by employing the c-NEB method and the obtained energy barriers for bond rotations lie in a range of 0.57–1.27 eV, which is much lower than that in graphene
Figure 4. The energy spectra and the transformation relationship of
the 14 different DV configurations in phosphorene. The red and green arrows represent the transformation processes from DV-1-1 and DV-1-2, respectively.
(∼5 eV) [23] and comparable with that in silicene (∼1.2 eV) [27]. To further confirm the DV’s dynamic stability, we have also performed the first-principles finite temperature molecular dynamics simulations on the lowest energy DV configurations in each basic type at 300 K. After 10 ps, we have found that all the four basic type DVs in their corresponding lowest energy variant configurations are still stable, indicating that all of them are thermo-dynamically stable configurations even at room temperatures, which could be observed possibly in future experiment. 3.3. Vibrational properties of MVs and DVs in phosphorene
It is known that the vibrational properties are closely related to the geometric structures of the materials with the defects and their Raman spectra could be an efficient experimental method to identify the specific vacancy structures. Thus, the detailed vibrational properties of MVs and DVs in phosphorene, as well as the pristine phoshporene have been studied in order to identify them easily. The vibrational frequencies and eigenvectors for the phonons at Γ point (k = 0) are obtained by the ab initio force constant method. According to the point group theory, the monolayer phosphorene belongs to the D2h space group, in which the Ag, B1g, B2g and B3g modes are the Raman-active modes while B1u and B3u are infrared active. The calculated Raman-active vibrational modes of monolayer phosphorene are illustrated in figure 5(a), which is in well consistent with previous studies [36]. However, due to existence of vacancies in phosphorene, some new vibrational modes would emerge, which are closely related to the different vacancy structures and could be useful for identifying them. Since there are miscellaneous vacancy structures, here we only consider the MV-(5|9) and the most stable variants in each type of DVs: DV-1-1, DV-2-1, DV-3-1 and DV-4-1 as examples. By checking their vibrational modes, we have found that some new topological defect modes have been induced, which are mainly localized at the 6
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 5. The vibrational vectors of (a) Raman-active modes of monolayer phosphorene and the localized defect modes of phosphorene with (b) MV-(5|9), (c) DV-1-1, (d) DV-2-1, (e) DV-3-1 and (f) DV-4-1.
vacancy sites and are denoted as LDM here. Their vibrational vectors are shown in figures 5(b)–(f), from which it is noticed that the MV-(5|9) induces two LDMs at 282.3 and 326.7 cm−1. In contrast, the three DVs, DV-1-1, DV-2-1 and DV-4-1, have low frequency LDMs around 110 cm−1, while the DV-3-1 has a typical high frequency LDM at about 488.8 cm−1. These typical LDMs could be used to distinguish the different DV structures in phosphoreene.
e.g., inducing the localized electronic states and even magnetic moment in the system. Thus it is important to investigate the electronic and magnetic properties of the typical vacancies in phosphorene. Figure 6(a) gives the band structure of the pristine phosphorene, showing a semiconducting behavior with a direct band gap of about 0.91 eV at Γ point, which is consistent with the previous calculations [9, 13, 34]. Then, both spin polarized and unpolarized DFT calculations have been performed for the defective phosphorene with the ground state MV-(5|9). The spin unpolarized DFT calculation result is given in figure 6(b). It is clearly seen from figure 6(b) that a nearly flat band, labeled as a, exists around the Fermi level. In order to
3.4. Electronic and magnetic properties of vacancies in phosphorene
It is known that existence of local defects can affect greatly the electronic and magnetic properties of the 2D material [37], 7
Nanotechnology 26 (2015) 065705
T Hu and J Dong
Figure 6. (a) The band structure of pristine phosphorene in a 4 × 4 supercell. (b) The spin unpolarized and (c) spin polarized band structures of the defective phosphorene with MV-(5|9). In (b), the pDOS of P3 atom and some other P atoms around the vacancy site in the energy range of −0.25 eV to 0.25 eV is shown on the right-hand side of the band structure. (d) The spin polarized charge density (ρup − ρdown) of phosphorene with MV-(5|9) with isosurface value of 4 × 10−4 e Å−3. Here, the ρup and ρdown denote the spin-up and spin-down electron densities, represented by the yellow and cyan colors, respectively. The black and red lines in the band structures denote the spin-up and spin-down states, respectively.
see what orbitals contribute the flat band, we have calculated the projected densities of states (pDOS) of P3 atom and some other P atoms around the vacancy site in the energy range of −0.25 eV to 0.25 eV around the Fermi level, which is given on the right side of the band structure in figure 6(b). Detailed analysis of pDOS indicates that the flat band is contributed mainly by the px and py orbitals and minor amount of s and pz orbitals of the above mentioned P atoms. The MV-induced localized state makes the system to be a metallic one. However, the spin polarized calculation indicates that the flat band split into two bands, opening a band gap of about 0.211 eV, as shown in figure 6(c), which lowers the system’s energy by 0.079 eV, compared with that of the nonmagnetic state. The corresponding spin polarized charge densities, shown in figure 6(d), indicate that the induced magnetic moments are mainly localized around the vacancy site. The total magnetic moment of the MV-(5|9) is found to be about 1.0 μB. The local spin moment can be calculated by using the Bader method [38], which is found to be about 0.50 μB at the P3 atom and 0.02–0.04 μB for other atoms around the vacancy. We have also calculated the band structures of DVs in phosphorene. Taking the most stable DV of DV-1-1 in a 4 × 4 supercell and the second-most stable one of DV-4-1 in a 4 × 5 supercell as examples, the calculated band structures of them are shown in figures 7(a) and (b), respectively. Both the DVs give rise to two defect states near the Fermi level, labeled as 1
Figure 7. The electronic band structures (left) and partial charge
densities (right) of divacancy band 1 and 2 of the defective phosphorene with (a) DV-1-1 in a 4 × 4 supercell and (b) DV-4-1 in a 4 × 5 supercell. Here, the isosurface is 1 × 10−4 e Å−3. 8
Nanotechnology 26 (2015) 065705
T Hu and J Dong
References
and 2, whose partial charge densities are given at the right side of figure 7. Both of their band structures indicate that introduction of DVs induces a transition from the original direct band gap into indirect one, increasing the band gap of pristine phosphorene to now 1.053 eV and 1.102 eV for the DV-1-1 and DV-4-1, respectively. Other DV configurations also exhibit similar semiconducting character.
[1] Novoselov K, Geim A, Morozov S, Jiang D, Zhang Y, Dubonos S, Grigorieva I and Firsov A 2004 Science 306 666–9 [2] Zhang Y, Tan Y, Stormer H and Kim P 2005 Nature 438 201–4 [3] Cahangirov S, Topsakal M, Akturk E, Sahin H and Ciraci S 2009 Phys. Rev. Lett. 102 236804 [4] Houssa M, Pourtois G, Afanas’ev V V and Stesmans A 2010 Appl. Phys. Lett. 96 082111 [5] Topsakal M, Akturk E and Ciraci S 2009 Phys. Rev. B 79 115442 [6] Mak K F, Lee C, Hone J, Shan J and Heinz T F 2010 Phys. Rev. Lett. 105 136805 [7] Splendiani A, Sun L, Zhang Y, Li T, Kim J, Chim C, Galli G and Wang F 2010 Nano Lett. 10 1271–5 [8] Li L, Yu Y, Ye G-J, Ge Q, Ou X, Wu H, Feng D, Chen X-H and Zhang Y 2014 Nat. Nanotechnology 9 372–7 [9] Liu H, Neal A T, Zhu Z, Tomanek D and Ye P D 2014 ACS Nano 8 4033–41 [10] Xia F, Wang H and Jia Y 2014 Nat. Commun. 5 4458 [11] Reich E S 2014 Nature 506 19 [12] Qiao J, Kong X, Hu Z-X, Yang F and Ji W 2014 Nat. Commun. 5 4475 [13] Tran V, Soklaski R, Liang Y and Yang L 2014 Phys. Rev. B 89 235319 [14] Jiang J-W and Park H S 2014 Nat. Commun. 5 4727 [15] Fei R and Yang L 2014 Nano Lett. 14 2884 [16] Kotakoski J, Jin C H, Lehtinen O, Suenaga K and Krasheninnikov A V 2010 Phys. Rev. B 82 113404 [17] Komsa H-P, Kotakoski J, Kurasch S, Lehtinen O, Kaiser U and Krasheninnikov A V 2012 Phys. Rev. Lett. 109 035503 [18] Palacios J J, Fernandez-Rossier J and Brey L 2008 Phys. Rev. B 77 195428 [19] Attaccalite C, Bockstedte M, Marini A, Rubio A and Wirtz L 2011 Phys. Rev. B 83 144115 [20] Girit Ç Ö et al 2009 Science 323 1705 [21] Meyer J C, Kisielowski C, Erni R, Rossell M D, Crommie M F and Zettl A 2008 Nano Lett. 8 3582–6 [22] Kotakoski J, Mangler C and Meyer J C 2014 Nat. Commun. 5 3991 [23] Lee G-D, Wang C Z, Yoon E, Hwang N-M, Kim D-Y and Ho K M 2005 Phys. Rev. Lett. 95 205501 [24] Yamashita K, Saito M and Oda T 2006 JJAP 45 6534 [25] El-Barbary A A, Telling R H, Ewels C P, Heggie M I and Briddon P R 2003 Phys. Rev. B 68 144107 [26] Yazyev O V and Helm L 2007 Phys. Rev. B 75 125408 [27] Gao J, Zhang J, Liu H, Zhang Q and Zhao J 2013 Nanoscale 5 9785 [28] Li R, Han Y, Hu T, Dong J and Kawazoe Y 2014 Phys. Rev. B 90 045425 [29] Hu W and Yang J 2014 Defect in phosphorene (arXiv:1411.6986.v2) [30] Kresse G and Hafner J 1993 Phys. Rev. B 48 13115 [31] Kresse G and Furthmüller J 1996 Comput. Mater. Sci. 6 15 [32] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 [33] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758–75 [34] Henkelman G, Uberuaga B P and Jónsson H 2000 J. Chem. Phys. 113 9901 [35] Peng X, Wei Q and Copple A 2014 Phys. Rev. B 90 085402 [36] Fei R and Yang L 2014 Appl. Phys. Lett. 105 083120 [37] Ugeda M M, Brihuega I, Hiebel F, Mallet P, Veuillen J-Y, Gómez-Rodríguez J M and Ynduráin F 2012 Phys. Rev. B 85 121402 [38] Tang W, Sanville E and Henkelman G 2009 J. Phys.: Condens. Matter 21 084204
4. Conclusions We have performed spin-polarized DFT calculations on the geometric structures, and stabilities of both the MVs and DVs in 2D phosphorene as well as MV’s diffusions. Further, the influences of these vacancies on the vibrational and electronic properties of the defective phosphorenes have been studied. It is found that two possible MVs, MV-(5|9) and MV-(55|66), exist in the phosphorene, among which the MV-(5|9) is the ground state MV with its formation energy lower than that of MV-(55|66) by about 0.378 eV. The diffusion of MV-(5|9) exhibits an anisotropic character, preferring to migrate along the zigzag direction in the same half-layer. In addition, the 14 possible DVs in phosphorene have been found, which could be divided into four basic types based upon their topological structures and can transform between their different variants via bond rotations. The four lowest energy DV configurations in each basic types follow an energy order of Ef (DV-1) < Ef (DV-4) < Ef (DV-3) < Ef (DV-2). And the DV-1-1 with the (5| 8|5) topological defects is the most stable DV in all the 14 variants of DVs in phosphorene, which is quite different from those in graphene, where the C-DV(555|777) is the most stable. The introduction of vacancies in phosphorene also influences the vibrational properties, inducing the LDM, which could be used to distinguish different vacancy structures. The MVs and DVs also have a significant influence on the electronic properties of phosphorene. Phosphorene with MV-(5|9) is a magnetic semiconductor with the magnetic moment of 1.0 μB and a band gap of about 0.211 eV, while the DV-1-1 and DV-4-1 induce a direct-indirect band gap transition and increase the band gap of pristine phosphorene to 1.053 eV and 1.102 eV, respectively. Our DFT calculations on the fundamental vacancy properties in 2D materials are important for the research and application of the low dimentional materials in nanoscience.
Acknowledgments This work is supported by the State Key Program for Basic Research of China through the Grant No 2011CB922100Q. Our numerical calculations are performed in the High Performance Computing Center of Nanjing University.
9
