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Defects in Phosphorene Wei Hu, and Jinlong Yang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06077 • Publication Date (Web): 18 Aug 2015 Downloaded from http://pubs.acs.org on August 19, 2015

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The Journal of Physical Chemistry

Defects in Phosphorene Wei Hu∗,† and Jinlong Yang∗,‡,¶ †Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA ‡Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China ¶Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China E-mail: [email protected]; [email protected] Phone: +1-5105416034; +86-55163606408

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ABSTRACT: Defects are inevitably present in materials and always can affect their properties. Here, We perform first-principles calculations to systematically investigate the stability and electronic structures of ten kinds of point defects in two-dimensional semiconducting phosphorene, including the Stone-Wales (SW-1 and SW-2) defect, single (SV-(5|9) and SV-(55|66)) and double (DV-(5|8|5)-1, DV-(5|8|5)-2, DV-(555|777)-1, DV-(555|777)-2, DV-(555|777)-3 and DV-(4|10|4)) vacancy defects. We find that these defects are all created quite easily in phosphorene with higher areal density compared with graphene and silicene. Most of them are easy to distinguish each other and correlate with their defective atomic structures with simulated scanning tunneling microscopy images at positive bias. The SW, DV-(5|8|5)-1, DV-(555|777) and DV-(4|10|4) defects have little effect on phosphorene’s electronic properties and defective phosphorene monolayers still show semiconducting with similar band gap values to perfect phosphorene. The SV-(5|9) and DV-(5|8|5)-2 defects can introduce unoccupied localized states into phosphorene’s fundamental band gap. Specifically, the SV-(5|9) and SV-(55|66) defects can induce hole doping in phosphorene, and the SV-(5|9) defect can result in local magnetic moments in phosphorene different from all other defects. Keywords: Point Defects, Phosphorene, Electronic Structures, and Density Functional Theory.

Introduction Two-dimensional (2D) atom-thick materials, 1–4 for example, graphene, 5 silicene, 6 hexagonal boron nitride (h-BN) 7 and molybdenum disulphide (MoS2 ), 8 show remarkable properties and potential applications on semiconductors, electronics and composites, and have recently attracted significant interest. In particular, graphene, 5 a 2D sp2 -hybridized carbon elemental monolayer, shows high performance optoelectronic properties. For example, graphene has a high carrier mobility, however, its zero-gap feature limits its wide applications on graphene2 ACS Paragon Plus Environment

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based nanoelectronics with large-off current and high on-off ratio. The same limitation also exists in silicene, 6 another well-known single silicon monolayer, which has most similar remarkable electronic properties to graphene but with buckled honeycomb structures. 9 Recently, a new 2D phosphorus elemental monolayer, namely phosphorene, 10–20 has been isolated experimentally from bulk black phosphorus through mechanical exfoliation. Compared with graphene and silicene, phosphorene shows more excellent optoelectronic properties and has immediately received outstanding attention. In particular, phosphorene is direct semiconducting, and it has a high hole mobility 10 up to 105 cm2 /V/s and a large drain current modulation 11 up to 105 in electronic devices. Furthermore, phosphorene possesses a thickness-dependent direct bandgap values from 0.3 eV (Bulk) to 1.5 eV (Monolayer). 10 Like graphene, 21 phosphorene also has high performance optical properties. 12 These advantages make phosphorene an ideal candidate for field effect transistors, 11 photovoltaic PN junctions 13 and thin-film solar cells. 15 Therefore, phosphorene can be used as an alternative to graphene, and may lead to new faster semiconductor optoelectronic devices in the future experiments. On the other hand, most properties and applications of materials are always affected by the presence of defects, especially, point defects, 22 which are generated usually by ion or electron irradiations. 23 For 2D materials, defects also can be extremely used to generate innovative devices. 24 Typical point defects in graphene and silicene include Stone-Wales (SW) defect, single and double vacancy (SV and DV) defects. 25–30 Generally, both graphene and silicene have two kinds of SVs (SV-(5|9) and SV-(55|66)) and DVs (DV-(5|8|5) and DV(555|777)), respectively. These defects are inevitably present in graphene and silicene and severely affect their structural and electronic properties, 28,29 thus alter their applications. 31–33 However, little attention has been focused on the defects in phosphorene. 34 In this work, we systematically investigate the stability and electronic structures of typical point defects in semiconducting phosphorene using the density functional theory and ab-initio molecular dynamics calculations. We find that phosphorene has a wide variety of defects



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due to its low symmetry structure. Furthermore, these defects are all quite easily created in phosphorene with regard to graphene and silicene and most of them are easy distinguish each other and correlate with their defective atomic structures with simulated scanning tunneling microscopy images at positive bias. These defects have different geometric structures and show different stability and electronic structures in phosphorene.

Theoretical Methods and Models We use the density functional theory (DFT) calculations implemented in the VASP package. 35 We choose the generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA-PBE) 36 owing to its good description of electronic structures of phosphorene, 14 graphene 28 and silicene. 29 All the atomic coordinates are fully relaxed by using the conjugate gradient (CG) algorithm until total energy and atomic forces are converged to 10−5 eV and 0.01 eV/˚ A, respectively. The unit cell lattice parameters of phosphorene is calculated to be a(P) = 4.62 ˚ A and b(P) = 3.30 ˚ A. 14 A large 5 × 7 supercell of phosphorene (140 phosphorus atoms) with a vacuum space about 15 ˚ A in the Z direction is adopted to study the effect of various local defects in phosphorene. All the phosphorus atoms in phosphorene are labeled by numbers as shown in Figure 1. We set the energy cutoff to be 500 eV and adopt a 3 × 3 regular mesh to sample the surface Brillouin zone. Ab-initio molecular dynamics (AIMD) simulations are employed to study the stability of defects in phosphorene. AIMD simulations are performed in a canonical ensemble. The simulations is performed during 2.0 ps with a time step of 2.0 fs at the temperature of 400 K controlled by using the Nose-Hoover method. 37

Results and Discussion We first investigate the geometric properties of defects in phosphorene as shown in Figure 1. Typical point defects, such as SW, SV-(5|9), SV-(55|66), DV-(5|8|5) and DV-(555|777) usu4 ACS Paragon Plus Environment

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ally generated in graphene 28 and silicene, 29 also can be formed in phosphorene, but which has a wide variety of defects because of lower symmetry structure of phosphorene compared with graphene and silicene. We find that there are two kinds of SW (denoted as SW-1 and SW-2) and DV-(5|8|5) (denoted as DV-(5|8|5)-1 and DV-(5|8|5)-2), three kinds of DV-(555|777) (denoted as DV-(555|777)-1, DV-(555|777)-2 and DV-(555|777)-3) defects in phosphorene as shown in Figure 1. Furthermore, we find a new stable structure of DV defect in phosphorene, namely DV-(4|10|4), as shown in Figure 1(h), which has not been observed in both graphene and silicene. For two kinds of SW defects as shown in Figure 1(a) and (b), different P-P bonds in phosphorene are rotated by about 90 degrees, P67 -P74 and P59 -P67 bonds for SW-1 and SW-2 defects, respectively. Two kinds of SV defects are both produced by removing the P67 atom from phosphorene as shown in Figure 1(d) and (e), but the distances between the P60 and P74 atoms are 3.60 and 2.53 ˚ A in the SV-(5|9) and SV-(55|66) defects, respectively. Thus, P60 and P67 atoms form a P-P bond in SV-(55|66) defect. There are six kinds of DV defects in phosphorene. For two kinds of DV-(5|8|5) defects as shown in Figure 1(f) and (g), different P-P bonds containing two phosphorus atoms are removed from phosphorene, P60 -P67 and P67 -P74 bonds for DV-(5|8|5)-1 and DV-(5|8|5)-2 defects, respectively. The DV(4|10|4) defect is also produced by removing the P67 -P74 bond from phosphorene, but they show different bonding configurations. In the DV-(5|8|5)-2 defect, P59 -P60 and P80 -P81 form two chemical bonds. But in the DV-(4|10|4) defect, P59 -P80 and P60 -P81 form two chemical bonds. Three configurations of DV-(555|777) defects are complex as shown in Figure 1(i), (j) and (k). Different from the DV-(5|8|5) and DV-(4|10|4) defects, they are all produced by removing two non-bonding-together phosphorus atoms, P53 and P59 , P67 and P68 , P60 and P75 for DV-(555|777)-1, DV-(555|777)-2 and DV-(555|777)-3 defects, respectively. To check the stability of defects in phosphorene, the formation energy is defined as

Ef = EPhosphorene − NP ∗ EP



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Figure 1: (Color online) Geometric structures of (a) perfect and defective phosphorene in the 5 × 7 supercell, including the (b) SW-1, (c) SW-2, (d) SV-(5|9), (e) SV-(55|66), (f) DV(5|8|5)-1, (g) DV-(5|8|5)-2, (h) DV-(4|10|4), (i) DV-(555|777)-1, (j) DV-(555|777)-2 and (k) DV-(555|777)-3 defects. In figure (a), all the phosphorus atoms are labeled by numbers and the red and blue balls denote the phosphorus atoms in two different upper and lower layers of phosphorene, respectively. In other figures, the violet and yellow balls denote unaffected and affected phosphorus atoms, respectively. 6 ACS Paragon Plus Environment

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where EPhosphorene represents the total energy of defective phosphorene, EP is the energy per phosphorus atom in a perfect phosphorene sheet and NP corresponds to the number of phosphorus atoms in phosphorene. Notice that for perfect phosphorene, Ef (Phosphorene) = 0 eV. Perfect phosphorene shows less stable with a smaller cohesive energy of 3.48 eV/atom compared with graphene (7.90 eV/atom) and silicene (3.96 eV/atom). 29 Our calculated stability of perfect and defective phosphorene, graphene and silicene are summarized in Table 1 and Table 2. Table 1: Calculated stability and electronic properties of perfect and defective phosphorene, including the formation energy Ef (eV ), total magnetic moment µ (µB ) and band gap Eg (eV ). Ef Perfect 0.000 SW-1 1.012 SW-2 1.322 SV-(5|9) 1.626 SV-(55|66) 2.025 DV-(5|8|5)-1 1.906 DV-(5|8|5)-2 3.041 DV-(4|10|4) 2.137 DV-(555|777)-1 2.081 DV-(555|777)-2 2.350 DV-(555|777)-3 2.613

µ 0.000 0.003 0.003 0.980 0.000 0.002 0.002 0.000 0.002 0.002 0.003

Eg 0.905 0.928 0.883 0.190/0.941 Hole doping 0.962 0.559 0.929 0.966 0.962 0.973

Table 2: Comparison results of cohesive energy Ec (eV/atom) of perfect phosphorene, graphene and silicene with corresponding various defects’ formation energy Ef (eV). Phosphorene Reference This work Ec (Perfect) 3.48 Ef (SW) 1.01−1.32 Ef (SV-(5|9)) 1.63 Ef (SV-(55|66)) 2.03 Ef (DV-(5|8|5)) 1.91−3.04 Ef (DV-(555|777)) 2.08−2.61 Ef (DV-(4|10|4)) 2.13

Graphene Ref. 28 7.90 4.50 7.80 − 7.52 6.40 −


Silicene Ref. 29 3.96 2.09 3.77 3.01 3.70 2.84 −


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We find that the SW-1 defect is most easily formed in phosphorene with the smallest formation energy of 1.01 eV among various defects similar to graphene 28 and silicene. 29 For DVs, the DV-(5|8|5) and DV-(555|777) defects are also stable in phosphorene similar to graphene and silicene. Interestingly, we find the most stable DV in phosphorene is DV(4|10|4) with a small formation energy of 2.13 eV, but which can not formed in graphene and silicene. To further study the thermal stability of perfect and defective phosphorene, AIMD simulations in the VASP are performed at 400 K. In the initial state (t = 0.0 ps), perfect and defective phosphorene monolayers are set to optimized geometric structures. We find that the perfect phosphorene and most of defective phosphorene monolayers are stable at 400 K during t = 2.0 ps. The only unstable one is the SV-(55|66) defect, which trends to change into more stable SV-(5|9) defect in phosphorene at 400 K, different from the situation of silicene. 29 At finite temperature T , the areal density NDefect (m−2 ) of defects in 2D materials follows the Arrhenius equation NDefect = NPerfect exp(−Ef /kB T ) where NPerfect is the areal density of atoms in perfect 2D materials, Ef is the formation energy of a defect formed in materials and kB is the Boltzmann constant. For perfect phosphorene, graphene and silicene, their areal densities are NPerfect (Phosphorene) = 2.62 × 1019 m−2 , NPerfect (Graphene) = 3.79 × 1019 m−2 and NPerfect (Silicene) = 1.55 × 1019 m−2 , respectively. The temperature-dependence areal density of the most stable defects in phosphorene, graphene and silicene is calculated and plotted in Figure 2. The results show that these defects have much higher areal density and they are created quite easily in phosphorene compared with graphene and silicene. In order to help recognize these point defects in the future experiments, the scanning tunneling microscopy (STM) images of perfect and defective phosphorene are also simulated at +1.0 and -1.0 V bias as shown in Figure 3. At positive bias (+1.0 V), the STM images 8 ACS Paragon Plus Environment

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Figure 2: (Color online) Areal density of various stable defects (SW, SV-(5|9), SV-(55|66), DV-(5|8|5), DV-(555|777) and DV-(4|10|4)) in (a) phosphorene, (b) graphene and (c) silicene as a function of temperature. of most defects are easy to understand and correlate with their defective atomic structures. But at negative bias (-1.0 V), the STM images of perfect and defective phosphorene are difficult to distinguish each other due to similar height variation for the buckled structures of phosphorene. The different phenomena of STM images of perfect and defective phosphorene can be understood by their projected density of states (PDOS) of a selected phosphorus atom in perfect and defective phosphorene as shown in Figure 4. We find that the valence bands of perfect phosphorene are mainly contributed by P3pz orbitals associated with lone pairs of electrons, and its conduction bands are composed of the sp3 hybridized states of P3s, P3px , P3py and P3pz orbitals (Figure 4(a)). Thus, for perfect phosphorene, there are symmetrical white bright spots with a distance of 3.54 ˚ A in the STM image at -1.0 V bias (valence bands), but symmetrical gray rings in the STM image at +1.0 V bias (conduction bands). For defective phosphorene, the defect-affected phosphorus atoms near the defects all have some occupied states contributing into the valence bands of phosphorene, but the peak strength and positions of these occupied states are mostly overlapped with P3pz states of other unaffected phosphorus atoms. Therefore, perfect and defective phosphorene show similar STM images at negative bias (-1.0 V) and thus they are difficult to distinguish each 9 ACS Paragon Plus Environment


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Figure 3: (Color online) Simulated STM images (+1.0 and -1.0 V) of (a) perfect and defective phosphorene with the (b) SW-1, (c) SW-2, (d) SV-(5|9), (e) SV-(55|66), (f) DV-(5|8|5)-1, (g) DV-(5|8|5)-2, (h) DV-(4|10|4), (i) DV-(555|777)-1, (j) DV-(555|777)-2 and (k) DV-(555|777)3 defects.


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other at this situation.

Figure 4: (Color online) Projected density of states (PDOS) of a selected phosphorus atom in (a) perfect and defective phosphorene, including (b) P67 in SW-1, (c) P59 in SW-2, (d) P60 in SV-(5|9) (spin-up plus spin-down states), (e) P74 in SV-(55|66), (f) P59 in DV-(5|8|5)-1, (g) P59 in DV-(5|8|5)-2, (h) P59 in DV-(4|10|4), (i) P60 in DV-(555|777)-1, (j) P60 in DV(555|777)-2 and (k) P68 in DV-(555|777)-3. The Fermi level is marked by green dotted lines and set to zero.

However, defective phosphorene systems show stronger unoccupied states than that of perfect phosphorene, and that is why most defects in phosphorene can be recognized by using the STM images at positive bias. The SV-(55|66) defect in phosphorene is most easily recognized in the STM image, because there is only a white bright spot at +1.0 V bias (Figure 4(e)), which is contributed by the stronger unoccupied states from the defectaffected phosphorus atom P74 (Figure 1(e)). For the SV-(5|9) defect in phosphorene, there are four grey spots at +1.0 V bias (Figure 4(d)), which are contributed by four defect-affected 11 ACS Paragon Plus Environment


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phosphorus atoms P59 , P60 , P68 and P74 (Figure 1(d)). The DV-(5|8|5)-2 and DV-(4|10|4) defects in phosphorene are also easily recognized in the STM image at +1.0 V bias due to their high symmetry (Figure 4(g) and (h)). For the DV-(5|8|5)-1 defect in phosphorene, there are a white bright spot and several gray spots at +1.0 V bias (Figure 4(f)). For two kinds of SW defects in phosphorene, they can be distinguished by comparing the atomic structures and STM images at positive bias (Figure 4(b) and (c)). But, three DV-(555|777) defects in phosphorene show similar and disordered STM images at positive bias (Figure 4(i), (j) and (k)) due to their lower symmetry and similar configurations. Further advanced methods need to be introduced to observe them in the experiments. Finally, we check the electronic band structures of perfect and defective phosphorene as shown in Figure 5. Monolayer phosphorene is a direct semiconductor with a band gap of 0.91 eV (Figure 5(a)), agreeing well with previous theoretical studies. 14 We find that the SW, DV-(555|777) and DV-(4|10|4) defects have little effect on phosphorene’s electronic properties, still showing semiconducting with similar band gap values (about 0.9 eV) to perfect phosphorene, different from graphene 28 and silicene. 29 That is because the occupied and unoccupied states contributed by the defect-effaced phosphorus atoms for these defects are respectively close that of other unaffected phosphorus atoms as shown in Figure 4. Defective phosphorene with the DV-(5|8|5) defects are also semiconductors but with different band gaps (0.96 and 0.56 eV respectively for DV-(5|8|5)-1 and DV-(5|8|5)-2). The SV(5|9) and DV-(5|8|5)-2 defects can introduce unoccupied localized states into phosphorene’s fundamental band gap as shown in Figure 5(d) and (g). The introduced states of SV-(5|9) and DV-(5|8|5)-2 defects are contributed by the P60 and P59 atom as shown in Figure 4(d) and (g), respectively. The P60 atom in SV-(5|9) defect shows a dangling bond different from other phosphorus atoms in phosphorene which can form three covalent P-P bonds and a lone pair of electrons via sp3 orbital hybridization of P3s, P3px , P3py and P3pz orbitals. The P59 -P60 atoms in the DV-(5|8|5)-2 defect are bonding very weekly with a longer bond length of 2.54 ˚ A compared with other P-P covalent bonds (2.22 ˚ A).


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Figure 5: (Color online) Electronic band structures of (a) perfect and defective phosphorene with the (b) SW-1, (c) SW-2, (d) SV-(5|9), (e) SV-(55|66), (f) DV-(5|8|5)-1, (g) DV-(5|8|5)2, (h) DV-(4|10|4), (i) DV-(555|777)-1, (j) DV-(555|777)-2 and (k) DV-(555|777)-3 defects. The Fermi level is marked by green dotted lines and set to zero.



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More interestingly, we find that two SV defects can induce hole doping in phosphorene as shown in Figure 5(d) and (e), which can increase the hole carrier concentration of semiconducting phosphorene. Notice that phosphorene has a high areal density for the SV defects, agreeing well with a high hole mobility observed in phosphorene in recent experiments. 10 Furthermore, among all the point defects in phosphorene, only the SV-(5|9) defect can induce local magnetic moments in phosphorene with a magnetic moment of 0.98 µB due to the presence of dangling bond in P60 atom, and it is ferromagnetic as shown in Figure 6. But, other defective phosphorene monolayers are not magnetic similar to the situation of silicene. 29 The magnetic property of the SV-(5|9) defect makes phosphorene an extremely promising material for spin qubits 38 and quantum spintronics. 39

Figure 6: (Color online) Spin-density isosurfaces for the SV-(5|9) defect in phosphorene. The red and blue color isosurfaces represent spin-up and spin-down states, respectively.

Conclusions We systematically study the stability and electronic structures of defects in semiconducting phosphorene using the density functional theory and ab-initio molecular dynamics calculations. We find that phosphorene has a wide variety of point defects (SW-1, SW-2, SV-(5|9), SV-(55|66), DV-(5|8|5)-1, DV-(5|8|5)-2, DV-(555|777)-1, DV-(555|777)-2, DV-(555|777)-3 14 ACS Paragon Plus Environment

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and DV-(4|10|4)) due to its low symmetry structure. Furthermore, these defects are all quite easily created in phosphorene compared with graphene and silicene and most of them are easy to distinguish each other and correlate with their defective atomic structures with simulated scanning tunneling microscopy images at positive bias. Defects of different structures shows different stability and electronic structures in phosphorene. The SW, DV-(5|8|5)-1, DV-(555|777) and DV-(4|10|4) defects have little effect on phosphorene’s electronic properties and defective phosphorene monolayers still show semiconducting with similar band gap values to perfect phosphorene. The SV-(5|9) and DV-(5|8|5)-2 defects can introduce unoccupied localized states into phosphorene’s fundamental band gap. Specifically, the SV-(5|9) and SV-(55|66) defects can induce hole doping in phosphorene, and the SV-(5|9) defect can result in local magnetic moments in phosphorene different from all other defects. Our theoretical calculations provide significant insights into the identification of point defects in the further experiments and the understanding of their effects on the electronic properties and potential applications of phosphorene.

Acknowledgement This work is partially supported by the Scientific Discovery through Advanced Computing (SciDAC) Program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences (W. H.). This work is also partially supported by the National Key Basic Research Program (2011CB921404), by NSFC (21421063, 91021004, 21233007), by Chinese Academy of Sciences (CAS) (XDB01020300). We thank the National Energy Research Scientific Computing (NERSC) center, USTCSCC, SCCAS, Tianjin, and Shanghai Supercomputer Centers for the computational resources.



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Defects in Phosphorene - The Journal of Physical Chemistry C (ACS

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