Two-Dimensional Mono-Elemental Semiconductor with Electronically

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Two-Dimensional Mono-Elemental Semiconductor with Electronically Inactive Defects: The Case of Phosphorus Yuanyue Liu, Fangbo Xu, Ziang Zhang, Evgeni S. Penev, and Boris I. Yakobson Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl5021393 • Publication Date (Web): 25 Aug 2014 Downloaded from http://pubs.acs.org on August 27, 2014

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Two-Dimensional Mono-Elemental Semiconductor with Electronically Inactive Defects: The Case of Phosphorus Yuanyue Liu, Fangbo Xu, Ziang Zhang, Evgeni S. Penev, and Boris I. Yakobson* Department of Materials Science and NanoEngineering, Department of Chemistry, and the Smalley Institute for Nanoscale Science and Technology, Rice University, Houston, Texas 77005 *[email protected] Abstract: The deep gap states created by defects in semiconductors typically deteriorate the performance of (opto)electronic devices. This has limited the applications of two-dimensional (2D) metal dichalcogenides (MX2), and underscored the need for a new 2D semiconductor without defect-induced deep gap states. In this work, we demonstrate that a 2D mono-elemental semiconductor is a promising candidate. This is exemplified by first-principles study of 2D phosphorus (P), a recently fabricated highmobility semiconductor. Most of the defects, including intrinsic point defects and grain boundaries, are electronically inactive, thanks to the homo-elemental bonding, which is not preferred in hetero-elemental system such as MX2. Unlike MX2, the edges of which create deep gap states and cannot be eliminated by passivation, the edge states of 2D P can be removed from the band gap by hydrogen termination. We further find that both the type and the concentration of charge carriers in 2D P can be tuned by doping with foreign atoms. Our work sheds light on the role of defects in the electronic structure of materials. Keywords: two-dimensional semiconductor, phosphorus, defects, density-functional theory

Defect-created deep states within the electronic band gap of semiconductors typically degrade device performance for electronics and optoelectroincs. They act as undesirable sinks for charge carriers1 and electron-hole recombination centers through the Shockley–Read–Hall process.2, 3 This has been one of the drawbacks for the applications of two-dimensional (2D) metal dichalcogenides (MX2),4-6 though they have attracted great interest for nano-devices.7, 8 In addition, the relatively low mobility of charge carriers, and the lack of efficient means to tune their type and concentration, together impede MX2 applications.7, 8 Most of the defect states in MX2, especially those of grain boundaries (GBs), originate from the chemical disorder brought about by the homo-elemental bonds (M–M or X–X), which are not present in the perfect lattice.4 Similarly, GBs in boron nitride (BN) with homo-elemental bonds (B–B or N–N) also create deep gap states.9 These “wrong” bonds can possibly be avoided in a mono-elemental system, even in presence of structural disorder. Therefore, a 2D semiconductor made of only one type of element is desirable (recently investigated monoelemental 2D boron shows all its polymorphs being metallic10). This brings into our focus 2D phosphorus (P), a semiconductor which has recently been exfoliated from black P—the most stable form of P at ambient conditions.11-13 It has attracted intense interest due to its proper band gap and high mobility.11, 12, 14-18 Here, based on density-functional-theory (DFT) calculations, we show that the structural defects in 2D P are electronically inactive, thanks to its mono-elemental makeup. In addition, we demonstrate the feasibility of tuning the charge carrier type and

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concentration by doping with foreign atoms. These properties together distinguish 2D P as promising candidate material for nano-electronics and optoelectronics. Although topologically (in its bonds-atoms connectivity) equivalent to hexagonal graphene, the 2D P is composed of buckled hexagons, and has a rectangular symmetry (Figure 1a). The P atoms are subdivided into two planes, forming an armchair-like pattern. Each P atom forms three bonds with its neighbors by sharing its three p electrons, leaving one lone-pair s electron. Two bonds are formed with the P atoms in the same layer, and the third one is with the other layer atom. The lattice direction in 2D P can be described by a vector na + mb, where a, b are the primitive vectors, with |a| = 4.62 Å, |b|=3.30 Å, and (n, m) = integers. The low symmetry of 2D P leads to higher structural complexity compared to other 2D materials, such as graphene, BN, and MoS2, which have a hexagonal symmetry. There are two types of in-plane armchair directions: A at 0° indexed (1,0) and A’ at 65° indexed (1,3), as well as two types of zigzag directions, Z at 90° indexed (0,1) and Z’ at 35.5° indexed (1,1), as shown in Figure 1a. In contrast, the hexagonal 2D materials have only one type of armchair direction. This complexity gives rise to more variation in defect structures, as shown later.


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Figure 1. (a) Structure of 2D P. Atoms in different layers are shown in black and white. Arrows indicate the primitive cell vectors, and lines show other basic lattice directions. (b) Band structure and density of states; inset shows the band gap calculated by different methods. (c) Charge density distribution of the states corresponding to the VBM and the CBM.

Figure 1b shows the electronic band structure of 2D P, a direct band gap semiconductor with an electrical band gap > 1.5 eV; computational details are given in the Supporting Information (SI). The state corresponding to the valence band maximum (VBM) is mainly located between the P atoms in different planes, while the state of the conduction band minimum (CBM) is formed by the atoms in the same plane, Figure 1c. These features will help distinguish the interior and the edge states, as shown later. The intrinsic defects in 2D materials can be categorized into two types: (i) line defects, i.e., edges, dislocations, and GBs; (ii) point defects, including bond-distortion complexes, vacancies,


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and interstitials. Figure 2a shows the core structure of the primary dislocation with a Burgers vector (0,1). The dislocation core consists of a buckled pentagon and heptagon pair (5|7). This is similar to the other 2D materials with hexagonal lattice, such as graphene,19, 20 BN9 and MoS2.4 Note that the bonding configuration at the dislocation core is the same as that in the prefect lattice, i.e., each atom forms three P–P bonds, two of which are with the atoms in the same layer, and one bond with that in the other layer. This is in contrast to the dislocation cores of MoS2 and BN, most of which have homo-elemental bonds never present in the perfect lattice.4, 9 The GBs are composed of linear dislocation arrays. Figure 2b shows the structures corresponding to different misorientation angles (α). These GBs are the lowest-energy ones at given α, and their energies are shown in Figure 2c. Most GBs are still made of 5|7s, which buckle in different ways depending on α. One interesting exception is the boundary between two Z’ terminated grains (71.1°), which does not have topological defects and thus represents a local minimum in the energy profile. In contrast, the boundary between two A’ terminated grains (130°) is made of quadrilaterals and octagons (4|8). These polygons have been observed in BN and MoS2.4, 9 Note that the GB energies are lower than those of graphene,19, 20 BN,9 and MoS2.4 This suggests that the chemical stability of GBs in 2D P is closer to the perfect lattice, compared with that in other 2D materials. To study the effect of GB on the electronic structure of 2D P, we embed the corresponding GBs in a polycrystalline sheet (see SI). Due to the computational limitations, the distance between GBs is ≈ 1.8 nm. The interaction between GBs could have additional effects on the electronic structure. Nevertheless, across all of the diverse structures considered, the GBs generally do not exhibit deep gap states, as shown in Figure 2d. These properties are in stark contrast to MoS2, where GBs create deep gap states and in some cases even become metallic.4 This difference originates from the absence of the chemical disorder (“wrong” bonds) within the GBs of 2D P.

Figure 2. (a) The core structure of the primary dislocation with a Burgers vector (0, 1), viewed from various directions. (b) Structure of grain boundaries at various misorientation angles. (c) Energy of grain boundaries, as a function of the misorientation angle. The line is to guide the eye. (d) Electronic density of states of the polycrystalline 2D P sheet, with corresponding grain boundaries embedded. α = 0° is equivalent to a perfect 2D P sheet.


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The edge is another important form of line defect. MoS2 edges are known to suffer from the deep gap states, regardless of passivation.21, 22 Similarly, the edge states of BN also cannot be eliminated by passivation.23 In contrast, we find that the edge states of 2D P can be removed from the band gap by hydrogen passivation. To study the effect of edge on the electronic structure of 2D P, we use a nanoribbon terminated with corresponding edges. Figure 3a shows the band structure of a P nanoribbon terminated along the AC direction. For a pristine edge, there are isolated bands in the gap. The charge density of the isolated bands is located at the edge (Figure S2) owing to the presence of dangling bonds. The edge can reconstruct, but the bonds cannot be fully saturated (see SI), and therefore the edge states still remain (Figure S3). However, after H passivation, that band disappears, and visualization of the nanoribbon VBM and CBM shows that they are contributed by the interior P (Figure 3b). The pattern of VBM and CBM is the same as that in the perfect 2D P, confirming that the edge states are fully eliminated from the band gap. The effect of H passivation applies to other edge directions, as verified by the charge density distribution of the VBM and CBM in the corresponding nanoribbons (Figure 3b).


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Figure 3. (a) Band structure of P ribbons with bare (left) and and H-passivated A edge (right). (b) Charge density distribution of the states at VBM and CBM, for P ribbons with various types of H-passivated edges. The energies of the bare edges, calculated from Eq. S1, are given under the corresponding geometries.

Point defects in the 2D P have structural similarities to graphene, since 2D P can be viewed as a mono-elemental sheet made of bucked hexagons. The lowest-energy point defect is a divacancy (VP2), which is composed of two buckled pentagons and one octagon (Figure 4). The bond rotation creates a Stone–Wales (SW) defect with two 5|7 pairs and slightly higher energy. A mono-vacancy (VP) reconstructs by forming a pentagon. The interstitial P atom (Pi) forms two bonds with P atoms in different layers, and leaves one dangling bond. Similar to GBs, the formation energies of the point defects are much lower than those in graphene.24 The primary defects—VP2 and SW—do not induce gap states because their bonds are fully saturated. The VP and Pi create spin-polarized p-type states right above the VBM (< 0.1 eV), due to the presence of dangling bonds. Those states, on one hand, are a possible origin of p-type conductivity observed experimentally in 2D P;11, 12 On the other hand, for a p-type 2D P, these defects will not act as sinks for the major charge carriers (holes), as there are no compensating electrons.

Figure 4. Intrinsic point defects in 2D P, including di-vacancy (VP2), Stone–Wales (SW), mono-vacancy (VP), and interstitial (Pi). Structures are shown in the top panels with the formation energies indicated, and the corresponding electronic densities of states are shown in the bottom panels. For spin-polarized systems, the two spin states are shown in different colors.

Next we discuss the possibility of tuning charge carrier type and concentration. Many electronic devices, such as p-n junctions, require the ability of the semiconductor to be both pdoped and n-doped. A good p-type dopant should have empty states close to the VBM. Group-IV elements have one less electron than P, and therefore can create empty states in the band gap. Among them, C has the strongest electron affinity, suggesting the lowest energy of the states.


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Indeed, Figure 5 shows that substitutional C (CP) is a good p-type dopant. We further find substitutional Zn (ZnP), which has less valence electrons than P, is also a good p-type dopant. Similarly, a good n-type dopant should have filled states close to the CBM. The chalcogen group has one more electron than P, and therefore can create filled states in the band gap. Among them, Te has the lowest electron ionization energy, suggesting the highest energy of the states. However, we find that these states are still far from the CBM (Figure 5, TeP), indicating that the chalcogen group is not a proper n-type dopant. Alternatively, the alkali group has lower ionization energy, and thus could have the donor states closer to the CBM. As an example, Figure 5 shows that potassium adsorption (Kad) can induce n-type conductivity in 2D P. The adsorption is thermodynamically stable (-0.81 eV, calculated using Eq. S2 and shown in Table S2) and therefore the K clustering is unlikely,25 yet K is very mobile on P (anisotropic diffusion barriers, 0.02 eV and 0.26 eV, Figure S7). Diffusion barriers could be increased by the gate oxides in the transistor. Nevertheless, given that Kad has been used experimentally to achieve high n-doping in MoS2 and WSe2,26 it is possible that it can also be utilized in the case of 2D P. On the other hand, the negative adsorption energy and low diffusion barriers suggest that 2D P could be a promising anode material for batteries. Indeed, bulk P and P nanoparticles/composites have been experimentally reported as high-capacity Li-ion battery anodes.27, 28 The formation energies of the other dopants studied here are all positive (with the chemical potential of the dopant atom referred to its bulk state). The high surface ratio of 2D materials could facilitate the doping kinetics. The dopants can be charged depending on the Fermi level. Our calculations of the band structures (Figure S6) show that, when the Fermi level is varied between VBM and CBM, CP and ZnP can sustain ±1 charge by changing the occupation of the defect level. However, it cannot have higher charge states. In contrast, Kad does not create defect level. The K electron is transferred to the 2D P by occupying the previously empty states while retaining the band dispersion (as described by a states-filling model detailed in a recent study29). The charge is therefore not localized on the Kad regardless of the Fermi level.


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Figure 5. The electronic density of states of 2D P doped by foreign atoms. For spin-polarized systems, the two spin states are shown in different colors.

It is interesting to compare the 2D P with bulk Si, a representative three-dimensional monoelemental semiconductor. Grain boundaries (where the dislocations are densely packed) in Si also do not create gap states as the bonds are fully saturated.30 However, the intrinsic point defects in Si (vacancies and interstitials) have dangling bonds and therefore create deep gap states.31 These unsaturated bonds also lead to higher formation energies (> 3 eV32, 33) of the point defects compared to those in 2D P. In summary, we find that the defects in 2D P are electronically inactive, in contrast to other 2D hetero-elemental semiconductors like MX2. Both the type and the concentration of charge carriers can by tuned by doping foreign atoms. These properties, together with its high charge carrier mobility, suggest 2D P as a promising candidate for electronic and optoelectronic applications. Supporting Information Available: Calculation details, structure of polycrystalline 2D P sheet, band structure of nanoribbons, charge density distribution of the edge state of a 2D P sheet terminated with A edge, edge structures and energies, atomic structure of dopants, band structure of neutral/charged dopants, diffusion paths and energies of K adsorbed on 2D P, energy of H-passivated edges, formation energy of dopants. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgements:


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This work was supported by the Department of Energy, BES Grant No. ER46598. Computations were performed on (1) NERSC, supported by DOE Grant DE-AC02-05CH11231, (2) XSEDE, funded by NSF Grant OCI-1053575, under allocation TG-DMR100029, and (3) DAVinCI, funded by NSF Grant OCI-0959097. References: 1. Blatter, G.; Greuter, F. Phys. Rev. B 1986, 33, 3952-3966. 2. Yin, W.-J.; Wu, Y.; Wei, S.-H.; Noufi, R.; Al-Jassim, M. M.; Yan, Y. Adv. Energy Mater. 2014, 4, 1300712. 3. Li, J.; Mitzi, D. B.; Shenoy, V. B. ACS Nano 2011, 5, 8613-8619. 4. Zou, X.; Liu, Y.; Yakobson, B. I. Nano Lett. 2012, 13, 253-258. 5. Zhou, W.; Zou, X.; Najmaei, S.; Liu, Z.; Shi, Y.; Kong, J.; Lou, J.; Ajayan, P. M.; Yakobson, B. I.; Idrobo, J.-C. Nano Lett. 2013, 13, 2615-2622. 6. Ghorbani-Asl, M.; Enyashin, A. N.; Kuc, A.; Seifert, G.; Heine, T. Phys. Rev. B 2013, 88, 245440. 7. Jariwala, D.; Sangwan, V. K.; Lauhon, L. J.; Marks, T. J.; Hersam, M. C. ACS Nano 2014, 8, 1102– 1120. 8. Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Nat. Nanotechnol. 2012, 7, 699-712. 9. Liu, Y.; Zou, X.; Yakobson, B. I. ACS Nano 2012, 6, 7053-7058. 10. Penev, E.; Bhowmick, S.; Sadrzadeh, A.; Yakobson, B. I. Nano Lett. 2012, 12, 2441-2445. 11. Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X. H.; Zhang, Y. Nat. Nanotechnol. 2014, 9, 372-377. 12. Liu, H.; Neal, A. T.; Zhu, Z.; Luo, Z.; Xu, X.; Tománek, D.; Ye, P. D. ACS Nano 2014, 8, 4033–4041. 13. Lu, W.; Nan, H.; Hong, J.; Chen, Y.; Liang, Z.; Ni, Z.; Jin, C.; Zhang, Z. Nano Res. 2014, DOI: 10.1007/s12274-014-0446-7. 14. Dai, J.; Zeng, X. C. J. Phys. Chem. Lett. 2014, 5, 1289-1293. 15. Rodin, A. S.; Carvalho, A.; Castro Neto, A. H. Phys. Rev. Lett. 2014, 112, 176801. 16. Zhu, Z.; Tománek, D. Phys. Rev. Lett. 2014, 112, 176802. 17. Fei, R.; Yang, L. Nano Lett. 2014, 14, 2884-2889. 18. Buscema, M.; Groenendijk, D. J.; Blanter, S. I.; Steele, G. A.; van der Zant, H. S. J.; CastellanosGomez, A. Nano Lett. 2014, 14, 3347–3352. 19. Liu, Y.; Yakobson, B. I. Nano Lett. 2010, 10, 2178-2183. 20. Yazyev, O. V.; Louie, S. G. Phys. Rev. B 2010, 81. 21. Chen, J.; Xi, J.; Wang, D.; Shuai, Z. J. Phys. Chem. Lett. 2013, 4, 1443-1448. 22. Pan, H.; Zhang, Y.-W. J. Mater. Chem. 2012, 22, 7280-7290. 23. Zhang, Z.; Guo, W. Phys. Rev. B 2008, 77, 075403. 24. Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. ACS Nano 2010, 5, 26-41. 25. Liu, Y.; Artyukhov, V. I.; Liu, M.; Harutyunyan, A. R.; Yakobson, B. I. J. Phys. Chem. Lett. 2013, 4, 1737-1742. 26. Fang, H.; Tosun, M.; Seol, G.; Chang, T. C.; Takei, K.; Guo, J.; Javey, A. Nano Lett. 2013, 13, 19911995. 27. Park, C. M.; Sohn, H. J. Adv. Mater. 2007, 19, 2465-2468. 28. Sun, J.; Zheng, G.; Lee, H.-W.; Liu, N.; Wang, H.; Yao, H.; Yang, W.; Cui, Y. Nano Lett. 2014, DOI: 10.1021/nl501617j. 29. Liu, Y.; Wang, Y. M.; Yakobson, B. I.; Wood, B. C. Phys. Rev. Lett. 2014, 113, 028304. 30. Liu, F.; Mostoller, M.; Milman, V.; Chisholm, M. F.; Kaplan, T. Phys. Rev. B 1995, 51, 17192-17195. 31. Schultz, P. A. Phys. Rev. Lett. 2006, 96, 246401.


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Two-Dimensional Mono-Elemental Semiconductor with Electronically

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