Two-Dimensional PC6 with Direct-Band Gap and Anisotropic Carrier

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Two-Dimensional PC with Direct-Band Gap and Anisotropic Carrier Mobility Tong Yu, Ziyuan Zhao, Yuanhui Sun, Aitor Bergara, Jianyan Lin, Shoutao Zhang, Haiyang Xu, Lijun Zhang, Guochun Yang, and Yichun Liu J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b11350 • Publication Date (Web): 04 Jan 2019 Downloaded from http://pubs.acs.org on January 4, 2019

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Journal of the American Chemical Society

Two-Dimensional PC6 with Direct-Band Gap and Anisotropic Carrier Mobility Tong Yu1‡, Ziyuan Zhao1‡, Yuanhui Sun2‡, Aitor Bergara3,4,5, Jianyan Lin1, Shoutao Zhang1, Haiyang Xu1, Lijun Zhang2, Guochun Yang1*, and Yichun Liu1* 1Centre

for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China 2College of Materials Science and Engineering and Key Laboratory of Automobile Materials of MOE, Jilin University, Changchun 130012, China. 3Departmento de Física de la Materia Condensada, Universidad del País Vasco, UPV/EHU, 48080 Bilbao, Spain 4Donostia International Physics Center (DIPC), 20018 Donostia, Spain 5Centro de Física de Materiales CFM, Centro Mixto CSIC-UPV/EHU, 20018 Donostia, Spain ABSTRACT: Graphene and phosphorene are two major types of atomically-thin two-dimensional

materials under extensive investigation. However, the zero band gap of graphene, and the instability of phosphorene greatly restrict their applications. Here, we make first-principle unbiased structure search calculations to identify a new buckled graphene-like PC6 monolayer with a

number of desirable functional properties. PC6 monolayer is a direct-gap semiconductor with a

band gap of 0.84 eV and has extremely high intrinsic conductivity with anisotropic character (i.e. its electron mobility is 2.94 × 105 cm2 V−1 s−1 along the armchair direction, whereas the hole mobility reaches 1.64 × 105 cm2 V−1 s−1 along the zigzag direction), which is comparable to graphene. On the other hand, PC6 shows a high absorption coefficient (105 cm-1) in a broad

band, from 300 to 2000 nm. Additionally, its direct-band gap character can be remained within a biaxial strain of 5%. All these appealing properties make the predicted PC6 monolayer a promising candidate for applications in electronic and photovoltaic devices.

1. INTRODUCTION The discovery of graphene in 2004 has boosted the research on two-dimensional (2D) materials.1 In the last years, some other types of 2D materials, such as, hexagonal boron nitride, transition metal dichalcogenides, phosphorene, and group IV monochalcogenides have also appeared.2 2D materials are not only interesting for being the thinnest crystalline solids, but also for presenting many attractive physical properties, which are distinct from their bulk counterparts. As a consequence, a series of research

breakthroughs on 2D materials, with attractive applications on catalysis, luminescence, sensors, and electronic devices, have recently emerged.3 In contrast to 3D crystals, 2D materials have unique advantages on developing high-performance field-effect transistors (FET), in which the leakage current can be effectively eliminated because all the electrons are confined in atomically-thin channels and, thus, all the carriers are uniformly influenced by the gate voltage.4 Graphene, with a remarkable high carrier mobility of 3.2~3.5×105 cm2 V−1 s−1, becomes an ideal candidate for FETs.5 However, its zero-band gap is the main obstacle

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for successful applications, and getting a sizable, robust, and reproducible band gap for graphene is difficult.6–9 On the other hand, FET devices built on MoS2 monolayers, with a direct band gap of 1.8 eV, show a good performance, with a high on/off ratios of ~108, but present a low carrier mobility, from 10 to 200 cm2 V−1 s−1, which restricts their practical applications.10–12 Additionally, phosphorene has a direct band gap and FET devices based on a few-layer phosphorene have reasonably high on/off ratios of 104 as well as a high carrier mobility, 55~1000 cm2 V−1 s−1.13,14 However, phosphorene is prone to degradation in a humid environment or air, and is also sensitive to a straininduced direct-to-indirect band gap transition.15 Therefore, new 2D materials with moderate band gaps, high carrier mobilities, and high stability remain to be discovered and are still highly needed. On the other hand, 2D materials with in-plane directional-dependent properties (i.e. anisotropic) provide an opportunity for developing novel devices. For example, phosphorene is a representative of anisotropic 2D materials, where using this feature allows a much higher on-off ratios (exceeding 105) in phosphorenebased FETs.16 Inspired by this, a few other anisotropic 2D materials with complementary properties to phosphorene, such as ReS2,17 ReSe2,18 GeSe2,19 and, Ge20,21 or Sn22,23 monochalcogenides have recently emerged. These materials demonstrate unique advantages when applied in polarization-sensitive photodetectors, crystal orientation-induced diodes, integrated digital inverters, and synaptic devices for neuromorphic applications.19 Graphene and phosphorene are two important types of 2D materials with different structures and interesting properties, originated from the sp2 bonds in graphene and the nonplanar sp3 ones in phosphorene, respectively. On the other hand, the three-coordinate configuration of C or P atoms facilitates the formation of planar structures. Therefore, a logical extension is to explore whether it is possible to form stable carbon phosphide (PC) monolayers complementing the properties of graphene and phosphorene. Actually, several PC monolayers exhibiting metallic, semi-metallic, and direct/indirect band gap semiconducting characters, have been theoretically proposed.24,25 The appearance of many different structures can be attributed to the competition between sp2 and sp3 bonds. Subsequently, the predicted 1-PC phase has been experimentally confirmed through doping C atoms into phosphorene.26 Notably, a few-layer PC FET shows a high hole mobility, 1995 cm2 V−1 s−1, which is consistent with the theoretical calculations.24,26 Infrared phototransistors made by few-layer PC exhibit good responsivity and detectivity performance.27 Considering the electron-accepting ability between P and C atoms, the diverse P-C configurations, and the strong P-C bonds in their compounds, there is a high chance

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they could also form different 2D PxCy materials with outstanding properties. Having in mind the excellent conducting and stability properties of C materials, in this article we mainly focus on C-rich PCx (x = 1 - 6) compositions. We have performed an extensive structural search to find the most stable monolayer with the particle swarm optimization approximation.28 As expected, we have identified an unusual stoichiometry, a PC6 monolayer, with a buckled graphene-like structure, which shows a high thermodynamic stability with respect to the already known 1-PC monolayer. More interestingly, PC6 presents very interesting functional properties (e.g. direct band gap, remarkably high and anisotropic carrier mobility, and excellent optical properties), with promising applications in nanoelectronics and photovoltaic devices. 2. COMPUTATIONAL DETAILS An unbiased swarm-intelligence structural method, as implemented in the CALYPSO code,28,29 is employed to explore stable two-dimensional phosphorus carbides.24 Its effectiveness has been validated reproducing already known materials, including either elemental solids and binary/ternary compounds as well.30–32 Moreover, many of the new materials predicted with CALYPSO have been experimentally confirmed.33,34 Our structural search procedure is described in the supporting information. Notably, theoretical calculations play an important role in discovering new 2D materials and understanding the physical mechanism implied by experimental phenomena.19,35–40 Structural optimization and property calculations are performed within the density functional theory framework,41 as implemented in the Vienna ab initio simulation package (VASP),42 where the ion-electron interaction is implemented by the projector-augmented plane wave (PAW) approach.43 The electronic exchangecorrelation functional is treated using the generalized gradient approximation (GGA)44 in the form proposed by Perdew, Burke and Ernzerhof (PBE).45 The energy cutoff of the plane waves is set to 700 eV, with an energy precision of 10−6 eV. Atomic positions are fully relaxed until the force on each atom is less than 10−3 eV/Å. The supercell method is considered to simulate the monolayer, where a vacuum distance of ~20 Å is used to eliminate the interaction between adjacent layers. Considering that the GGA usually underestimates the band gaps, we adopt the Heyd−Scuseria−Ernzerhof (HSE06) hybrid functional46 to calculate the band structures and optical absorption coefficients. Dynamic stabilities and phonon dispersion curves are computed with the supercell approach as implemented in the Phonopy code.47 On the other hand, in the molecular dynamics (MD) simulations, the initial configuration in the supercell is annealed at different temperatures, each


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MD simulation in the NVT ensemble lasts for 10 ps with a time step of 1.0 fs, and the temperature is controlled by using the Nosé-Hoover method.48 3. RESULTS AND DISCUSSION After an extensive structure search, besides reproducing the already known 1-PC structure,24–26 we found a new PC6 monolayer stabilizing into a trigonal structure (space group P-3, 2 formula units, Figures. 1a and 1b). As can be seen in Figure. 1c, the basic building block is a P6C18 unit, in which a C6 ring locates at the center surrounded by another six edge-sharing PC5 rings, akin to the configuration of benzene. Interestingly, an alternate arrange of ethylene-like C2 units interconnected by two P atoms constitutes the outer edge ring of the P6C18 unit (Figure. 1c). On the other hand, each P is surrounded by three C atoms forming a PC3 unit, with the same geometrical configuration as the P4 units in black phosphorus. The average C-C bond length is 1.41 Å, almost the same as the sp2 C-C bond length in graphene (1.42 Å).49 The P-C bond length of 1.81 Å is also comparable to 1.80-1.83 Å in phosphorus carbides50 and 1.84 Å in 1-PC monolayer.25 The analysis of the electron localization function clearly shows that the bonds between nearest-neighbor C atoms or P and C atoms are covalent (Figures. 1d and 1f). Notably, there is a non-bonding lone electron pair around each P atom (Figure. 1g). Overall, the unique atomic arrangement described above, the bond features, and the presence of a lone electron pair in PC6, indicate that C atoms are in the sp2 configuration, as in graphene, and P atoms adopt a sp3 hybridization, in which one of the hybrid orbitals is filled with a lone electron pair, and the other three hybrid orbitals form covalent bonds with the neighboring C atoms. Actually, these bonding configurations satisfy the chemical octet rule on both C and P sites, inevitably enhancing its structural stability. The presence of sp3 hybridization in P atoms makes PC6 show a buckled honeycomb structure (Figure. 1b), with a thinness of 2.14 Å, and, therefore, it has a lower symmetry compared to graphene. On the other hand, the arrangement of P and C atoms in zigzag and armchair directions are clearly different (Figure. S1).

views of the isosurfaces plotted in (Figures. 2c and 2d)], which is in sharp contrast to graphene (Figure. S2), in which π electrons are fully delocalized and continuous.51 Therefore, the presence of lone electron pairs in P atoms and its unique arrangement restrain the formation of extended π-electron states.52 To confirm this, we have built a hypothetical PC6, in which all the atoms are arranged in a plane, breaking the sp3 hybridization of P. As expected, this hypothetical PC6 structure is metallic (Figure. S3). On the other hand, the charge density associated to the conduction band minimum (CBM) distributes along the whole monolayer. Again, the lone electron pair of P atoms is not connected with the charge densities of the other atoms (Figures. 2e and 2f). The partial density of states (PDOS) shows that valence bands present a strong hybridization between neighboring C or C-P atoms. Moreover, VBM mainly comes from the contributions of P 2pz and C 2pz orbitals (Figure. 2b).

Figure. 1. (a) Top and (b) side views of the predicted PC6 monolayer with P-3 symmetry. The unit cell is indicated by a black dashed line. (c) The basic building block (P6C18) in the PC6 monolayer. Electron localization function (ELF) maps of (d, f, and g) a PC6 monolayer along planes containing specified bonding atoms and (e) graphene. The chemical bonding in the C6 ring in PC6 is nearly the same as in graphene (d and e), and there appears a lone electron pair around the P atom (g).

In comparison with graphene, PC6 presents different structural properties and chemical bonds that might induce unexpected physical properties. PC6 monolayer is a direct gap semiconductor with a band gap of 0.84 eV at the M point (Figure. 2a), calculated with the HSE06 hybrid functional. To further explore the origin of the semiconducting character, we calculated the band decomposed charge density. The charge density of the valence band maximum (VBM) distributes on the outer edge ring of the basic building block (Figure. 2c). However, the charge density of P atoms, existing as lone electron pairs, disconnects the π electrons originated from C 2pz orbitals of ethylene-like C2 units [see the side ACS Paragon Plus Environment

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magnitude larger than the hole mobility (2.48×104 cm2 V−1 s−1). In other words, electron transport is facilitated along the armchair direction, while the zigzag direction favors the hole transport. Since the stiffness and effective mass are isotropic, the direction-dependent deformation potentials are mainly responsible for the anisotropic charge transport. Notably, both hole and electron mobility are much higher than that in phosphorene (~ 104 cm2V−1s−1)54 and comparable to graphene (3.2~3.5×105 cm2V−1s−1).5 Based on the analysis above, the high carrier mobility of PC6 can be attributed to the large in-plane stiffness, the small effective mass, and small deformation potential. Moreover, we also explore the effect of the biaxial strain on electronic properties of PC6. Interestingly, its directband gap character is still remained within compressive or tensile 5% (Figure. S4). However, the band gap becomes larger under compression, and the opposite when it is stretched. More interestingly, under compression PC6 shows a strong hole transport ability, while it favors the electron transport when stretched, indicating that conductivity can be effectively modulated with strain. Figure. 2. (a) Electronic band structure calculated at the HSE06 level for the PC6 monolayer. Horizontal dashed line represents the Fermi level. The high-symmetry points of , M, and K represent (0, 0, 0), (0, 1/2, 0), and (-1/3, 2/3, 0), respectively. (b) PDOS of C atoms in C6 rings and P atom in PC3 units. Top and side views of the band decomposed charge densities for (c, d) VBM, and (e, f) CBM. The carrier (electron or hole) mobility of 2D materials has a great effect on the performance of electronic devices. Here, we evaluate the charge transport of a PC6 monolayer within the effective mass approximation and the electron-acoustic phonon scattering mechanism.53 The resulting deformation-potential constant (EDP), 2D in-plane stiffness (C), effective mass (m*), carrier mobility (μ), and relaxation time (τ) are summarized in Table 1. The effective masses in PC6 are 0.22 m0 (0.17 m0) for holes and 0.22 m0 (0.16 m0) for electrons along the armchair (zigzag) direction, which are much smaller than the effective mass values of monolayer and fewlayer black phosphorene,54 and larger than that in graphene.1,55 Interestingly, the effective masses of PC6 are highly isotropic, which is consistent with the nearly symmetric energy band structure (Figure. S4a). Moreover, the in-plane stiffness values are also isotropic, and much larger than in phosphorene (28.94/101.60)54 and MoS2 (127.44/128.16).56 On the other hand, the deformation potentials (Table 1) show an obvious direction-dependent anisotropy, which can be understood by the different arrangement of P and C atoms along zigzag and armchair directions (Figure S1). The calculated electron mobility along the armchair direction is 2.94 × 105 cm2 V−1 s−1, which is an order of

PC6, with a direct band gap of 0.84 eV, presents an interesting potential application for visible-light solar harvesting/utilizing techniques or making narrow-gapsemiconductor devices. On the other hand, recent studies show that 2D materials with narrow band gaps (e.g. PC and AsP) become good candidates as infrared photodetectors.27,57 Thus, we have further characterized its optical performance by calculating the absorption coefficients using the GW approximation in conjunction with the Bethe-Salpeter equation (BSE).58 The absorption coefficients of graphene, phosphorene, PC, and MoS2 are also included for comparison. PC6 monolayer shows a remarkable high absorbance coefficient (105 cm-1) in a broad band (i.e. from 300 to 2000 nm), which is much larger than the absorption region of MoS2. Moreover, its absorption coefficients are isotropic in the two-dimensional plane, as observed in grapheme, but different from phosphorene or PC (anisotropic). When absorption wavelength is longer than 500 nm, the absorption coefficient of PC6 becomes larger than that of commercial intrinsic Si. Moreover, PC6 shows the highest absorption in the long wavelength region (>~1000 nm). Its broad absorption range and large absorbance coefficient makes PC6 a potential material for photovoltaic solar cells and optoelectronic devices.37,59,60 Table 1. Calculated deformation-potential constant (EDP), 2D in-plane stiffness (C), effective mass (m*), carrier mobility (μ), and relaxation time (τ) along the zigzag and armchair directions for a PC6 monolayer at 300 K.


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Carrier type

EDP (eV)

C (J m-2)

m*/m 0

μ (cm2V1s-1)

τ (ps)

Electron (armchair)

0.61

211.85

0.22

2.94×105

36.7 7

Hole (armchair)

2.07

211.85

0.22

2.48×104

3.10

Electron (zigzag)

6.94

213.86

0.16

3.16×103

0.29

Hole (zigzag)

0.92

213.86

0.17

1.64×105

15.8 6

Figure. 3. Calculated in-plane absorption coefficients of PC6 monolayers at the BSE level. The yellow background indicates the reference solar spectral irradiance (right y-axis, Air Mass 1.5, ASTM G17303).61 The material stability is another critical factor for practical applications. The thermodynamic stability in 2D materials correlates with their cohesive energy, and the calculated cohesive energy of a PC6 monolayer (6.98 eV/atom) is much higher than that of phosphorene (3.30 eV/atom)62 and comparable to that of graphene (7.91 eV/atom).63 Considering that the 1-PC monolayer can be synthetized through C doping into black phosphorus,26 we have calculated the relative phase stabilities of PC6 and 1-PC monolayers. It is found that PC6 monolayer does not decompose into 1-PC and carbon (Figure. S5). Moreover, the formation energy/atom of PC6 monolayer is much lower than that of 1-PC. These calculations indicate there is a strong possibility to synthesize PC6 monolayer by appropriate methods. Additionally, we have calculated the phonon dispersion curves of the PC6 monolayer and the absence of any imaginary mode ensures its dynamical stability

(Figure. S6). The phonon projected density of states shows that the high-frequency modes mainly come from vibrations of C atoms, while the low-frequency stretching modes are associated with the strong coupling between P and C atoms. Moreover, the highest optical frequency reaches 1529 cm−1, which is close to 1-PC (1450 cm−1)24 and b-PC (1510 cm−1),64 and comparable to the G mode of graphite.65 This mode corresponds to the stretching of C sp2 atoms, indicating the strong chemical bonds between them in the PC6 monolayer. On the other hand, in order to analyze its thermal stability, we have performed MD simulations at 1000 and 2000 K, using a 3 × 3 × 1 supercell with a time step of 1 fs. The snapshots of the resulting structures clearly indicate that the PC6 monolayer remains stable at these temperatures (Figure. S7). It is well known that the air instability of phosphorene, mainly due to its reaction with O2, greatly restricts the development of phosphorene for practical devices.66–68 Therefore, examining the stability of PC6 at ambient conditions becomes critical. In order to analyze the oxidation of PC6 we have calculated the energy barrier from physisorption to chemisorption of an O2 molecule on the surface of PC6 (see supporting information).19,69– 72 In general, the larger energy barrier, the higher is the stability. The calculated energy barrier (1.08 eV, Figure S8) is much higher than phosphorene (0.70 eV)70 and comparable to the air-stable 1-P3Cl2 (0.94 eV),69 indicating that PC6 might be chemically stable in the air at low temperatures. To further confirm this, we have carried out molecular dynamic simulations at 300 K for PC6 and O2 molecules within a 3 x 3 x 1 supercell. After 5 ps PC6 remains intact (Figure S9), and O2 molecules move away from the monolayer without dissociating into oxygen atoms. This unique stability of PC6 could be attributed to its high carbon content, as it is the case of phosphorus-doped graphene.73 Besides PC6, we find the other three metastable monolayers (i.e. PC2, PC3, and PC5, Figure. S10). However, the formation of energies of these three monolayers only slightly sit above the convex hull (Figure. S5), indicating they might be synthesized under certain conditions. On the other hand, they demonstrate intriguing structures and electronic properties. In more detail, PC2 consists of eight-membered ring C4P4 and C4P with the same configuration of pyrrol, which are connected via edge-sharing to form a 2D crystal. More interesting, PC2 shows the Dirac-type band dispersion at the Fermi level. For PC3, its basic building block is a C6P6 unit, in which a C6 ring locates at the center surrounded by another six P atoms, just like benzene molecule, C6H6. PC3 is an indirect-band semiconductor with a gap of 2.15 eV, originating from the lone electron pair of P atom isolating the π electrons of C6 ring (Figure. S10h). All the C atom in PC5 form the


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graphene-like nanoribbon, and P atoms, evenly distributes at the edge of the C nanoribbon. PC5 demonstrates a Dirac cone at the Fermi level siting between Γ and Y points. The presence of Dirac cone in PC2 and PC5 mainly comes from the contribution of C orbital (Figures. S10j and S10l). The presence of the interesting structures and electronic properties in P-C system inevitably stimulates the craze for exploring the 2D materials consisting of light main elements.

of Economy and Competitiveness (FIS2016-76617-P) and the Department of Education, Universities and Research of the Basque Government and the University of the Basque Country (IT756-13). The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1 (A).

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4. CONCLUSIONS In summary, we have applied first-principle swarmintelligence structural search calculations to predict a hitherto unknown buckled graphene-like semiconducting PC6 monolayer with a direct band gap of 0.84 eV. It has high carrier mobilities with anisotropic character, which can be effectively tuned with strain. PC6 presents a strong visible-light absorption and the band gap remains direct under compressive and tensile strains as large as 5%. The high cohesive energy and excellent thermal stability of the PC6 monolayer, resulting from its unique bonding arrangement (i.e C-C sp2 and P-C sp3 hybridization), provides a high possibility for its experimental synthesis. All these appealing properties make the PC6 monolayer a promising candidate for applications in electronic and photovoltaic devices.

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ASSOCIATED CONTENT Supporting Information Detailed description of the computational method and structural prediction, relative stability, phonon spectra, thermal stability, evolutions of the carrier mobility, and structural information of PC6 monolayer. Band structure of a hypothetical PC6 monolayer, and strained PC6 monolayer.

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AUTHOR INFORMATION

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Corresponding Author

*E-mail: [email protected] *E-mail: [email protected] ORCID Shoutao Zhang: 0000-0002-0971-8831 Guochun Yang: 0000-0003-3083-472X

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Author Contributions

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‡These authors contributed equally. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors acknowledge the funding supports from the Natural Science Foundation of China under No. 21873017, 21573037, 11704062, and 51732003, the Postdoctoral Science Foundation of China under grant 2013M541283, the Natural Science Foundation of Jilin Province (20150101042JC), and the Fundamental Research Funds for the Central Universities (2412017QD006). A.B. acknowledges financial support from the Spanish Ministry

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Two-Dimensional PC6 with Direct-Band Gap and Anisotropic Carrier

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