Nitrophosphorene: A 2D Semiconductor with Both Large Direct Gap

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Nitrophosphorene: A 2D Semiconductor with Both Large Direct Gap and Superior Mobility Lei Zhao, Wencai Yi, Jorge Botana, Feng Long Gu, and Maosheng Miao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09650 • Publication Date (Web): 04 Dec 2017 Downloaded from http://pubs.acs.org on December 6, 2017

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The Journal of Physical Chemistry

Nitrophosphorene: A 2D Semiconductor with Both Large Direct Gap and Superior Mobility Lei Zhao1,2, Wencai Yi2, Jorge Botana3,2, Fenglong Gu*1, and Maosheng Miao*2 1

Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education;

School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China. 2

Department of Chemistry and Biochemistry, California State University Northridge,

Northridge, CA 91330, USA. 3

Beijing Computational Science Research Center, Haidian District, Beijing 100193,

China.

Abstract: A new two-dimensional phosphorus nitride monolayer (P21/c-PN) with distinct structural and electronic properties is predicted based on first-principle calculations. Unlike pristine single-atom group V monolayers such as nitrogene, phosphorene, arsenene, and antimonene, P21/c-PN has an intrinsic direct band gap of 2.77 eV that is very robust against the strains. Strikingly, P21/c-PN shows excellent anisotropic carrier mobility up to 290829.81 cm2 V-1s-1 along a direction, which is about 18 times of that in monolayer black phosphorus. This put P21/c-PN way above the general relation that carrier mobility is inversely proportional to bandgap, making it a very unique two-dimensional material for nanoelectronics devices.

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1. Introduction The discovery and synthesis of graphene has ignited increasing interest of two-dimensional (2D) layered crystal materials.1-2 In recent years, much effort has focused on single atom-thin sheets formed by group V atoms such as phosphorene,3 arsenene,4 antimonene,5 and bismuthene.6 However, many monolayers are indirect band-gap semiconductors or insulators (see Table S1). Some of them need an in-plane strain to tune the band gap form indirect to direct. For example, free-standing arsenene needs a biaxial strain (1%) to be converted into a direct band-gap semiconductor.7 The direct gap materials in this family usually have a small gap, such as black phosphorus3(1.0 eV), b-Bi (0.32 eV) and w-Bi (0.03 eV).8 There is an intensive need of direct-gap group V monolayers with large band gaps, especially larger than 2.0 eV, in order to develop 2D semiconductor based optoelectronic devices, such as blue- and ultraviolet-light emitting diodes, photodetectors and phagosensors.9 Another challenging problem of monolayer semiconductor is the carrier mobility. Generally, the carrier mobility is inversely proportional to band-gap. Therefore, it is hard to find a material that has both a large gap and high carrier mobility. Black phosphorus is in layered structure, and the corresponding monolayer and few-layer structure (phosphorene), were fabricated recently.10-11 Compared with gapless graphene and wide-gap boron nitride,12-13 phosphorene possesses finite direct band gap in the range of 0.6−1.5 eV depends on the number of layers.14-17 Moreover, phosphorene possesses high carrier mobility and high on/off ratio when applied as a field-effect transistor at room temperature. However, the band-gap of phosphorene is below 2.0 eV and is sensitive to the strain that can trigger a direct-to-indirect transition.3, 18 These properties hinder the application in the field of electronics and optoelectronics. In the past few years, several monolayer phosphorene allotropes with either honeycomb lattice19 or non-honeycomb structures,20 have been predicted from first-principles calculations. However, the band-gaps of these materials, either indirect or direct, are all smaller than 2.0 eV, which is not suitable for ultraviolet–blue photoresponse.


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The monolayers consist of lighter elements usually have larger band gap. While monolayer nitrogen is not stable and will decompose into N2 molecules, monolayer phosphorous nitride (PN) might be attainable because of the strong N-P bond. Several monolayer PN, α-, β-, and γ-, based on the structures of black and blue phosphorene had been proposed,21 all of them have an indirect band gap, 2.689, 3.282 and 2.532 eV, respectively. However, the monolayer PN may not take the structures of monolayer phosphorous, and the electronic properties may also be very different while the structure changes. In this paper, we employ the automatic structure search method to study the possible stable structures of monolayer PN. We find a structure with lower energy than PN layer conceived from the structures of black and blue phosphorous. Importantly, this PN monolayer is a direct band gap semiconductor with a band gap of 2.77 eV, and the feature of direct band gap can sustain large strains. More strikingly, the carrier mobility of this 2D phosphorus nitride sheets goes up to 290829.81 cm2 V-1s-1 along a direction, almost 18 times to that of single-layered black phosphorene (15518.18 cm2 V-1s-1). 2. Computational Methods Structural search simulations for PN system are performed using the CALYPSO code22 with the local PSO minimization schemes, and the unit cells of P4N4, P6N6, P8N8 totally up to 1500 structures are considered in our calculations, all the initial structures are with the thickness of about 2.0 Å and allowed to relax in the perpendicular direction. Local structural relaxations are performed by density functional theory as implemented in the Vienna ab initio simulation package (VASP code).23-24 The electron-electron interaction was treated with a generalized gradient approximation (GGA) formulated as Perdew-Burke-Ernzerh (PBE) functional.25 The interaction

between

valence

electrons

and

core

is

described

by

projector-augmented-wave (PAW) potentials.26-27 The atomic positions and lattice constants were optimized using the conjugate gradients (CG) scheme until the force components on each atom were less than 0.01 eV/Å, the self-consistent field calculations were stopped when energy smaller than 1×10-8 eV/atom. Electronic wave



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functions are expanded with plane waves up to a kinetic-energy cutoff of 500 eV, and a vacuum region larger than 16 Å was used to avoid interactions between adjacent atom layers. Brillouin zone (BZ) integrations is performed using a Monkhorst-Pack28 k-point mesh of 12 × 13 × 1. The Heyd–Scuseria–Ernzerhof (HSE06) hybrid exchange–correlation functional29-30 was also used to correct the band structure. Phono spectrum was calculated to examine dynamical stability, with a 3×4 supercell using the PHONOPY package.31 The canonical ensemble (NVT) was implemented in molecular dynamics simulations with a large 3×4 supercell containing about 96 atoms to check the thermal stability. 3. Results and Discussions 3.1 Structures and stabilities Nitrogen and phosphorus atoms both favor the formation of three-coordinated structures and most of their allotropes are derivative from well-known structures. For example, the structures of α-PN and β-PN are variations of the structure of black phosphorene. Using automatic structure search program, we found a new allotropic form of PN monolayer, that has a lower energy than all previously known structures. This new phase has a P21/c symmetry, so we will refer to it as P21/c-PN. The structure search is performed several times, which always found that P21/c-PN is the most stable structure of the PN monolayer allotropes. The optimized structure of P21/c-PN is shown in Fig.1a. The resulting PN monolayer material consists of square and octagonal rings. There are four nitrogen atoms and four phosphorus atoms in the rectangular primitive cell and the optimized lattice constants are a = 5.11 Å and b = 4.72 Å. Due to the different local environments of N and P atoms, there are three non-equivalent P-N bond lengths in P21/c-PN, a1 = 1.696 Å, a2 = 1.752 Å and a3 = 1.783 Å. This configuration is not planar and has a thickness of 1.98 Å, which is resulted from the fact that the P atoms prefer to form tetrahedrons with the other three neighboring N. In the PN monolayer, the N and P atoms are sp3- hybridized, in which one of the hybrid orbitals is filled with lone pair electrons and the other three orbitals form covalent bonds with neighboring atoms that adopt a tetrahedral geometry. Consequently, the atoms are


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triply coordinated with one inter-unit bond and two intra-unit bond. Along a direction N-P bonds play a leading role and arranged alternately to form a ladder shaped chains. Along b direction N atoms form zigzag chains with P atoms lined up on both sides9. The side view of the PN shows a ridge-like configuration that is, to some extent, analogous to that of α- and δ-phosphorene.32

Fig. 1. (a) Top and side view of the optimized structure of orthorhombic buckled P21/c-PN monolayer with four N atoms (blue ball) and four P atoms (pink ball) in per primitive cell; (b) the phonon spectra of P21/c-PN. In order to test the stability of P21/c-PN, the formation energy (Ef) of the P21/c-PN monolayer formed from bulk P3N533-34 and black phosphorene monolayer was calculated. P3N5 + 2P → 5PN

5 ∗

2 ∗

5∗2

where ,

and are the energies of the P21/c-PN monolayer, bulk P3N5 and phosphorene monolayer, respectively. According to this definition, the formation energy for P21/c-PN is calculated to be 0.094 eV/atom, which indicates the stability of P21/c-PN is comparable with P3N5 and phosphorene. Furthermore, we found that while the monolayer P21/c-PN stacked to form a bulk structure, the energy will be lowered for about 0.130 eV. This energy is very similar to the stacking energy of black phosphorous. As a matter of fact, if the bulk P21/c-PN and bulk black phosphorous are used in the above reaction, the corresponding energy becomes 0.092



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eV/atom, which is very closed to that of the monolayers. These calculations indicate that monolayer P21/c-PN might be attained by direct fabrication or by exfoliating the corresponding bulk materials. Considering the successful synthesis of graphene, boron monolayer and silicene on metal surfaces,35-37 we also performed simulations of P21/c-PN growing on Ag (110) surface (Fig. S1). For comparison, similar calculations are performed for P on the same surface. The lattice mismatch of the P21/c-PN is controlled within 1% by matching different size of in-plane unit cells. The energies of P21/c-PN is obtained by subtracting the energy of the Ag slab from the total energy of P21/c-PN /Ag (110). This results in a large reduction of the formation energy, = 0.057 eV/atom. Our calculations reveal that the energy of P21/c-PN is smaller with a substrate of Ag than on a free-standing form, indicating a strong possibility of synthesis for this material on metal surfaces. To confirm the dynamic stability of monolayer P21/c-PN, the phonon band structure along high-symmetry directions was calculated. As shown in Fig.1b, no imaginary frequencies were found, ensuring its dynamic stability. The highest optical frequency is up to 1041 cm-1at Γ point, which is higher than those of nitrogene (∼1000 cm−1),38 black phosphorene (∼450 cm−1),39 and MoS2 (∼500 cm−1),40 indicating the strong bonding nature of P21/c-PN. Even if all acoustic branches with positive frequencies ensure stability, the material can still become unstable at a finite temperature. In order to further examine the thermal stability of the predicted structure, we performed ab initio molecular dynamics simulations (AIMD). The total simulation time is 3 ps with a time step of 1.5 fs. Snapshots of the P21/c-PN sheet at temperatures of 300, 800 and 1200 K exhibit that the structure neither experiences serious disruption nor dissociation up to 1200 K. The final configurations for each molecular dynamic simulation are shown in Fig. S2. These MD calculations confirm that the P21/c-PN structure is stable at high temperature. 3.2 Electronic structures The band structure of the P21/c-PN monolayer is plotted in Fig. 2a. The results show that P21/c-PN is a direct band gap semiconductor with the energy gap of 1.69 eV at Г point at PBE level. However, GGA underestimates the band gap of


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semiconducting materials, so we also calculated the electronic structure using the hybrid functional HSE06. After this revision, the direct gap value increased to 2.77 eV. Other reported 2-dimensilnal semiconductors with direct band gaps, like α-, δ- and εphosphorene,3, 20, 32 and b- and w- Bismuthene,8 have band gaps smaller than 2.0 eV (Table S1), which restricts their potential applications in blue- and ultraviolet-light emitting devices. In comparison with them, P21/c-PN appears to be a promising candidate for applications in wide-gap semiconductor devices. The band-decomposed charge density of the valence band maximum (VBM) state shows major distribution on p orbitals of N atoms and smaller distribution on P atoms (Fig. 2b). On the other hand, the conduction band minimum (CBM) states distribute mainly on the p orbitals of P atoms. The partial density of states (PDOS) for the monolayer P21/c-PN is shown in Fig. 2c. The result indicates that the VBM of P21/c-PN main contribution comes from the pz orbitals of the N and P atoms and the s orbitals of the P atoms. The charge transfer between N and P atoms can be clearly verified by the charge density difference as shown in Fig. 2d. The results show that electrons transfer from P to N and a mushroom-shaped electron cloud is generated around P due to this redistribution. Bader charge analysis41-42 also reveals there are 1.93e transferred from P to N, indicating strong interaction between P and N atoms.



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Fig. 2. (a) Computed DFT-PBE (black line) and HSE06 (blue line) band structure of P21/c-PN; the Brillouin zone is rectangular along Г (0, 0, 0) →X (0.5, 0, 0) →S (0.5, 0.5, 0) →Y (0, 0.5, 0) → Г (0, 0, 0) line. The Fermi level is set to zero; (b) The band decomposed charge densities of the highest occupied orbital and lowest unoccupied orbital at the Γ-point for the monolayer P21/c-PN, the isosurfaces is 0.015 e/Å3; (c) Partial density of states of P21/c-PN; (d) Charge density difference of P21/c-PN. The yellow and blue colors stand for charge increase and decrease region corresponding to isolated atoms, respectively. The isosurface is 0.02 e/Å. 3.3 Carrier mobility and anisotropy The carrier mobility is a property that directly related to the electronic conductivity of 2D materials. Based on the effective mass approximation and the electron-acoustic phonon scattering mechanism,43 the expression of carrier mobility of 2D materials can be given by a simplified model:

μ

ћ

∗

(1)

∗ is the effective mass in the transport direction (i = h for holes, i = e for electrons) based on the effective mass approximation ∗ ћ2 ⁄ ! #$ , and md is the


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average effective mass obtained by % &'∗ (∗ . The term E1 stands for the deformation potential constant of the VBM for holes or CBM for electrons, along the transport direction. It corresponds to the slope of a linear fitting of VBM or CBM as a function of the applied strain in the a and b directions (Fig. S4). These quantities represent the strength of the electron-phonon scattering. All the energies of VBM and CBM are obtained using the vacuum energy correction. l0 is the lattice constant in the transport direction and Δl is the deformation of l0. Here, values of the ration ∆*,* + ranging from -1.0% to 1.0% are used to quantify the deformation. The elastic modulus C2d in the equation is derived from

#.-

/

%

0∆1,1 2 -

, where E is the total energy

and S0 is the lattice area at equilibrium for a 2D system. The fitting process is shown in Fig. S5. The temperature is set to 300K. Table 1. Calculated Effective Mass (m*), Deformation Potential Constant (E1), 2D Elastic Modulus (C2d), and Mobility (µ) for Electron (e) and Holes (h) along a and b directions. Direction a

b

m*/m0

E1(eV)

C2d (Nm-1)

µ (cm2 V-1s-1)

e

0.57

0.117

72.08

290829.81

h

2.94

1.053

72.08

205.31

e

0.80

0.997

29.98

1179.37

h

1.79

1.535

29.98

65.87

Carrier type

The obtained C2d, E1, and m*, the carrier mobility calculated by equation (1) and related data are summarized in Table 1. The effective masses in P21/c-PN are 2.94 m0 (1.79 m0) for holes and 0.57 m0 (0.80 m0) for electrons taken from HSE06 along the a (b) direction, m0 is the effective mass of free electrons. All these results are comparable with the effective mass values of monolayer and few layers black phosphorene44. The VBM and the CBM values as functions of the strains along a and b are shown in Fig. 3b. The total energy changes after a specific strain are shown in Fig. 3c. The results clearly show highly anisotropic properties along a and b directions.



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The electron mobility for the P21/c-PN monolayer at 300 K is 290829.81 and 1179.37 cm2 V-1s-1 along the a and b directions, respectively. The corresponding hole mobility are 205.31 cm2 V-1s-1 (a direction) and 65.87 cm2 V-1s-1 (b direction). The carrier mobility along a direction is 18 times larger than that of single-layer black phosphorene (15518.18 cm2 V-1s-1), and the hole mobility along a direction is comparable with that of single-layer MoS2 (~200 cm2 V-1s-1).45 Concerning directional anisotropy, hole mobility for direction a is 3.0 times larger than b. Even more notably, the electron mobility along a is ~246 times larger than that along b, making a the direction of higher electron conductivity. This extraordinarily large value for monolayer P21/c-PN is a consequence of the extremely small deformation potential, E1a = 0.117 eV, and relatively light carriers (0.57 m0). The value of E1a for electrons in the monolayer is an order of magnitude smaller than typical values of E1, for example 2.72±0.02 eV for single-layer black phosphorus,44 5.14 eV for graphene,46 5.9 eV for MoS2,47 and 3.66 eV for h-BN.48 This rare characteristic should be valuable in applications such as the separation of electrons and holes.

Fig. 3 (a) Schematic of the strain along a and b direction; (b) relationship between


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energy shift of the band edge position and the dilation ∆*,* , the Fermi level is set to + zero. (c) total energy shift E-E0 on per unit area as a function of lattice deformation

∆*, along a and b directions in P21/c-PN. Solid lines are the parabolic fittings, from *+ which we can get the elastic constant; (d) band gaps predicted by the HSE06 method for compressive and tensile strains. As already demonstrated by several research groups, strain has a remarkable effect in modifying the electronic properties of 2D monolayers. It is shown that many 2D layered materials such as graphene, MoS2 and phosphorene, can sustain strains larger than 10%. Therefore, it is interesting to explore the effect of in-plane strain on the band structures of P21/c-PN. While directly applying in-plane strains on P21/c-PN monolayer, we found that P21/c-PN show no obstructive structural change under a tensile strain up to 24% in a direction and 32% in b direction. However, such large strains usually go beyond the elastic limits of the 2D materials. As a matter of fact, P21/c-PN monolayer starts to show imaginary phonon frequencies while the strain (tensile or compressive) is larger than 15%. We therefore constrained our studies within 15% strains. As shown in Fig. 3c, the total energy versus strains in a and b directions fit very well to parabolic functions. The energies increase faster while the strain is along a direction, indicating the material is stiffer in this direction. Fig. 3d shows how the energy gap changes under in-plane strains. It shows very different behavior for strains along a and b directions. For the studied strain range, the energy gap decreases with increasing b value almost linearly. In contrast, the gap decreases for smaller a (compressive strain) and start to increase at a compressive strain of -3%. Therefore, it is more effective to tune the gap by applying strains along b direction. The band gap changes from 3.034 eV to 2.470 eV while the strain in b direction changes from -10% to 10%. In contrast, the band gap changes from 2.837 eV to 2.985 eV while the strain in a direction changes from -10% to 10%. It is interesting that P21/c-PN remains a direct gap locating at Γ point throughout the above strain range. In order to understand the trend of band gap under strains, we calculated the band edge states under various strains along a and b directions, including the valence



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band maximum (VBM) and the conduction band minimum (CBM). Both VBM and CBM are found to locate at Γ point with and without strain. As shown in Fig. S6, the CBM shows a parabolic function with respect to the strain along a direction. In contrast, it decreases monotonically with the strain along b direction. VBM shows monotonic change with strains along both a and b directions. The band gap changes are the overall effect of both CBM and VBM. Furthermore, we examined the N-P bond lengths as functions of the applied strains. As shown in Fig. S7, there are in total three different N-P bond lengths, notating as d1, d2 and d3. As shown in Fig. 3b, all three bond lengths increases monotonically with increasing strain along b direction. The increasing N-P bond lengths weaken the coupling of N and P orbitals. Correspondingly, the bonding states (in valence bands) increase in energy whereas the anti-bonding states decrease in energy, which is in consistent to the change of VBM and CBM under strains along b direction. In contrast, d3 shows a parabolic change with increasing strain along a direction. This may explain the parabolic change of the CBM under the same strain. Because d3 is the shortest length, its change may have largest effect on the CBM. On the other hand, the fast increase of d2 may cause the monotonic decrease of VBM.The relation between the interatomic distances and the band edges are not always straightforward.

3.4 Multi-layer structures As absorbed in many other 2D semiconductors, van der Waals (vdW) interactions allow layers of P21/c-PN to be stacked. To investigate the interlayer interaction between two P21/c-PN layers, the optB88-vdW functional was used to take into the account van der Waals interactions,49-50 which leads to four different stacking configurations of bilayer P21/c-PN (shown in Fig. 4a–d). Keeping the upper layer fixed, the lower layer in the AA stacking (a) can be viewed as shifting along the basis lattice vector in a direction by half of a primitive cell, and the same with b direction in the AB stacking (b). Different from those two bilayer structures above, both the upper and lower layer in the AC stacking (c) shifting by half of a primitive cell with the same direction in a and b direction, and with opposite direction along basis lattice


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vector in the AD stacking (d). The optimized interlayer distance differs slightly for different stacking structures, which varies from 2.75 Å in the AC stacking to 2.82 Å in the AB-stacking. The AA-stacking bilayer is the energetically most stable configuration with the lowest total energy: it is 21.89, 21.66 and 22.16 meV lower than the AB-, AC- and AD-stacking, respectively. Regarding of the stacking pattern, the four different stacking configurations of P21/c-PN bilayers have almost similar band gaps from 0.93 to 1.11 eV, and still maintain the direct-gap semiconducting feature.

Fig. 4. Side views of configurations and band structures of bilayer P21/c-PN for (a) AA-, (b) AB-, (c) AC-, and (d) AD- stacking patterns, respectively. The corresponding band structures get from PBE calculations. The optimal interlayer spacing of the bilayer P21/c-PN for the AA stacking pattern is 2.79 Å (Fig. S8), and the total energy increases very rapidly for decreasing distances, this indicates no chemical bonds between two stacking layers. Increasing the stacking to 3- and 4- layers, we found that the energy of 2-, 3- and 4- layer are 66.7, 90.2 and 78.3 meV lower than that of monolayer. The energy difference between the monolayer and the bulk P21/c-PN is small enough to maintain stable either as freestanding single layer or fabricated on a substrate. The weak interlayer interaction indicates that P21/c-PN can be exfoliated into monolayers for potential electronic applications. As shown in Fig.S9, the corresponding band gap of 2-, 3- and 4- layer are 1.89, 1.52 and 1.36 eV (HSE06 level), representing a decreasing trend with the



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increasing layers, and the feature of direct band gap maintained. The reason for decreasing band gap is caused by the quantum confinement effect, as described in phosphorene and Sb (111) nanofilms.51-52

4. Conclusion In this work, we predicted a new 2D phosphorus nitride allotrope semiconductor P21/c-PN, that possesses both a large direct gap (2.77 eV) as well as superior carrier mobility. The energy of this allotrope is slightly above the convex hull between black phosphorous and phosphorous nitride (P3N5) and is 46.4 meV/PN lower than the most stable phosphorus nitride allotropes in previous reports. The AIMD simulations and phonon calculations verify its thermal and dynamic stability. P21/c-PN remains as a direct gap semiconductor under compressive and tensile strains as large as 10%. The intrinsic carrier mobility is calculated to be significantly larger than that of single-layered black phosphorene, and electric transport also show high anisotropy. All these results render P21/c-PN a very promising candidate material for applications in nanoelectronics and optoelectronics devices.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (M.S.M) *E-mail: [email protected] (F.L.G)

Author Contributions L.Z. and Wc.Y. contributed equally to this work.

Notes The authors declare no competing financial interest.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant 21673085). The authors are grateful to the referees for their valuable comments, which significantly improved the manuscript. Part of the calculations are performed on NSF-funded XSEDE resources (TGDMR130005) especially on the Stampede cluster run by Texas Advanced Computing Center.


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ASSOCIATED CONTENT Supporting Information Band gap of groupⅤand NP monolayers; simulations of P21/c-PN growing on Ag (110) surface; molecular dynamics simulations; relation of carrier mobility and band gap of two-dimensional materials; fitting progress of deformation potential and elastic modulus; P-N bond lengths change with dilation; the relationship between the total energy and the distance in bilayer; band structures of 2-,3- and 4- layers P21/c-PN.

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Sb (111) Nanofilm: The Interplay between Quantum Confinement and Surface Effect. Phys. Rev. B. 2012, 85, 201410.

TOC Graphic

A new two-dimensional phosphorus nitride monolayer (P21/c-PN) with direct band gap and superior mobility is predicted based on first-principle calculations and automatic structure search method.


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Nitrophosphorene: A 2D Semiconductor with Both Large Direct Gap

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