Structural, electrical and optical properties of halogen doped phosphorene based on density functional theory

Journal of Alloys and Compounds 812 (2020) 152125

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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom

Structural, electrical and optical properties of halogen doped phosphorene based on density functional theory Kaiwen Pu a, b, Xianying Dai a, b, *, Difan Jia a, b, Wenluo Tao a, b, Fang Liu a, b, Xiaodong Zhang a, b, Jianjun Song a, b, Tianlong Zhao a, b, Yue Hao a, b a b

School of Microelectronics, Xidian University, Xi'an, 710071, China State Key Discipline Laboratory of Wide Bandgap Semiconductor Technologies, Xidian University, Xi'an, 710071, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 May 2019 Received in revised form 31 August 2019 Accepted 1 September 2019 Available online 2 September 2019

The structural, electrical and optical properties of four halogen elements F, Cl, Br, I doped phosphorene (X-phosphorene) were investigated by applying first principle calculations based on density functional theory. X-phosphorene have different bonding characters based on Mulliken population and differential charge analysis. The ionization energies of halogen atoms in X-phosphorene shown that F, Cl, Br are ptype dopants while I is n-type. In terms of the bandgap type, F-phosphorene and I-phosphorene are indirect, while Cl-phosphorene and Br-phosphorene are direct, besides, it is worth to note that Clphosphorene and I-phosphorene are promising spin-gapless semiconductors. All X-phosphorene show the anisotropic transport property after calculating its carrier effective masses based on obtained E-k relationship. The absorption abilities of X-phosphorene are increased in UV-A and UV-B regions, as well as in visible and infrared regions over against the intrinsic condition. © 2019 Elsevier B.V. All rights reserved.

Keywords: Phosphorene Density functional theory Doping Halogen elements

1. Introduction The first two dimensional material, known as graphene, was fabricated by Geim in 2004 [1] with ultra-high mobility at room temperature. Since then, several kinds of two dimensional materials with novel structures and excellent properties are found by experiments or theoretical calculations successively, such as transition metal dichalcogenides (TMDs) [2], covalent organic frameworks (COFs) [3], CrBr3 [4], silicene [5] et al., which have favorable application foreground in many fields. However, limited by the Dirac cone band structure at G point of Brillouin zone, intrinsic graphene-based devices cannot achieve effective channel control by applying voltage bias on gate electrode, which is pivotal to microelectronic devices. As another potential candidate with direct bandgap, MoS2 has lower carrier mobility due to the large scattering effect of heavier Mo atoms, limits its applications in high speed devices. So that the two dimensional material with moderate bandgap and high carrier mobility is urgently needed in microelectronic and optoelectronic devices.

* Corresponding author. School of Microelectronics, Xidian University, Xi'an, 710071, China. E-mail address: [email protected] (X. Dai). https://doi.org/10.1016/j.jallcom.2019.152125 0925-8388/© 2019 Elsevier B.V. All rights reserved.

In 2014, p-type field effect transistor with undoped ultra-thin black phosphorus as the channel material was fabricated by Li [6]. They revealed that the mobility can reach 1000 cm2V
1s
1 with phosphorus thickness of 10 nm at room temperature, and on/off ratio was close to that of MoS2 FET. Follow-up studies have shown that single layer black phosphorus, so-called phosphorene, has direct bandgap of 1.5 eV, which can be modulated by altering the number of layers [7,8]. With puckered hexagonal structure, phosphorene shows strong anisotropic feature on electrical, mechanical and optical properties, thus ensured its bright application prospect in semiconductor devices and circuits [9,10], photodetectors [11,12] and so on [13e16]. Nowadays, there are several ubiquitous modulation means in materials research, e.g., doping [17e19], surface decoration [20e22], construct heterosturctures [23e25], all these methods will induce fresh characteristics to the intrinsic systems. As a kind of widely used salt-formation elements, halogen elements F, Cl, Br and I are facile to acquire and utilize, former reports have proven the attractive application potential of halogen doped graphene in both experiments [26,27] and calculations [28,29]. However, to our knowledge, halogen doped phosphorene have not been systemically investigated up to now. In this paper, the structural, electrical and optical properties of halogen atoms doped phosphorene are studied in detail. For convenience, we will use X-phosphorene

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K. Pu et al. / Journal of Alloys and Compounds 812 (2020) 152125

instead of halogen doped phosphorene in subsequent sections. 2. Methods All the calculations implemented in this paper were performed by using the Cambridge Serial Total Energy Package (CASTEP) code based on density functional theory [30]. The generalized gradient approximation (GGA) exchange-correlation functional putted forward by Perdew, Burke and Ernzerhof (PBE) [31] was used. DFT-D2 correction proposed by Grimme [32] was used to deal with the van der Waals interactions in the doping system. The interactions between outer electrons and inner ion cores were described by OTFG ultrasoft pseudo-potential, where the atom configuration of P is [Ne]3s23p3, that means the electrons in 3s and 3p orbitals were treated as valence electrons, for halogen elements F, Cl, Br, I, the atom configurations are [He]2s22p5, [Ne]3s23p5, [Ar]4s24p5, [Kr] 5s25p5, respectively, and the electrons localized at outer s and p orbitals were considered as valence electrons. To model the monolayer phosphorene, a rectangular 4  3  1 supercell with 48 phosphorus atoms was constructed, then the P atom on X site was substituted by a halogen atom, hence the doping concentration was nearly 2.08%, as shown in Fig. 1. The periodic boundary conditions were applied along x and y directions, while a 20 Å vacuum slab was established along z direction to prevent interference between neighboring layers. The cut-off energy and Monkhorst-Pack k-point [33] were defined by convergence tests with the value of 450 eV and 5  5  1, respectively. Before properties calculations, all slab models were fully relaxed using Broyden-Fletcher-Goldfarb-Shanno (BFGS) method [34]. The energy, force, stress and displacement tolerances were 10
5 eV/atom, 0.03 eV/Å, 0.03 GPa, 0.001 Å, respectively. Besides, spin-orbitalcoupling effect was also take into account during properties calculations. The lattice parameters of intrinsic phosphorene (a ¼ 3.311 Å, b ¼ 4.589 Å) are well matched with previous researches [35e37], proved the reliability of our parameter settings. The intrinsic direct bandgap value acquired by GGA-PBE method is 0.89 eV, almost half

smaller than the experiment result (1.73 eV) [8], therefore the HSE06 functional was employed as a comparison, its result (1.53 eV) agrees well with experiment, and related band structures are shown in Fig. S1 (see supplementary materials). However, due to the trade-offs between computational cost and accuracy, all calculations in this paper were performed by widely accepted GGAPBE method unless special annotation. The binding energy (Eb) of the halogen atom can be calculated by


Eb ¼ EX
P
EV
EX2 2:

(1)

where EX-P, EV, EX2 are the total energy of the X-phosphorene, single-vacancy phosphorene and isolated halogen molecule, respectively. Negative Eb indicates the dopant is easier to bonding with phosphorene, thus the structure is more stable. As one of the most important parameters to determine the doping properties, the ionization energy (IE) is the energy to excite free electrons or holes from dopant bands to conductive bands or valence bands, respectively. Dopants which have lower IEs can provide desired free carrier densities, on the contrary, dopants with higher IEs usually act as the nonradiative combination centers or carrier traps, which have negative effects on transport and optical properties of devices, so that it is valuable to determine the IEs of halogen elements in X-phosphorene. For charged two dimensional materials, the process of energy convergence is slower due to unevenly charge distributions, to solve this problem, several effective solutions were proposed [38,39]. In this paper, we adopt the asymptotic form offered by Wang [38] to calculate the IEs, the formula is given as follows:

a

b

IEðS; Lz Þ ¼ IE0 þ pffiffiffi þ Lz : S S

(2)

where a is the defect-specific Madelung constant, which relies primarily on the geometry of systems, for each system, we can calculate it only once. b is the fitting parameter, and S is the surface area of two dimensional slabs, Lz is the vertical length of the system including vacuum slab. IE0 is the converged IE value, which can be rewritten as [40]:

IE0 ¼ ε0 þ Erelax ¼ Dε þ U0 þ Erelax :

(3)

where Dε ¼ εCBM-εd indicates the dopant eigenenergy between the dopant band and CBM at the neutral state, U0 gives the energy difference of the neutral state and the charge state with the structure fixed, and Erelax describes the energy gain due to the geometry optimization at the charge state. 3. Results and discussion 3.1. Crystal structure of X-phosphorene Intrinsic phosphorene owns a puckered hexagonal ring

Table 1 Lattice parameters, bond lengths, binding energies and charge transfer amount of optimized X-phosphorene. Positive (Negative) Q indicates electrons transfer amount from phosphorene to dopant (dopant to phosphorene).

Fig. 1. Schematic illustration of intrinsic and doped phosphorene. Purple and cyan atoms are indicate phosphorus and doped atom, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

System

a/Å

b/Å

h/Å

dX-P1/Å

dX-P2/Å

Eb/eV

Q/e

Intrinsic F-doped Cl-doped Br-doped I-doped

13.25 13.17 13.22 13.29 13.27

13.77 13.82 13.88 13.82 13.63

2.11 1.22 1.30 1.91 3.09

2.26 1.66 2.16 2.83 3.62

2.23 3.28 2.86 2.52 2.70

e
3.90
1.96
1.52
1.63

e 0.57 0.27 0.04
0.07

K. Pu et al. / Journal of Alloys and Compounds 812 (2020) 152125

structure because of sp3 hybridization among P atoms. Table 1 lists the lattice constants, bond lengths, binding energies and charge transfer amount of pure and X-phosphorene. As we can conclude from this table, several bond lengths correlative with dopants are notably changed, indicates the equilibrium structure of phosphorene are broken by induced halogen atoms, which can attribute to the difference of atomic radius. Related atom radius is F < Cl < P < Br < I with the increase of its atomic number, so that the height of dopant over lower P sub-layer h and atoms distance dX-P1 are increase gradually according to the radius rule mentioned above. The bonding types in X-phosphorene were also studied. For F-/ Cl-phosphorene, F/Cl atom located between the lower and upper sub-layer, the distance with P2 atom labelled as dX-P2 is 3.28 Å/ 2.86 Å, basically the same as dX-P3, which is far longer than undoped condition (2.23 Å). Such a long distance is very difficult for charge transfer and redistribution between atoms, which are the fundamental characters of the chemical bonds formation. From our charge density difference results shown in Fig. 2 (a) (b), there is no obvious charge transfer or redistribution between F/Cl atom and P2/ P3 atom, indicates there is no bond formation between them. On the contrary, the values of dF-P1 and dCl-P1 are 1.66 Å and 2.16 Å, respectively, almost equal to the sum of their atom covalent radii, 1.75 Å (FeP) and 2.10 Å (CleP) [41]. Furthermore, charge transfer from phosphorene to F can be clearly observed in Fig. 2 (a), and the

3

electronegativity difference led to a considerable transfer amount about 0.57 e, implies ionic bond formation between them. Besides, charge accumulation occurs between Cl and P1 atoms may lead to covalent bond behavior. To clarify the bonding type, we performed Mulliken population analysis [42], and the bond population of CleP1 is 0.14, indicates CleP1 is a covalent bond. The bonding situations in Br-phosphorene and I-phosphorene are very different from F-/Cl-phosphorene. Br atom is nearly lies in the plane of upper sub-layer, while I atom is remarkably higher, which bring about relatively larger dX-P1, 2.83 Å/3.62 Å for BreP1/ IeP1, far outweigh the sum of atom covalent radii, 2.25 Å/2.44 Å. Moreover, there are no significant charge transfer expressed in Fig. 2 (c) (d), which imply no bond formation between Br/I and P1 atom. However, the distance between Br/I atom and P2/P3 atom is smaller than that in F/Cl-phosphorene, the dX-P2 is 2.52 Å/2.70 Å for BreP2/IeP2, only slightly larger than the sum of their covalent radii. In addition, palpable charge transfer and accumulation between Br/ I and P2/P3 can be observed in Fig. 2 (c) (d). The bond population results of BreP2, BreP3, IeP2, IeP3 are 0.04, 0.05, 0.04, 0.02, respectively, which are the typical value of weak covalent bonds, may originate from less overlap of electron density caused by the longer bond lengths. By calculating the binding energy, we can check the stability of different doping systems. Results listed in Table 1 shown that the binding energies of X-phosphorene are all negative, indicate stable configuration. F-phosphorene is the most stable structure among four X-phosphorene, this can contribute to the shortest FeP bond and highest charge transfer amount because of the largest electronegativity of F atom, which lead to a strong FeP ionic bond formation. 3.2. Electrical properties The calculated IEs of halogen atoms in X-phosphorene are plotted in Fig. 3. F, Cl and Br are act as acceptors while I is electron donor, these results can meet our charge transfer analysis based on Mulliken method shown in Table 1 pretty well. F is a potential ptype dopant of phosphorene with the smallest IE of 0.16 eV among four halogen elements, equivalent to IE of indium doped in silicon. Unlike shallow impurities which IEs located closer to the CBM or VBM, Cl, Br and I are all deep dopants, their dopant levels lie in the middle of the bandgap, which may lead to the recombination of photogenerated carrier or slower carrier transport by acting as the nonradiative combination centers or carrier traps, these could restrict the applications of X-phosphorene to achieve their promised potential. Fortunately, IE positions induced by halogen atoms in MoS2 can be modulated effectively by choosing suitable

Fig. 2. Charge density difference of X-phosphorene. Plot (a)e(d) corresponding to F, Cl, Br, I doped phosphorene, respectively. Cyan and yellow regions represent the accumulation and depletion of charge, while the value of isosurface is 0.02 e/Å3. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3. The IE positions for the halogen dopant in X-phosphorene. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

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substrates due to the substrate screening effect based on DFT study [40], it is reasonable to believe that similar effect may also occur in X-phosphorene which placed on the specific substrate. To investigate the doping effect of halogen elements on the electrical properties, the band structures and density of states (DOS) were calculated. Fig. 4 represents the band structures of Xphosphorene, Fermi level (EF) is fixed at the top of valence band and labelled with dotted line. X-phosphorene are all semiconductors, while Cl-phosphorene and Br-phosphorene possess direct bandgap, in contrary, F-phosphorene and I-phosphorene show indirect bandgap character [43,44]. The bandgap values of X-phosphorene are dramatically decreased compare with intrinsic phosphorene (0.89 eV), and the position of band extreme points are also changed, related results are shown in Table 2. Although pure phosphorene is an inherent nonmagnetic material, and halogens are not magnetic elements, Cl-phosphorene and I-phosphorene are showing astonishing spin-split band structures. The obtained magnetic moments of Cl-phosphorene and I-phosphorene are 1.86 mB and 1.08 mB, respectively. Cl-phosphorene has a spin-up bandgap of 0.90 eV, while its spin-down bandgap is 0.14 eV. For I-phosphorene, Kutlu et al. [45] reported that I-phosphorene shown spin polarized behavior, on the contrary, Zheng et al. [46]. demonstrated that I-phosphorene is a non-magnetic material. To clarify this issue, after checking several initial magnetic states, it is clear that the magnetism of I-phosphorene cannot be ignored, detail calculation processes and results can be seen in supplementary materials. The band structure of I-phosphorene exhibits apparently spin-split character with a bandgap of 0.036 eV, the spin-up and spin-down bandgap are 0.313 eV and 0.523 eV, respectively. Cl-phosphorene and I-phosphorene are similar as spin-gapless semiconductors, electrons can be excited from VB to CB without any energy requirement, and easy to acquire 100% spinpolarized carriers. Furthermore, the properties of spin-gapless semiconductors can be easily tuned by external fields, which is desirable for spintronic devices. F-phosphorene and Brphosphorene are non-magnetic semiconductors for no significant spin-up and spin-down band splitting features shown in Fig. 4 (a) (c), well matched with previous study [17]. Fig. 5 shows the total density of states (TDOS) and partial density of states (PDOS) for X-phosphorene. Compared with the TDOS of intrinsic phosphorene (See Fig. S2 (a)), there are new peaks occurred, leading to the narrower bandgaps of X-phosphorene.

Table 2 Band structures of intrinsic and X-phosphorene. System

Type

Eg (eV)

CBM

VBM

Intrinsic (PBE) Intrinsic (HSE06) F-phosphorene Cl-phosphorene Br-phosphorene I-phosphorene

direct direct indirect direct direct indirect

0.890 1.530 0.145 0.077 0.645 0.036

G G

G G G

S Y

Y

G

G

between G&X

Y

From the TDOS, the p states are the dominant states in the energy range around EF, therefore in PDOS analysis we only take p states into account. For F-phosphorene, F-2s and F-2p states are mainly localized at lower valence bands with high energy peaks at
27.30 eV and
6.34 eV, respectively (See Fig. S2 (b)). Unlike traditional doping mode of semiconductors, states induced by F atom are negligible near EF from Fig. 5 (a), P2-3p and P3-3p states are almost completely equal in a wide range, as well as contribute mainly to the CBM and VBM. In contrast, the P atom which bonded with F atom, labelled as P1, shows no significant contribute to them, our orbital analysis results (See Fig. S3 (a)) match the PDOS results and our analysis above very well. Fig. 5 (b) shows the apparent spin-spilt behavior of Clphosphorene, while the density peaks are located at
0.42 eV,
0.06 eV, 0.21 eV and 0.72 eV, respectively. The spinup VBM is mainly composed by P2-3p and P3-3p states, as well as less contribution from Cl-3p states, on the other hand, spin-down CBM is also originated from P2-3p and P3-3p states, which can be supported by orbital analysis in Fig. S3 (b). The spin splitting of DOS is the symbolic phenomenon of magnetic moment emergence, for Cl, P1, P2, P3, P4 and P5 atom, the magnetic moments are 0.06, 0.03, 0.67, 0.67, 0.02 and 0.01 mB, respectively. Besides, Cl-3s states are localized mainly around
16.80 eV, while Cl-3p states shown fairly strong hybridization with P1-3p in lower valence band, indicates the bond formation between Cl and P1. The presence of magnetism is relate to the bonding character and nonbonding electron states. Owing to the single CleP1 covalent bond, unpaired electrons in P23p and P3-3p states inspire the net magnetic moments, while electrons in Cl-3p states are also involved. The relatively lower contribution of P4, P5 to total magnetic moments are originate from

Fig. 4. Band structures of X-phosphorene. EF is fixed at zero and labelled with dotted line. Red and blue lines indicate spin up and spin down bands, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

K. Pu et al. / Journal of Alloys and Compounds 812 (2020) 152125

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Fig. 5. TDOS and PDOS of X-phosphorene. Plot (a)e(d) corresponding to F, Cl, Br, I doped phosphorene, respectively. The green, blue, orange, dark yellow, violet and red lines represent the p states of P1, P2, P3, P4, P5 and halogen atom, respectively, while the vertical line fixed at zero represents the EF. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

longer distance away from dopant and the resulting weaker hybridization. For Br-phosphorene, Br-4s states are not only localized around
16.71 eV, but also distributed in conduction bands higher than 4 eV. Br-4p states are widely scattered from
6.5 eV to 1.0 eV, and hybridized with P2-3p and P3-3p in valence bands, indicate bonds formation between Br and P atoms. It can be seen from Fig. 5 (c) and Fig. S3 (c) that the VBM is mainly composed by P1-3p, P2-3p and P3-3p states, while Br-4p states are involved in the formation of the CBM. I-phosphorene has high asymmetrical charge density states near EF, indicates magnetic behavior, sharp peaks occurred at
0.28 eV,
0.03 eV, 0.03 eV and 0.27 eV corresponding to four spin-split bands near EF. In Fig. 5 (d), I-5p states split obviously near EF, and the 2p spin-split states of adjacent P atoms are mutually hybridized with I atom. The spin up VBM is composed by nearly equal contributions of I-5p, P3-3p and P2-3p states with strong hybridization, while the spin down CBM is formed mainly by P1-3p states, see Fig. S3 (d). For I, P1, P2, P3, P4 and P5 atom, the magnetic moments are 0.17, 0.38, 0.18, 0.20, 0.03 and 0.04 mB, respectively. I atom is bonding with P2 and P3 atoms in I-phosphorene, so that the P1 atom has one unpaired electron on 2p orbital, which may cause the net magnetic moments. Furthermore, the hybridization of 2p states of P2, P3 atoms with I-5p states is also an essential part in the appearance of magnetic moments. Effective mass m* is an important index for carrier

transportation, which is especially valued in device applications. Here, by using formula Z2 ½v2 EðkÞ=vkx vky 
1 and parabolic nonlinear fitting method, the m* of carriers in X-phosphorene are examined as shown in Fig. 6. The intrinsic electron mass is 3.73 me* along G-X direction and 0.22 me* along G-Y direction, in agreement well with pervious researches [47,48], mh* along G-X direction is relatively bigger because of the flat band is more sensitive to fitting calculations. Identical with intrinsic situation, the effective mass of carriers in X-phosphorene are also show strong anisotropic feature. Such a strong in-plane anisotropic behavior may suggest possible novel applications of X-phosphorene. Moreover, several effective masses, e.g., me* along SeY direction of F-phosphorene, mh* along G-Y direction of F-phosphorene, as well as mh* along G-Y direction of the Br-phosphorene are similar to the mh* of intrinsic phosphorene, may indicate superb transportation properties, which are essential in microelectronic applications. 3.3. Optical properties Since phosphorene is a promising candidate for optical materials, clarify the optical properties of modulated X-phosphorene is highly demanded. In this section, we investigated the optical properties of X-phosphorene by calculating the dielectric function ε(u) ¼ ε1(u)þiε2(u). The imaginary part ε2(u), which considered by summing the transitions between occupied and unoccupied states, can be given by following equation [49]:

6

K. Pu et al. / Journal of Alloys and Compounds 812 (2020) 152125

1=2 .pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nðuÞ ¼ 1 2 ε1 ðuÞ2 þ ε2 ðuÞ2
ε1 ðuÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε ðuÞ þ jε ðuÞ
1 2 1 2 RðuÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε1 ðuÞ þ jε2 ðuÞ þ 1

Fig. 6. Effective masses of electrons (a) and holes (b) in intrinsic and X-phosphorene. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

ε2 ðuÞ ¼



 ð   16p2 e2 X 〈ijMjj〉2 fi ð1
fi Þ  d Ej;k
Ei;k
u d3 k 2 mu i;j (4)

where e/m is the charge/mass of a free electron, u is the frequency of incident photons, M is the dipole matrix, i and j are the initial and final states, respectively. Parameter fi is the Fermi distribution function for i-th state with wave function vector k. From this equation, the real part ε1(u) can be deduced from Kramers-Kronig transformation and can be expressed as:

ε1 ðuÞ ¼ 1 þ

2

p

∞ ð

P 0

0

0

0

u ε2 ðu Þdu  0 u 2
u2

(5)

where P is the principal value of the integral. Other optical properties, such as absorption coefficient a(u), loss function L(u), refractive index n(u) and reflectivity R(u) can be derived from dielectric function and expressed as [50]:

pffiffiffi

aðuÞ ¼ 2ðuÞ

LðuÞ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 ε1 ðuÞ2 þ ε2 ðuÞ2
ε1 ðuÞ

ε2 ðuÞ ε1 ðuÞ2 þ ε2 ðuÞ2

(6)

(7)

(8)

(9)

Fig. 7 (a) (b) display the real and imaginary parts of the dielectric function of intrinsic phosphorene and X-phosphorene, respectively. For intrinsic phosphorene, our results are consistent with previous publications in tendency [22,51]. It is worth mentioning that for the intrinsic and X-phosphorene, the real and imaginary parts show different characters as the incident radiation has linear polarization along the (100) or (010) direction, indicates anisotropic optical properties. For (100) polarized direction, combined with band structures and DOS results, intrinsic phosphorene which two highest peaks located at 4.03eV and 4.98 eV are all indicate intrinsic p-p excitations from valence bands to conduction bands. For Xphosphorene, the peak located at 4.32 eV (F-phosphorene) are caused by the p-p transitions of P atoms, on account of few impurity states induced by F atom near EF, however, for Cl-phosphorene (4.06 eV), Br-phosphorene (4.20 eV) and I-phosphorene (3.96 eV), their peaks are obviously demonstrate the transitions from P-3p states in VB to impurity induced p states in CB. For (010) polarized direction, highest peaks of X-phosphorene (4.49 eV, 4.60 eV, 4.69 eV and 4.36 eV for F-phosphorene, Cl-phosphorene, Br-phosphorene and I-phosphorene, respectively) are very close to the values along (100) polarized direction, indicate similar transition behaviors. The static dielectric constant ε1(0) can be derived from the low energy limit of ε1(u). The calculated ε1(0) of intrinsic phosphorene are 3.92 eV and 4.10 eV for (100) and (010) polarized direction, respectively. After halogen atoms were induced in phosphorene, their ε1(0) are all increase, which can attributed to extra levels in the bandgap introduced by impurity atoms or adjacent P atoms. For linear polarization along (100)/(010) direction, ε1(0) are 7.18/ 5.36 eV, 4.14/5.56 eV, 5.42/6.21 eV and 4.95/6.25 eV for F-phosphorene, Cl-phosphorene, Br-phosphorene and I-phosphorene, respectively. The absorption coefficient a of intrinsic and X-phosphorene are plotted in Fig. 7 (c). The intrinsic absorption edge of phosphorene is consistent with the bandgap value (0.89 eV), and the urgently increased absorption edge indicates phosphorene is a promising optical material in near infrared and visible region. For (100) or (010) polarization direction, the intrinsic absorption is related to the interband electron transition from P-3p states in the VBM to P3p states in the CBM. Compared with pure phosphorene, the absorption coefficients of the X-phosphorene are decrease in UV-C region, but mildly increase in UV-B and UV-A regions, as well as visible and infrared regions. New absorption peaks occurred near zero point are fairly weak because of the weak transitions between VBM and induced states in bandgap. The loss function and refractive index are shown in Fig. 7(d)e(f). It can be deduced from Fig. 7 (d) that the energy loss peaks are located at 10.50 eV/10.26 eV, 9.62 eV/9.85 eV, 9.35 eV/9.90 eV, 9.51 eV/9.93 eV and 10.41 eV/10.30 eV for intrinsic, F-phosphorene, Cl-phosphorene, Br-phosphorene and I-phosphorene along (100)/ (010) polarized direction, which are corresponding to where the reflectivity are rapidly decreased. For X-phosphorene, enhanced refractive index can be observed in low energy region, as well as reflectivity (See Fig. S4) for both (100) and (010) polarization directions, which may contributed to the induced mid-gap states by doped atoms or adjacent P atoms.

K. Pu et al. / Journal of Alloys and Compounds 812 (2020) 152125

7

Fig. 7. The real part (a), the imaginary part (b) of the dielectric function, absorption coefficient (c), loss function (d), and the refractive index for polarization direction along (100) (e) and (010) (f) of intrinsic and X-phosphorene. The black, red, blue, orange and olive lines indicate intrinsic, F-, Cl-, Br- and I-phosphorene, respectively. The solid/dash lines in plot (a)e(d) represent the (100)/(010) polarized direction, while in plot (e) and (f), they describe the real/imaginary part of refractive index. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

4. Conclusion In summary, the structural, electrical and optical properties of halogen atom (F, Cl, Br and I) doped phosphorene were studied by using density functional theory. The ionic bond is formed between F and phosphorene, while Cl, Br, I are covalently bonded to phosphorene. Furthermore, F, Cl is bonding to one P atom while Br, I are bonding to two P atoms. Among all four halogens, F induces the shallowest dopant level, so that it can be used as potential p-type dopant, while Cl, Br, I are all deep dopants, which need further modulations to make them shallower. X-phosphorene are all semiconductors, it is remarkable that Cl-phosphorene and I-phosphorene are exhibit nearly as spin gapless semiconductors, which may favorable in spintronic applications. The carrier effective masses of X-phosphorene are anisotropic, calculated values along several particular directions are similar compared with that in pure phosphorene, which may herald great transport properties. The absorption coefficients of X-phosphorene are increase in UV-A and UV-B regions, as well as in visible and infrared regions compared with intrinsic condition. Our theoretical investigations pave way towards X-phosphorene in potential microelectronic and optical applications.

Conflicts of interest There are no conflicts of interest to declare.

Author contributions Xianying Dai, Jianjun Song, Tianlong Zhao and Yue Hao designed this project. Kaiwen Pu performed the first principles calculations, analyzed the calculated results and wrote the original manuscript. Difan Jia and Wenluo Tao checked the calculation settings and results. Xiaodong Zhang and Fang Liu modified the manuscript. All authors discussed the results and worked on the final manuscript. Acknowledgements This work was supported by the 111 Project (No. B12026), the National Natural Science Foundation of China (No. 51802242), the Innovation Fund of Xidian University (No. 20109194873) and the Natural Science Foundation of Shaanxi Province (No. 2019JQ-313). It is also supported by High Performance Computing Center of Xidian University, China.

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Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jallcom.2019.152125.

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