Tuning the electronic and optical properties of phosphorene by transition-metal and nonmetallic atom co-doping

Abstract

The electronic and optical properties of phosphorene co-doped with vanadium and nonmetallic atoms (B, C, N and O) are investigated by employing first-principles calculations based on density functional theory. It is found that the geometrical, electronic and optical properties are affected distinctly by these dopants. Significant local lattice distortions are observed in all of the V–X (X = B, C, N or O) co-doped systems. All the substituted systems retain their semiconducting character, but their band gaps become smaller than that of primitive phosphorene. This indicates that impurity doping is an effective way to modulate the band gap of phosphorene for different applications in electronic devices. Obvious covalent interactions exist between the impurities and their adjacent phosphorus atoms. In these doped systems, an interesting redshift phenomenon and significant anisotropy are observed in their optical properties. Our theoretical investigations suggest an alternative method towards modulating the electronic and optical properties of phosphorene, and predict potential applications of phosphorene in nanoelectronic and optical devices.

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1 Introduction

As a prototype of two-dimensional (2D) crystal materials, graphene has dominated 2D research for many years because of its enticing physical properties arising from the quantum confinement associated with its ultrathin structure.^1–10 Although graphene exhibits many exquisite phenomena, the inherent lack of a band gap greatly limits its use in many electronic and photonic devices. For instance, the zero-gap property hinders graphene’s applications in semiconductor switches in computer circuits.¹¹ This intrinsic drawback of graphene prompted researchers to search for alternative materials possessing exotic properties similar to or even surpassing those of graphene. In this regard, transition-metal dichalcogenides (TMDs)^12–18 (such as monolayer MoS₂) have emerged as semiconducting alternatives to gapless graphene for next-generation nanodevices because of their intrinsic band gaps. However, the carrier mobility of MoS₂ is relatively low, thereby its applications in spintronics are also limited.^19,20 Thus tremendous efforts are still ongoing to explore other alternative single-layer materials with desired properties such as an electronic band gap and high carrier mobility.

Recently, monolayer black phosphorous (MBP), a new 2D material, has been mechanically exfoliated by using sticky tape to peel the layers off a larger sample.^11,21,22 The MBP is dubbed phosphorene due to its single-layer configuration. Phosphorene and graphene are two well known stable elemental 2D materials that can be mechanically exfoliated. The advent of phosphorene largely enhanced the application range of 2D materials because phosphorene presents some significant features superior to other previous 2D materials. In contrast to the vanishing band gap in graphene, phosphorene exhibits a finite direct band gap at the center of the Brillouin zone,^21,23–25 which makes phosphorene a potential candidate for applications in optoelectronic devices.^26,27 Compared with typical semiconducting monolayer TMDs such as MoS₂, phosphorene possesses quite a high carrier mobility of ∼10³ cm² V⁻¹ s⁻¹ and gives an on/off ratio of ∼10⁴,^{21,22,28–30} making it more attractive for application in spintronics.^31–33 In addition, phosphorene distinguishes itself from other 2D layered materials by its unique structure characteristics. Similar to graphene, inside the phosphorene, each phosphorus (P) atom covalently bonds with three other phosphorus atoms, forming a honeycomb structure. But the surface of the phosphorene is slightly puckered. Such a peculiar corrugated honeycomb structure leads to the anisotropic electronic, transport, optoelectronic, thermoelectric, and mechanical properties of phosphorene.^{23,25,34–39} Given these excellent properties, it is not a surprise that this material has been considered the ideal platform for a multitude of applications^40–44 and immediately became one of the research hotspots.^45–53

Tuning the properties of a material is essential for optimizing device functionality. In the case of phosphorene, this can be realized not only by means of controlling the number of layers but also by external controls such as strain engineering, adsorption and foreign atom doping. The remarkable strain effects on modifying the electronic and structural properties of phosphorene have already been demonstrated by several research groups.^23,25,27,29 Rastogi et al.⁵⁴ systematically investigated the effect of the surface adsorption of 27 different adatoms on the electronic and magnetic properties of MBP by using density functional theory (DFT). They provided a rich variety of electronic and magnetic transformations depending on the different adatoms. The structures, stabilities, and electronic properties of phosphorene with different kinds of defects (vacancies and foreign atom doping) have been studied within DFT.⁵⁵ The authors revealed that the band gap could be modulated for different applications by introducing vacancies or dopants. In addition, the foreign atom substitutional doping was also an effective and flexible method toward modulating the magnetic and electronic properties of phosphorene. For instance, Khan et al.⁵⁶ by using the full-potential linearized augmented plane wave method, explored the electronic band structure, binding energy, and magnetic and structural properties of nonmagnetic impurity (Al, Si, S or Cl) doped phosphorene. They found that the magnetic state of phosphorene can be manipulated by even non-magnetic impurity doping. Besides, Yu and his coworkers did detailed research on the anomalous doping effect of various dopants (group III, IV, V, and VI elements) on the electronic properties and thermodynamic stabilities of phosphorene.⁵⁷ They demonstrated that the electronic properties of phosphorene are drastically modified by the number of valence electrons in the dopant atoms. The same research group also provided some first-principles information on 3d transition-metal doped phosphorene to demonstrate that the Ti-, V-, Cr-, Mn-, Fe, and Ni-doped systems have dilute magnetic semiconductor properties, while Sc- and Co-doped systems have no magnetism.⁵⁸ Similarly, transition-metal doped phosphorene systems have been studied by Hashmi et al.⁵⁹ via density functional calculations. The main outcome of this investigation was that the phosphorene layer still has a semiconducting band gap in the Sc- and Cu-doped case, but has a half-metallic state in the V- and Fe-doped structures. Despite these extensive studies available on modifying the physical and chemical properties of phosphorene, investigations into the fundamental properties and applications of phosphorene are still at an early stage.⁶⁰ Hence, it is necessary to employ specific methods to modulate the electronic and optical properties of phosphorene so as to make this new 2D material suitable for broader applications.

To the best of our knowledge, there are few theoretical studies describing explicitly the synergistic effect of transition-metal and nonmetallic atom dopants on the electronic and optical properties of phosphorene. In the present paper, we carry out first-principle calculations to examine the microscopic electronic structure of V (on behalf of transition-metal atoms) and B, C, N, and O (represent nonmetallic atoms) co-doped phosphorene to explore the synergistic effects of the dopants on the electronic and optical properties. This study reveals a number of interesting observations. Firstly, these dopants induce local lattice distortion. Secondly, doping with vanadium and nonmetallic atoms decreases the band gap by forming impurity energy levels in the band gap. Thirdly, individual V atom doping and V–B (C, N, and O) co-doping both make the optical absorption edges shift towards a lower energy and generate a redshift phenomenon. It is expected that these results may open a new route for phosphorene in nanoelectronic and optical device applications in the foreseeable future.

2 Methodology

To explore the effect of V–B, V–C, V–N, and V–O pair co-doping on the geometric, electronic, and optical properties of phosphorene, first-principles spin-polarized calculations are carried out using the Cambridge Serial Total Energy Package (CASTEP) code based on DFT.⁶¹ The plane wave of the ultrasoft pseudopotential method⁶² is adopted to deal with the interaction of the ion-core with the valence electrons; and the generalized gradient approximation (GGA) within the Perdew–Burke–Ernzerhof (PBE) is adopted to treat the exchange–correlation effects between the valence electrons.⁶³ In order to model the two types of different elements co-doped in phosphorene, we chose a 4 × 3 × 1 supercell in which the two nearest-neighbor P atoms are replaced by V–B, V–C, V–N, or V–O. The structural model for co-doped phosphorene is periodic in the xy plane and separated by a vacuum layer of 15 Å along the z axis, which is adopted to make the spurious interaction between neighboring slabs negligible. Note that the interaction between two adjacent vanadium atoms or nonmetal atoms (B, C, N or O) closely relates to the distance of two nearest-neighbor V (B, C, N or O) atoms. The nearest distance between two same type doping atoms (V–V, B–B, C–C, or O–O) is 12.99 Å and the interaction between them can be ignored. The electron wave function was expanded in plane waves up to a cut-off energy of 400 eV. The Monkhorst–Pack⁶⁴ scheme with a 3 × 3 × 1 k-point grid is used to generate the k-points for reciprocal space sampling. The minimum energy structure optimization method within the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm⁶⁵ is selected. Geometry optimization is carried out before the single point energy calculations, and the self-consistent convergence accuracy is set as 1.0 × 10⁻⁵ eV per atom. The convergence criterion of the largest force on the atoms is 0.02 eV Å⁻¹, the maximum displacement is 0.001 Å, and the stress is no more than 0.05 GPa. Electronic structures and optical properties are calculated on the corresponding optimized crystal geometries.

It should be noted that the on-site electron correlation effect of the transition-metal elements may play a key role due to the localized d-orbital. Besides, it has been shown that the conventional DFT fails to predict both qualitative and quantitative properties for strongly correlated electron materials.⁶⁶ Therefore, to deal with the strong on-site Coulomb interactions in the localized 3d orbital of the transition element V, the rotationally invariant GGA+U method is used to amend the electronic structure of the V and B, C, N, and O co-doped phosphorene systems. At the GGA+U level, the total energy can be obtained by:⁶⁷

where ρ^σ, U and J are the polarized on-site density matrix, the spherically averaged screened coulomb energy and the exchange energy, respectively. An effective on-site Coulomb parameter U_eff = U − J can be introduced. The calculated total energies are insensitive to J even when the U_eff is fixed.⁶⁸ In the present work, the effective value U_eff is used to investigate the effective on-site Coulomb interactions of the transition-metal V atom in phosphorene, and is set to be U_eff = 2.5 eV. Such an effective value (U_eff = 2.5 eV) is a default value of the V atom in the CASTEP package, and was also successfully adopted to describe the electronic, and magnetic properties of V-doped phosphorene.⁵⁹ As mentioned above, the U_eff belongs to an empirical parameter. However, it is worth mentioning that the Hubbard value (U) can be determined non-empirically. For instance, Guss et al. obtained accurate band structures and band gaps of the Ca²⁺ doped CeBr₃ bulk material by using the DFT+U approaches, and the Hubbard U was determined non-empirically.⁶⁹

To investigate the optical properties of co-doped phosphorene, we decide to calculate the frequency-dependent complex dielectric function ε(ω). The ε(ω) = ε₁(ω) + iε₂(ω) contains two parts, namely the imaginary part ε₂(ω) and the real part ε₁(ω). The ε₂(ω) is proportional to the absorption spectrum and the ε₁(ω) is associated with the dispersion properties. The ε₂(ω) is calculated from the momentum matrix elements between the occupied and unoccupied electronic states, and is defined as:⁷⁰

where Ω is the volume of the elementary cell, and ω is the light frequency. ψ^c_k and ψ^v_k are the wave functions at the k point of conduction and the valence band wave functions at the k point, respectively. û is the vector defining the polarization of the electric field of the incident light, which is averaged over all spatial directions in the polycrystalline case. The real part ε₁(ω) can be evaluated using ε₂(ω) through the Kramer–Kronig relations⁷¹

3 Results and discussion

3.1 Geometric structure

Before further discussing the electronic properties of pure phosphorene, we decided to review the structure of pristine phosphorene including the bond lengths and bond angles. A schematic illustration of the top view of the primitive phosphorene is depicted in Fig. 1(a). It can be seen from Fig. 1(a) that unlike the flat structure of graphene, phosphorene has a puckered honeycomb structure. Each unit cell of phosphorene consists of four P atoms, which are all bonded with three adjacent phosphorus atoms (see Fig. 1(b)). Hence, there are three bonds for each P atom: two of them are formed by the P atoms in the same plane with a distance of 2.191 Å, and the third bond is between the interlayer P atoms with a distance of 2.264 Å. Bond angles in and out of the plane are 95.604° and 104.590°, respectively. In addition, phosphorene has a puckered structure along the armchair direction (see Fig. 1(c)), but it looks like a bilayer in the zigzag direction (see Fig. 1(d)). The unique structural arrangement indicates structural anisotropy which is the origin of the anisotropic physical and mechanical properties. All of these numerical results are in good accordance with previous work.^31,50

Fig. 1 Optimized geometric structures of pristine phosphorene: (a) top view; (b) primitive cell; (c) and (d) side views from the zigzag and armchair directions.

Then, to assess how the substitutional dopants affect the structural properties of phosphorene, the geometric structure of each substitutionally doped phosphorene is optimized. In Fig. 2, (panels a and b) and (panels c and d) show the top and side views of single and co-doped phosphorene, respectively. The phosphorus atoms near the impurity site are labeled by numbers to describe the bond lengths between the dopants and these P atoms below. To quantify the local structure deformation in doped phosphorene caused by the substitutional doping, Table 1 summarizes the calculated bond lengths in the vicinity of the dopants. It is found that, due to the impurity doping, the phosphorus atoms close to the dopant are displaced from their original position and show buckling features. Because of this, noticeable internal distortion surrounding the doping atom is observed.

Fig. 2 Schematic description of doped phosphorene: (a) top view and; (b) side view of a single V atom doped 4 × 3 × 1 supercell; (c) top view and (d) side view of a V and nonmetallic atom co-doped 4 × 3 × 1 supercell. The violet, red, and green spheres, represent phosphorus, vanadium and nonmetallic atoms, respectively. Phosphorus atom in the phosphorene layer labeled as P₂ is replaced by X atoms (X = B, C, N or O).

Table 1 Calculated bond lengths of impurity doped phosphorene

Dopant atom (s)	V–P1 (Å)	V–P2 (Å)	V–P3 (Å)
V	2.417	2.417	2.315
V–B	2.384	2.015 (P2 = B)	2.292
V–C	2.391	1.899 (P2 = C)	2.331
V–N	2.384	1.887 (P2 = N)	2.396
V–O	2.459	2.150 (P2 = O)	2.374

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In the case of single V-doped MBP, the calculated bond lengths (V–P₁, V–P₂, and V–P₃) are 2.417, 2.417 and 2.315 Å, respectively. These calculated values are in good agreement with previous calculations.⁵⁹ The bond lengths of the intra-planar V–P₁ and V–P₂ bond lengths are larger than that of the inter-planar V–P₃, which indicates that the vanadium atom moves from the top layer to the bottom layer. As discussed above, the single V dopant does not induce significant local lattice distortion. In contrast, from Table 1 we find that V and nonmetallic X (X = B, C, N, and O) atom co-doping induces pronounced local lattice distortion, therefore the values of V–P₁, V–X, and V–P₃ are not identical. This may be due to the large difference in atomic radii and electronegativity between the P atom and substitutional dopants.

In order to explore the synergistic effect of the two different dopants on the electronic and optical properties of phosphorene, four main possible co-doping models should be considered. Here, we take the V and N atoms as an example to analyze the four different co-doping cases. As shown in Fig. 2(b), besides the fixed V dopant, the N dopant will occupy one of the four possible sites P₂, P₃, P₄, and P₆ for the four different cases. And, they are respectively named as the first, the second, the third and the fourth cases in the following analysis. Subsequently, the related stabilities of the four different co-doping cases are discussed by calculating their corresponding formation energies. The co-doped formation energy can be defined as E_form = E_tot (V–N) − E_tot (MBP) + 2E_P − E_V − E_N, where E_tot (V–N) is the total energy of V–N co-doped phosphorene, and E_tot (MBP) denotes the total energy of the pure phosphorene supercell. E_P, E_V and E_N represent the energies of the single P, V and N atoms, respectively. It is well known that the smaller the value of the formation energy is, the greater the stability of the structure should be. According to our calculated results, we find that the formation energies of the first and the second cases are −7.902 and −7.988 eV respectively, while those of the third and the fourth cases are −6.616 and −7.109 eV respectively. It is obvious that the former two cases with the smaller formation energies are more stable than the latter two cases. Furthermore, the formation energies of the former two cases have only a little difference, which means both of them should be possible stable structures. However, as shown in Table 1, the bond length of the intra-planar V–N bond in the first case is much shorter than that of the inter-planar V–N bond in the second case. To investigate the synergistic effect of the dopants, we restrict our discussions to the first case only, which has the shorter intra-planar bond and stronger interactions between both doping atoms.

3.2 Electronic properties

3.2.1 Energy band structures. To examine the effect of doping on the electronic properties of phosphorene, the band structures of pure and doped phosphorene are computed under the same computational conditions. Fig. 3 (panels a–f) presents the energy band structures of all the pristine and doped cases. As shown in Fig. 3(a), pristine phosphorene is a direct-band-gap semiconductor, with its valence band maximum (VBM) and conduction band minimum (CBM) both located at the G point, which is very beneficial for the electron transport. The band gap of pure phosphorene is about 1.034 eV, which agrees well with the previous report.^21,51,57 Such a calculated value is smaller than the experimental value 2.0 eV,⁴¹ which should be due to the reason that DFT usually underestimates the band gap of a semiconductor because of a self-interaction error.

Fig. 3 Band structures of pure (a); single V-doped (b); V–B co-doped (c); V–C co-doped (d); V–N co-doped (e); V–O co-doped (f) phosphorene. The horizontal zero line represents the Fermi level.

Fig. 3(b) shows the band structure of single V doped phosphorene. The band structure reveals that the V atom substitutionally doped 2D phosphorene retains a direct band gap of about 0.604 eV. This means that V-doped phosphorene is a semiconductor, which is in qualitative agreement with the recent theoretical result from Yu et al.⁵⁸ that all Ti-, V-, Cr-, Mn-, Fe-, and Ni-doped black phosphorenes show semiconducting characters. The only difference is that the band gap of V-doped phosphorene calculated by us is larger than that obtained by Yu et al. We suppose that such a difference originates from the neglecting of the strong Coulomb repulsion among V 3d electrons in ref. 58. Besides, via density functional calculations, Hashmi et al.⁵⁹ also investigated the substitutional doping of phosphorene systems with a series of 3d transition-metal atoms such as Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu. They suggested that most of the transition-metal doped phosphorenes still have a semiconducting band gap, whereas only V- and Fe-doped systems are half-metallic states. As discussed above, there is still a debate on whether V-doped phosphorene is a semiconductor. Because there are no available experimental data, we expect that the electronic properties of V-doped phosphorene will be uncovered by experimental measurement. Therefore, we think that it may be an interesting issue worthy of further study. It can be seen from Fig. 3(b) that a flat impurity state appears just above the Fermi level, which is mainly contributed by the 3d state of the vanadium atom. More detailed analysis with respect to the composition of the energy band will be provided below.

The band structures of V–B (C, N or O) co-doped phosphorene are also investigated to further understand how the electronic structure is affected by different dopants. Fig. 3(c)–(f) represents the band structures of the V–B, V–C, V–N and V–O co-doped systems, respectively. We find that different dopants induce different band structures. The new impurity energy levels introduced by the substitutional dopants have an increasing tendency, as we change the nonmetallic atom from B to O. The band gaps are about 0.327, 0.737, 0.851 and 0.940 eV for V–B, V–C, V–N and V–O co-doped phosphorene, respectively. It is noteworthy that both the mono- and co-doped phosphorene systems retain direct band gap characters. In addition, doping with transition-metal and nonmetallic atoms can make the energy band gap smaller than that of primitive phosphorene by forming impurity states in the band gap. Such results reveal that these dopants can be used to modulate the band gap of phosphorene.

3.2.2 Density of states. To achieve deeper insight into the electronic properties of the substitutional dopant modified phosphorene systems, we computed the total density of states (DOS) and projected density of states (PDOS) of the different modified phosphorene systems. The DOS and PDOS of pure phosphorene, as illustrated in Fig. 4(a), are displayed for comparison. It is found that the region near the Fermi level is mainly attributed to the p orbital of the P atoms of the phosphorene layer, and the contribution of the s orbital of P is relatively small. Then the DOS and PDOS of the V dopant and its neighboring P atoms in the V-doped case are calculated (see Fig. 4(b)). Compared with that in pristine phosphorene, the PDOS curve of the P atoms in the V-doped case is significantly changed due to the introduction of the 3d transition-metal impurity (vanadium atom). From Fig. 4(b), a distinct contribution from the V-3d PDOS near the Fermi level is observed because of the strong localization of the V-3d states. Furthermore, the bottom of the conduction band is also mainly contributed by the V-3d states. While the majority of the top of the valence band is determined by the V-3d and P-3p states, and an obvious hybridization between them is observed.

Fig. 4 Density of states (DOS) and projected density of states (PDOS) of primitive phosphorene (a); single V atom substitutionally doped phosphorene (b). The Fermi level is labeled by a dash line, and the smearing width is set to be 0.05 eV.

The DOS and PDOS of phosphorene co-doped with vanadium and nonmetallic atoms are depicted in Fig. 5. Comparing Fig. 4(b) with Fig. 5(a), we find that the B atom incorporated into single V-doped phosphorene doesn’t significantly change the distribution of the DOS. Besides, it can also be observed that the highest occupied valence band is derived mainly from the V-3d, P-3p, and B-2p orbitals. Similar to the V–B co-doped case, the valence bands of the other co-doped systems (V–C, V–N and V–O) are mainly attributed to the hybridization between the 3d states of the V atom, the 3p states of the nearest P atoms, and the 2p states of the nonmetallic atom (see Fig. 5(b)–(d)). Further noted from Fig. 5(b)–(d) is that the overlap between the 2p orbitals of the C or N atom and the 3p orbitals of the P atom is obvious, whereas the overlap between the O-2p and P-3p states is relatively unobvious. So this indicates that the interaction between the P-3p and C (N)-2p states is stronger than that between the P-3p and O-2p states, implying that the C (N)–P bonds may possess stronger covalent bonding strength than the O–P bonds. This phenomenon is mainly due to the different electronegativities of the C, N and O atoms. In addition, the lowest conduction bands of the co-doping systems are mainly formed by the 3d states of the vanadium atom.

Fig. 5 DOS and PDOS of co-doped phosphorene: (a) V–B co-doped; (b) V–C co-doped; (c) V–N co-doped; (d) V–O co-doped. The Fermi level is labeled by a dash line, and the smearing width is set to be 0.05 eV.

3.2.3 Mulliken population analysis. Mulliken population analysis based on Mulliken formalism⁷² is performed to study more details of the chemical bond characters. It is well known that the bond (overlap) population reflects the degree of electron sharing between two atoms, and can be used to assess the covalent or ionic nature of a chemical bond. A larger value of overlap population represents a higher covalence level, while an ideal ionic bond will have zero overlap population.⁷³ In addition, positive and negative values indicate bonding and antibonding states, respectively. Table 2 illustrates the overlap populations of the transition-metal and nonmetallic atom substitutional doping systems. The overlap population of two neighboring P atoms in primitive phosphorene is about 0.45, indicating covalent bonding between them. Once one V atom substitutes for a P atom in the single phosphorene sheet, the overlap population of V–P (0.35 or 0.36) is slightly smaller than that of the original P–P bond (0.45). When a nonmetallic B atom is incorporated into V-doped phosphorene, the calculated bond populations are 0.44, −0.01, 0.35, 0.95 and 0.81 for V–P₁, V–B, V–P₃, B–P₄ and B–P₅, respectively. It shows that there exists a very weak antibonding (or no bonding) state between the V and B atoms. We think that the valence electron configurations V (3d³4s²) and B (2s²2p¹) make it easier for both of them to lose electrons, therefore very weak repulsive interaction or no bonding between them can be observed. Moreover, the B–P bonds possess more significant covalent character than the V–P bonds. Unlike the antibonding character of V–B, the overlap populations of V–C, V–N, and V–O are 0.27, 0.27 and 0.14 respectively, indicating the existence of the covalent interaction between the V and nonmetallic atoms. It can also be seen from Table 2 that the overlap population between C (N) and the adjacent phosphorus is larger than that between O and the neighboring P atoms. This indicates that the covalent bonding of C (N)–P is stronger than that of O–P, which coincides with the analysis of the PDOS. This is because the O atom has a higher electronegativity than the C and N atoms. Interestingly, from the Mulliken population analysis of V–N co-doped phosphorene, we find that two N–P bonds have comparable bond populations (0.48 and 0.40) to those of the P–P (0.45) in the pure case, indicating that N–P has a similar hybridization to that of the P–P bond.

Table 2 Mulliken overlap population of substitutionally doped phosphorene

Dopant atom (s)	Bond	Overlap population	Length (Å)
V	V–P1	0.36	2.417
	V–P2	0.36	2.417
	V–P3	0.35	2.315
V–B	V–P1	0.44	2.384
	V–B	−0.01	2.015
	V–P3	0.35	2.292
	B–P4	0.95	1.864
	B–P5	0.81	1.877
V–C	V–P1	0.44	2.391
	V–C	0.27	1.899
	V–P3	0.38	2.331
	C–P4	0.70	1.757
	C–P5	0.71	1.763
V–N	V–P1	0.44	2.384
	V–N	0.27	1.887
	V–P3	0.44	2.396
	N–P4	0.48	1.711
	N–P5	0.40	1.717
V–O	V–P1	0.38	2.459
	V–O	0.14	2.150
	V–P3	0.38	2.374
	O–P4	0.25	1.707
	O–P5	0.11	1.822

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3.3 Optical properties

Here, the optical properties of pure and differently doped MBP are systematically discussed on the basis of the dielectric function. It is well known that the imaginary part of the dielectric function (ε₂(ω)) is an effective parameter to measure the optical absorption of materials. The imaginary parts of the dielectric function along three directions for pristine and dopant modified phosphorenes are shown in Fig. 6. Due to the anisotropy of phosphorene along the x, y and z directions, the computed ε₂(ω) in the three directions presents different characteristics. As shown in Fig. 6(a)–(c), the ε₂(ω) of impurity doped phosphorene shows a distinctive difference from that of pristine phosphorene along the three directions, demonstrating that substitutional dopants have a profound influence on the optical spectra. As a representative system, we discuss the curves of ε₂(ω) along the x direction in detail (see Fig. 6(a)), since ε₂(ω) along the other two directions can be understood in a similar way. For pure phosphorene, a quite wide absorption band in the region from 1.964 eV to ∼9.0 eV is observed clearly (see the black curve in Fig. 6(a)). The light within such an energy range will be strongly absorbed by the pristine case. In Fig. 6(a), the absorption edge of the pure phosphorene monolayer is ∼1.964 eV, which is in good agreement with the experimental value of the band gap of phosphorene (2 eV).⁴¹ After introducing dopants, the absorption edges are shifted to a lower energy range compared with that of pristine phosphorene. That is, individual V atom doping and V–B (C, N, and O) co-doping all make the optical absorption edges generate the redshift phenomenon, which results in the enhancement of the absorption of infrared light in phosphorene. The absorption edges of the V-doped, V–B, V–C, V–N and V–O co-doped systems become 0.708, 0.457, 0.750, 0.805 and 0.959 eV, respectively (see details in the inset of Fig. 6(a)). As is known, the order of the radius size for nonmetallic atoms is O > N > C > B. As the nonmetallic atom is incorporated into V-doped phosphorene, the absorption edge increases as the radius of the nonmetallic atom increases. For the ε₂(ω) spectra along the y direction, the absorption edges of primitive and one vanadium atom doped phosphorene are about 2.508 and 1.085 eV, respectively, indicating an obvious redshift phenomenon. Nevertheless, the edges of the co-doped systems are nearly the same as each other about ∼1.433 eV. In addition, the edges of ε₂(ω) along the z direction are ∼1.057, 0.617, 0.373, 0.680, 0.736 and 0.903 eV for pure, single V doped, and V–B, V–C, V–N and V–O co-doped phosphorene, respectively. The redshift phenomenon is also obtained along the z direction. It should be noted that the optical absorption edges of all cases along the z direction are consistent with the corresponding energy band gaps mentioned above. In brief, all the doped cases reflect redshift phenomena along the x, y and z directions and all the absorption peaks become weaker.

Fig. 6 Imaginary parts of the dielectric function versus energy for pristine and substitutional impurity modified phosphorenes along the x (a), y (b), and z (c) directions.

4 Conclusions

In summary, based on the first-principle calculations within the framework of DFT, we carried out a systematic investigation on the geometric, electronic and optical properties of phosphorene with various dopants. This study aimed to identify possible doping strategies for phosphorene. Electronic structures and optical properties of single V atom doped or V–B, V–C, V–N and V–O co-doped phosphorene systems were analyzed and compared to identify the general trends and individual characteristics. According to our calculations, the optimized structural parameters (bond lengths and angles) are in good agreement with previous works. The impurity doping induces local lattice distortion and the detailed local geometric structures are dependent on the specific dopants. One vanadium atom substitutional doping does not induce huge local lattice distortion, while pronounced distortion is induced by V and nonmetallic atom (B, C, N, and O) co-doping.

Next, the band structures of all the substituted systems were explored. The results reveal that both one V atom doped and V–B (C, N, O) co-doped phosphorene all exhibit semiconducting behavior but with smaller band gaps than that of the pure case. Doping atoms considered in the present paper decrease the band gap by forming impurity states in the band gap region. The band gap in co-doped phosphorene increases from 0.327 to 0.940 eV as we change the substitutional nonmetal atoms from B to O. Band structure analysis also shows that by introducing nonmetallic atoms into a V-doped single phosphorene sheet, the band gap of dopant modified phosphorene can further increase or decrease, which may broaden the applications of phosphorene in developing nanoelectronics and optoelectronics.

Furthermore, the DOS, PDOS and Mulliken population were analyzed by us explicitly. It was found that V atom doping in phosphorene leads to the formation of V (3d)–P (3p) hybridized states at the top of the valence band. In addition, incorporation of a nonmetallic atom into V-doped phosphorene induces the interaction between the P-3p and 2p states of the nonmetallic atom. Among the doping nonmetallic atoms, the strongest covalent interaction was found between the B and P atoms. Meanwhile, there exists a very weak antibonding (or no bonding) state between the B and V atoms. These fascinating phenomena can be explained by the different electronegativities of the nonmetallic atoms.

Finally, the optical properties of phosphorene with different dopants were studied and compared with the pristine case. As a result, the computed imaginary parts of the dielectric function display different characters along the x, y, and z directions because of the anisotropy of phosphorene which is the origin of the anisotropic physical and mechanical properties. Besides, in the single V doping and V–B (C, N, O) co-doping cases, the optical absorption edges exhibit a distinct redshift phenomenon. Therefore, foreign atom substitutional doping is shown to be an effective way for modulating the electronic and optical properties of phosphorene. We hope that our findings may facilitate wider applications of phosphorene.

Acknowledgements

This work is supported by the Chinese National Science Foundation under Grant No. 21576208. It is also partly supported by the founding from the State Key Laboratory of Separation Membranes and Membrane Processes (Tianjin Polytechnic University). Numerical calculations for this work were carried out on the Parallel Computer Cluster of the School of Materials Science and Engineering at Tianjin Polytechnic University.

References

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science, 2004, 306, 666–669.
2. C. Lee, X. Wei, J. W. Kysar and J. Hone, Science, 2008, 321, 385–388.
3. A. A. Balandin, S. Ghosh, W. Z. Bao, I. Calizo, D. Teweldebrhan, F. Miao and C. N. Lau, Nano Lett., 2008, 8, 902–907.
4. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim, Rev. Mod. Phys., 2009, 81, 109–162.
5. X. Du, I. Skachko, F. Duerr, A. Luican and E. Y. Andrei, Nature, 2009, 462, 192–195.
6. R. Rasuli, A. I. zad and M. M. Ahadian, Nanotechnology, 2010, 21(185503), 1–6.
7. A. H. Castro Neto and K. Novoselov, Rep. Prog. Phys., 2011, 74, 82501–82509.
8. A. A. Balandin, Nat. Mater., 2011, 10, 569–581.
9. N. O. Weiss, H. Zhou, L. Liao, Y. Liu, S. Jiang, Y. Huang and X. Duan, Adv. Mater., 2012, 24, 5782–5825.
10. P. Nath, D. Sanyal and D. Jana, Physica E: Low-dimensional Systems and Nanostructures, 2015, 69, 306–315.
11. E. S. Reich, Nature, 2014, 506, 19.
12. H. Wang, H. Yuan, S. S. Hong, Y. Li and Y. Cui, Chem. Soc. Rev., 2015, 44, 2664–2680.
13. Q. H. Wang, K. Z. Kourosh, A. Kis, J. N. Coleman and M. S. Strano, Nat. Nanotechnol., 2012, 7, 699–712.
14. M. Chhowalla, H. S. Shin, G. Eda, L. J. Li, K. P. Loh and H. Zhang, Nat. Chem., 2013, 5, 263–275.
15. A. L. Elas, N. Perea-López, A. Castro-Beltrán, A. Berkdemir, R. Lv, S. Feng, A. D. Long, T. Hayashi, Y. A. Kim and M. Endo, ACS Nano, 2013, 7, 5235–5242.
16. K. F. Mak, C. Lee, J. Hone, J. Shan and T. F. Heinz, Phys. Rev. Lett., 2010, 105, 136805.
17. D. Lagarde, L. Bouet, X. Marie, C. R. Zhu, B. L. Liu, T. Amand, P. H. Tan and B. Urbaszek, Phys. Rev. Lett., 2014, 112, 1–4.
18. A. M. Hu, L. L. Wang, W. Z. Xiao, G. Xiao and Q. Y. Rong, Comput. Mater. Sci., 2015, 107, 72–78.
19. B. Radisavljevic and A. Kis, Nat. Mater., 2013, 12, 815–820.
20. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti and A. Kis, Nat. Nanotechnol., 2011, 6, 147–150.
21. H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek and P. D. Ye, ACS Nano, 2014, 8, 4033–4041.
22. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen and Y. Zhang, Nat. Nanotechnol., 2014, 9, 372–377.
23. A. S. Rodin, A. Carvalho and A. H. CastroNeto, Phys. Rev. Lett., 2014, 112, 176801.
24. Z. Zhu and D. Tománek, Phys. Rev. Lett., 2014, 112, 176802.
25. R. Fei and L. Yang, Nano Lett., 2014, 14, 2884–2889.
26. V. Tran, R. Soklaski, Y. Liang and L. Yang, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 235319.
27. X. Peng, Q. Wei and A. Copple, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 90, 085402.
28. F. Xia, H. Wang and Y. Jia, Nat. Commun., 2014, 5, 4458.
29. J. Qiao, X. Kong, Z. X. Hu, F. Yang and W. Ji, Nat. Commun., 2014, 5, 4475.
30. S. P. Koenig, R. A. Doganov, H. Schmidt, A. H. Castro Neto and B. Öezyilmaz, Appl. Phys. Lett., 2014, 104, 103106.
31. H. Zheng, J. Zhang, B. Yang, X. Du and Y. Yan, Phys. Chem. Chem. Phys., 2015, 17, 16341–16350.
32. B. Sa, Y. L. Li, J. Qi, R. Ahuja and Z. Sun, J. Phys. Chem. C, 2014, 118, 26560–26568.
33. V. V. Kulish, O. I. Malyi, C. Persson and P. Wu, Phys. Chem. Chem. Phys., 2015, 17, 13921–13928.
34. Y. Xu, J. Dai and X. C. Zeng, J. Phys. Chem. Lett., 2015, 6, 1996–2002.
35. G. Qin, Q. B. Yan, Z. Qin, S. Y. Yue, H. J. Cui, Q. R. Zheng and G. Su, Sci. Rep., 2014, 4, 6946.
36. A. Jain and A. J. H. McGaughey, Sci. Rep., 2014, 5, 8501.
37. Q. Wei and X. Peng, Appl. Phys. Lett., 2014, 104, 251915.
38. J. W. Jiang and H. S. Park, J. Phys. D: Appl. Phys., 2014, 47, 385304.
39. L. Wang, A. Kutana, X. Zou and B. I. Yakobson, Nanoscale, 2015, 7, 9746–9751.
40. J. Dai and X. C. Zeng, J. Phys. Chem. Lett., 2014, 5, 1289–1293.
41. M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. vander Zant and A. C. Gomez, Nano Lett., 2014, 14, 3347–3352.
42. X. Ling, H. Wang, S. Huang, F. Xia and M. S. Dresselhaus, Proc. Natl. Acad. Sci. U. S. A., 2015, 112, 4523–4530.
43. M. Engel, M. Steiner and P. Avouris, Nano Lett., 2014, 14, 6414–6417.
44. C. Zhang, G. Xiang, M. Lan, Z. Tang, L. Deng and X. Zhang, RSC Adv., 2015, 5, 40358–40362.
45. L. Kou, T. Frauenheim and C. Chen, J. Phys. Chem. Lett., 2014, 5, 2675–2681.
46. L. Kou, Y. Ma, S. C. Smith and C. Chen, J. Phys. Chem. Lett., 2015, 6, 1509–1513.
47. X. Sui, C. Si, B. Shao, X. Zou, J. Wu, B. L. Gu and W. Duan, J. Phys. Chem. C, 2015, 119, 10059–10063.
48. T. Hu and J. Hong, J. Phys. Chem. C, 2015, 119, 8199–8207.
49. H. Guo, N. Lu, J. Dai, X. Wu and X. C. Zeng, J. Phys. Chem. C, 2014, 118, 14051–14059.
50. Y. Jing, Q. Tang, P. He, Z. Zhou and P. Shen, Nanotechnology, 2015, 26, 095201.
51. R. Zhang, B. Li and J. Yang, J. Phys. Chem. C, 2015, 119, 2871–2878.
52. M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. J. van der Zant and A. Castellanos-Gomez, Nat. Commun., 2014, 5, 4651.
53. J. Yuan, S. Najmaei, Z. Zhang, J. Zhang, S. Lei, P. M. Ajayan, B. I. Yakobson and J. Lou, ACS Nano, 2015, 9, 555–563.
54. P. Rastogi, S. Kumar, S. Bhowmick, A. Agarwal and Y. S. Chauhan, Effective Doping of Monolayer Phosphorene by Surface Adsorption of Atoms for Electronic and Spintronic Applications, arXiv:1503.04296.
55. X. B. Li, P. Guo, T. F. Cao, H. Liu, W. M. Lau and L. M. Liu, Sci. Rep., 2015, 5, 10848.
56. I. Khan and J. Hong, New J. Phys., 2015, 17, 023056.
57. W. Yu, Z. Zhu, C. Niu, C. Li, J. H. Cho and Y. Jia, Phys. Chem. Chem. Phys., 2015, 17, 16351–16358.
58. W. Yu, Z. Zhu, C. Y. Niu, C. Li, J. H. Cho and Y. Jia, Dilute magnetic semiconductor and half-metal behaviour mediated by 3d transition-metal doped in black/blue phosphorene, arXiv:1504.01592.
59. A. Hashmi and J. Hong, J. Phys. Chem. C, 2015, 119, 9198–9204.
60. L. Kou, C. Chen and S. C. Smith, J. Phys. Chem. Lett., 2015, 6, 2794–2805.
61. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson and M. C. Payne, Z. Kristallogr., 2005, 220, 567–570.
62. D. Vanderbilt, Phys. Rev. B: Condens. Matter Mater. Phys., 1990, 41, 7892–7895.
63. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
64. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Condens. Matter Mater. Phys., 1976, 13, 5188–5192.
65. B. G. Pfrommer, M. Ca.te., S. G. Louie and M. L. Cohen, J. Comput. Phys., 1997, 131, 233–240.
66. M. D. Krcha and M. J. Janik, Int. J. Quantum Chem., 2014, 114, 8–13.
67. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 57, 1505–1509.
68. L. Wang, T. Maxisch and G. Ceder, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 195107.
69. P. Guss, M. E. Foster, B. M. Wong, F. P. Doty, K. Shah, M. R. Squillante, U. Shirwadkar, R. Hawrami, J. Tower and D. Yuan, J. Appl. Phys., 2014, 115, 034908.
70. S. Saha, T. P. Sinha and A. Mookerjee, Phys. Rev. B: Condens. Matter Mater. Phys., 2000, 62, 8828–8834.
71. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors, Springer Verlag, Berlin, 1996.
72. R. S. Mulliken, J. Chem. Phys., 1955, 23, 1833–1840.
73. M. D. Segall, C. J. Pickard, R. Shah and M. C. Payne, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 16317–16320.

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