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Tuning Electronic Properties of Blue Phosphorene/GrapheneLike GaN van der Waals Heterostructures by Vertical External Electric Field
Nanoscale Research Lettersvolume 14, Article number: 174 (2019)
Abstract
The structural and electronic properties of a monolayer and bilayer blue phosphorene/graphenelike GaN van der Waals heterostructures are studied using firstprinciple calculations. The results show that the monolayerblue phosphorene/graphenelike GaN heterostructure is an indirect bandgap semiconductor with intrinsic type II band alignment. More importantly, the external electric field tunes the bandgap of monolayerblue phosphorene/graphenelike GaN and bilayerblue phosphorene/graphenelike GaN, and the relationship between bandgap and external electric field indicates a Stark effect. The semiconductortometal transition is observed in the presence of a strong electric field.
Introduction
Twodimensional (2D) materials such as graphene [1], transition metal dichalcogenides (TMDs) [2], black phosphorene (BP) [3], and graphenelike GaN (gGaN) [4] have been in the spotlight, owing to their fascinating physical properties and potential applications in devices. As a fastemerging research area, the way in which the heterostructures are assembled from the isolated atoms remains to be an exciting research filed. It is considered as a novel way to construct devices, which integrates the properties of each isolated component with ideal properties applied in nanoelectronics [5, 6]. Due to atomic layers’ interaction [7], these heterostructures possess outstanding properties comparing with the pure 2D materials, and their properties are preserved without degradation when they are bonded together in the layerbylayer way. To date, many efforts have been made to obtain van der Waals (vdW) heterostructures. It is worth noting that the blue phosphorene (blueP)based vdW heterostructures such as blueP/TMDs [8,9,10] and blueP/graphene [11] have attracted increasing attention due to their excellent electronic and optical characteristics.
Among the abovementioned 2D semiconductor materials, blueP monolayer has been prepared by epitaxial growth on Au (111) substrates for the first time in 2016 [7]. Z. Zhang et. al. predicted the epitaxial growth of blueP monolayers on GaN (001) substrates, and proposed an unconventional “halflayer” growth mechanism. It is also pointed out that blueP is more stable on the surface of GaN (001) due to the chemical affinity between phosphorus and gallium and the good lattice matching [12]. BlueP, consisting of a vertically corrugated yet single layer of phosphorus atoms, attracts intense research interest due to its superb properties such as sizable bandgap and high mobility [13, 14]. In addition, gGaN, as a novel 2D material, can be synthesized experimentally by means of a migrationenhanced encapsulated growth (MEEG) technique [15]. Theoretical simulation has shown that gGaN is a semiconductor with an indirect bandgap, which can be efficiently manipulated by an external electric field [16]. Like other 2D materials, gGaN can also be hydrogenated and halogenated conveniently. All these studies have shown that gGaN is an alternative 2D semiconductor for applications in many important fields in the future. The lattice parameter of gGaN could match well with blueP, which indicates that blueP/gGaN is an ideal material system for the construction of heterostructures, as well as an excellent inserting layer for tuning of their electronic properties by the interlayer interaction. In this regard, it matters to investigate the electronic and optical properties of the blueP/gGaN vdW heterostructures. However, few researches have been investigated to study the properties of blueP/gGaN vdW heterostructures [17, 18].
In this work, the electronic structural properties and the variation tendency of the bandgap energy (E_{g}) with the vertical external electric field (E_{ext}) in the blueP/gGaN vdW heterostructures are evaluated and conducted by using the firstprinciples calculations with vdWcorrected exchangecorrelation functional.
Computational Methods
The band structures and electrical properties of the monolayer and bilayer blueP/gGaN vdW heterostructures have been investigated using the Cambridge Serial Total Energy Package (CASTEP) [19], which is based on the density functional theory (DFT) [20, 21] in a planewave basis set with the projector augmented wave (PAW) method potential [22, 23]. The generalized gradient approximation (GGA) with the PerdewBurkeErnzerhof (PBE) [24] function is adopted to describe the electrons exchangecorrelation energy. Since the GGAPAW approximation usually underestimates the E_{g} of semiconductors, the hybridization functional HSE06 is carried out to correct them. The effect of vdW interaction [25] is described by the Grimme’s DFTD2 method. Here, a 500 eV cutoff energy for the plane wave basis was set to ensure the convergence of total energy. A vacuum thickness of 20 Å along the Z direction of the blueP/gGaN heterostructures is added to eliminate the interaction with the spurious replica images. The atomic positions are optimized until the convergence tolerance of the force on each atom is smaller than 0.001 eV/Å. The first Brillouinzone integration is used by a fine grid of 7 × 7 × 1 for the structure optimization and 21 × 21 × 1 for electronic state calculation.
Results and Discussion
Several structures shown in our previous work have been studied as a benchmark to obtain the most stable structure of the bilayer heterostructures [18]. The optimized lattice constants are 3.25 Å and 3.20 Å for bilayerblueP and gGaN, respectively, whose values are in agreement with the reported studies [9, 26]. The lattice mismatch is about of 2% only [18]. In order to obtain the minimum energy configuration and evaluate the thermal stability of the structures, the blueP layer is moved relating to the gGaN layer and the lowest energy configuration is found by finite amounts δ_{x/y}. The evolution of the total energy difference as a function of δ_{x} and δ_{y} is shown in our previous studies [18]. Figure 1a shows the atomic structures of side and top view of bilayerblueP on gGaN. The optimum stacking mode of blueP bilayers is consistent with the previous paper [27]. Figure 1b demonstrates the relation between the binding energy (E_{b}) at the interface and the interlayer distance of blueP and gGaN (d_{blueP/gGaN}). Its definition has been described in detail in our previous studies [18]. The E_{b} is about 49 meV for the singlelayer blueP with an equilibrium distance of 3.57 Å. For the bilayer, the binding energy is almost the same as that of the single layer, whereas the equilibrium distance is 3.52 Å. Those binding energies have the same magnitude order as other vdW crystals, such as BP/graphene [E_{b} = 60 meV] [11], blueP/graphene [E_{b} = 70 meV] [6], and bilayer blueP [E_{b} = 25 meV] [27].
Figure 2ab displays the band structures of monolayer blueP/gGaN heterostructure and bilayer blueP/gGaN heterostructure, with E_{g} of 1.26 eV and 1.075 eV calculated by using GGA, respectively. For the HSE06 method, the E_{g} is 2.2 eV and 1.91 eV, respectively. For both heterostructures, the minimalenergy states in the conduction band are near M point and the maximalenergy states in the valence band are at K point, the two points are not at the same crystal momentum in the Brillouin zone. Thus, the bandgap is an indirect band gap for both semiconductor heterostructures. The E_{g} of monolayerblueP/gGaN heterostructure decreases 0.63 eV compared with the monolayerblueP (1.89 eV), while the E_{g} of bilayerblueP (1.118 eV) shrinks 0.043 eV in contrast to bilayerblueP/gGaN heterostructure. The band bending can be achieved from the difference between the Fermi levels of the blueP with the gGaN system and the freestanding blueP [28]: ΔE_{F} = W − W_{P}, where W is the work function of the composed system (blueP/gGaN), and W_{P} is the work function of the pristine blueP. The ΔE_{F} of − 1.17 eV and − 0.81 eV for the monolayerblueP/gGaN heterojunctions and the bilayerblueP/gGaN heterojunctions are obtained respectively, as shown in Fig. 2c, d. As one can see, the type of the energy band alignment is the staggered gap (type II) at the interfaces for all the monolayerblueP/gGaN heterostructures and the bilayerblueP/gGaN heterostructures.
The heterostructure is often subjected to an external electric field to tune its electronic properties while applied to nanoelectronic devices. In order to study the influence of the E_{ext} on the electronic structure, the band structures are calculated with different E_{ext} for the blueP/gGaN heterostructures. As reported in previous work, the geometrical structure of the heterostructure can be neglected, but the band structure changes greatly under different E_{ext} [29]. Figure 3a shows the evolution of the E_{g} as a function of the E_{ext} from − 1.0 eV/Å to 1.0 eV/Å. The direction of E_{ext} from top (gGaN layer) to bottom (blueP layer) is taken as the forward direction. It is clearly shown that monolayerblueP/gGaN and bilayerblueP/gGaN heterostructures exhibit a bandgap modulation with the E_{ext}. For monolayerblueP/gGaN, in the case of the forward E_{ext}, the E_{g} increases linearly with the increasing E_{ext} ≤ 0.4 eV/Å (Lincrease range). The monolayerblueP/gGaN obtains its maximum E_{g} when E_{ext} = 0.5 eV/Å and shows little change when E_{ext} is in the range 0.4 < E_{ext} < 0.6 eV/Å (saturation range), which enhances the band offsets so as to promote the separation of electronhole pairs. The initial enlargement in E_{g} is attributed to the counterbalance of E_{ext} to some extent by the builtin electric field (E_{int}). The E_{g} comes to a linear decrease range with increasing E_{ext} > 0.6 eV/Å (Ldecrease range). Thus, the heterostructure shows a metal behavior when it is subjected to a stronger electric field. This is originated from the dielectric breakdown as well as charge tunneling. In contrast, the E_{g} declines linearly with increasing E_{ext} (Ldecrease range) under a reverse E_{ext}, caused by the conduction band minimum (CBM) band edge shifting toward to the valence band maximum (VBM). However, when E_{ext} = − 0.7 eV/Å, the bandgap begins to decrease sharply, which may be due to the breakdown. When E_{ext} < − 0.8 eV/Å, the blueP/gGaN heterojunction experiences a transition from semiconductor to metal (metal range). These results reveal that both E_{g} and semiconductor to metal transition of the blueP/gGaN heterostructure is dependent on electrostatic gating, which could be used in highperformance electronic and optoelectronic devices. In addition, the effect of E_{ext} on the E_{g} between the bilayers of blueP and gGaN heterostructure is the same as the single layer but with a smaller electronic field for transition from semiconductor to metal.
To explore the effect of electric field on the band structure, the relation between the energy band structures and the external electric field are calculated. The band structures of the monolayerblueP/gGaN heterostructures with E_{ext} of 0.3 eV/Å, 0.5 eV/Å, − 0.3 eV/Å, and 0.7 eV/Å are shown in Fig. 3b–e. In Fig. 3bc, under the 0.3 eV/Å and 0.5 eV/Å of E_{ext}, the E_{g} increases to 1.651 eV and 1.757 eV. This indicates the quasiFermi level of the gGaN monolayer is shifted downward, and the quasiFermi level of blueP monolayer is lifted upward. However, in Fig. 3de, for the − 0.3 eV/Å and − 0.7 eV/Å of E_{ext}, the E_{g} decrease to 0.888 eV and 0.49 eV. The quasiFermi level of gGaN moves upward, and the quasiFermi level of blueP moves downward. The results show that the bandgap varies linearly with the applied vertical E_{ext}, indicating a giant Stark effect [30]. Upon applying a vertical E_{ext}, the subband states of the valence and conduction valence would undergo a mixing, leading to a fieldinduced splitting of the electronic levels. The electrostatic potential difference induced by the external field considerably changed the electronic structures near the Fermi level [31].
Figure 4a–d shows the isosurface of charge accumulation (with color in orange) and depletion (light green), which exhibits the change of charge density of the blueP/gGaN heterojunction with the E_{ext} value of 0.3 eV/Å, 0.5 eV/Å, − 0.3 eV/Å, and − 0.7 eV/Å, respectively. Upon applying a forward E_{ext}, as exhibited in Fig. 4ab, positive charges (holes) tend to transfer from blueP layer to gGaN layer, and negative charges (electrons) transfer from gGaN to blueP layer. At the same time concurrently, one can see that the chargetransfer amount is more than 0.3 eV/Å when the electric field is 0.5 eV/Å. Essentially, a positive external electric field orients the charge along the direction of the stress field, restricting the charge to the atomic plane, but leaving the charge in these planes, thereby facilitating the transfer of the charge from blueP to gGaN. In contrast, the negative E_{ext} induces electrons to accumulate/deplete at the opposite side, as visualized in Fig. 4cd. Mainly negative external electric fields position the charge back towards the stress field and thus transfer the charge from gGaN to blueP. Accordingly, the quasiFermi level of gGaN monolayer and E_{VBM} rise, while the quasiFermi level of blueP monolayer and E_{CBM} decrease, resulting in a linear reduction on bandgap. Simultaneously, electrons are transferred from blueP to gGaN under a reverse E_{ext}. It is found that the amount of the transferred charge increases with the increase of electric field intensity.
To make it clear that how E_{ext} modulates the electronic property, the integrated charge density difference of the monolayerblueP/gGaN heterostructure as a function of the perpendicular distance is calculated, displayed in Fig. 4e. The positive values in Fig. 4e indicate charge accumulation, and the negative values represent charge depletion. For E_{ext} = 0, the charge density difference of the heterostructure is obtained by ∆ρ = ρ_{heterostructure}−ρ_{gGaN}−ρ_{blueP}. The change of the planeaverage charge density difference at interfaces indicates that the electrons were transferred from the gGaN layer to blueP layer across the interface, whereas the holes remained in the gGaN side. The surface averaged differential charge with an electric field is calculated for 0.3 eV/Å and − 0.3 eV/Å. The E_{ext} can exert influence on transferring charges in the heterostructure. It can be described as [29]
where \( \int {\rho}_{E_{\mathrm{ext}}}\left(x,y,z\right) dxdy\ \mathrm{and}\int {\rho}_{E_0}\left(x,y,z\right) dxdy \) are the charge density at (x, y, z) point in the supercell of the monolayerBP/gGaN heterostructure with and without E_{ext}, respectively. The direction of charge transfer induced by the negative (blue line) E_{ext} is opposite to that of the positive (red line) E_{ext}. The integrated charge density quantitatively illustrates that the amount of transferred charges increases with the strength of the E_{ext}. The value of the charges transfers for the blueP/gGaN heterostructure with 0.3 eV/Å of E_{ext} is larger than that of 0 eV/Å and − 0.3 eV/Å, because the positive external electric field localizes the charges along the direction of the applied field, confining the charges to gGaN planes.
In order to distinguish the contributions of blueP and gGaN in the band structure, the projected state density of the heterostructures is calculated and shown in Fig. 5a. It can be seen that the contribution of VBM mainly comes from the gGaN, and the entrainment contribution is mainly from the blueP. Figure 5b displays the isosurface of charge accumulation and depletion of the monolayer blueP/gGaN and bilayerblueP/gGaN under 0.5 eV/Å and 0.7 eV/Å external field, respectively. Due to the dielectric breakdown of the bilayerblueP/gGaN at 0.7 eV/Å external field, the current relathed the charge transfer would have saturated under the increasing external field, which is in accordance with that in Fig. 3a.
Conclusion
In summary, the structural and electronic properties of the monolayerblueP/gGaN and bilayerblueP/gGaN vdW heterostructures are investigated by using firstprinciple calculations. The results show that the monolayerblueP/g GaN heterostructure is an indirect band gap semiconductor with intrinsic type II band alignment. The band offset and E_{g} of monolayerblueP/gGaN and bilayerblueP/gGaN can be continuously tuned by E_{ext}, and the relation between E_{g} and E_{ext} indicates a Stark effect. The E_{g} becomes zero at − 0.8 and 0.9 eV/Å for monolayerblueP/gGaN, and − 0.5 and 0.7 eV/Å for bilayerblueP/gGaN, indicating a transition from semiconductor to metal.
Abbreviations
 2D:

Twodimensional
 BlueP:

Blue phosphorene
 BP:

Black phosphorene
 CASTEP:

Cambridge Serial Total Energy Package
 CBM:

Conduction band minimum
 DFT:

Density functional theory
 GGA:

Generalized gradient approximation
 GGaN:

Graphenelike GaN
 MEEG:

Migrationenhanced encapsulated growth
 PAW:

Projector augmented wave
 PBE:

PerdewBurkeErnzerhof
 TMDs:

Transition metal dichalcogenides
 VBM:

Valence band maximum
 vdW:

van der Waals
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Acknowledgements
The authors are grateful to Dr. Xiaodong Yang from Nanjing University, Prof. Shengzhan Lu and Prof. Tianxing Wang from Henan Normal University for their help on the DFT calculation. This work is supported by the HighPerformance Computing Center of Henan Normal University.
Funding
This work is supported by the NSFC nos. 11404100 and 11304083, the Young Scholar Foundation of Henan Normal University no. 5101029470616, and the surplus foundation for vertical scientific research projects of Henan Normal University no. 5201029120301. This work is also supported by the China Scholarship Council (nos. 201608410308 and 201608410415).
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The datasets generated during and/or analyzed during the current study are available from the corresponding author on request.
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JG and ZZ designed the simulation, analyzed the data, and wrote the paper. HL, HW, and CL checked the manuscript. All authors read and approved the final manuscript.
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Correspondence to Zhongpo Zhou.
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Keywords
 Heterostructure
 Blue phosphorene
 Graphenelike GaN
 External electric field
 Electronic properties