Theoretical Study on the Electronic Properties of Two-Dimensional Covalent Triazine Frameworks/As van der Waals Heterostructures

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Introduction
Since the successful isolation of black phosphorous [1], the group-V elements of two-dimensional (2D) substances have been largely researched because they have signifcant physical properties [2][3][4][5]. Monolayer arsenic (As), a standard group-V 2D substance, has been synthesized recently [6]. Recent research suggests that monolayer gray As has a buckled honeycomb crystal structure and is an indirect band-gap semiconductor, contingent on both indirect-direct and semiconducting-metallic transitions under the external electric feld or strain [6,7]. On the other side, organic 2D covalent triazine frameworks (CTF), featured by the crystalline extended organic confgurations including covalently bonded building entities, have also attracted recent eloquent consideration [8][9][10]. 2D CTF exhibits semiconductor features built by trimerization reaction of carbonitriles and utilized triazine ring (C 3 N 3 H 3 ) as the building units. Aside from photocatalysis, 2D CTF has been employed in electronic and optoelectronic properties due to their adjustable band-gap and the correlated structure between their geometric structure and electronic properties [11,12]. Noted that 2D As and CTF share the same hexagonal crystal structures, and the lattice parameters of CTF are approximately equal to two times those of As, making it applicable to ft CTF/As heterostructures or superlattices in the experiment.
Recently, van der Waals heterostructures (vdWh), where one layered low-dimensional confguration is stacked on the other with the aid of vdW forces, have been built experimentally and theoretically and utilized to establish electronic and optoelectronic devices with novel physical attributes [13][14][15][16][17][18][19][20][21]. For example, theoretical research by Wei et al. [22] suggested that the external strain could constantly tune the electronic structures of the GaS/GaSe vdWh including the indirect band-gap. Our group demonstrated that the germanane/antimonene vdWh endures semiconductingmetallic transitions under external electric felds and transitions from type-II to type-I band alignment (BA) under the in-plane biaxial strain [23]. We also found that the transitions from type-III to type-II and type-II to type-I BA could be conformed to carbon nanotubes/graphene nanoribbons one-dimensional vdWh under axial strains or external electric felds [24]. In particular, vdWh utilizing 2D As or CTF has been also explored. For instance, a theoretical investigation by Su et al. [25] demonstrated that the indirect band-gap of the MoS 2 /As vdWh can be regulated by varying the interlayer distance. Another theoretical work about As/ graphene vdWh demonstrated that altering the interlayer distance can tune the Schottky barriers and contacts of vdWhs [26]. Our group studied the electronic properties of the CTF/GaS vdWh and found that external electric felds and strain can alter the band confgurations [27]. All of the above conclusions imply that stacking two 2D materials into vdWhs ofers an accessible method to build substitute artifcial materials that have enjoyable properties. Terefore, purporting a 2D CTF/As vdWh has been so engaging to see whether they can form a stable 2D CTF/As vdWh and validate their eye-catching electronic properties. Te research implements the frst-principle calculations to evaluate the structural and electronic properties of the 2D CTF/As vdWhs. Te electronic properties and the band-gap of the 2D CTF/As vdWh are adjusted by employing the in-plane biaxial strain and external electric feld.

Strategies Used for Computations
Te optimum crystal structure and electronic properties of CTF/As vdWhs are conducted by using the frst-principle calculation through the theory of density functional (DFT) as a part of the package available in the ATK simulation [28]. Te generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional is implemented to ascertain the relaxation of the crystal confguration [29,30]. Afterward, the Kohn-Sham equations are resolved by utilizing the algorithm called the PseudoDojo [31]. 100 Hartree is picked as the value of cutof energy, and a 15 × 15 × 1 Brillouin area sampling K-mesh is selected. More precise outcomes are reached by utilizing a 21 × 21 × 1 K-mesh to compute the structure of the energy band. Te relaxation is obtained by utilizing a 10 −4 eV energy measurement and the force of the residual is less than −0.01 eV/Å. An approximately 10Å thick vacuum layer is selected to evade relations with neighboring layers. vdW relations in a broad range need to be implemented to protect the vdWh, and its relational impacts are denoted by utilizing vdW-DF 2 functional [32].
Te thermal frmness of the CTF/As vdWhs is validated by running simulations called the AIMD [33], which is the ab initio molecular dynamics and is succeeded by employing the nose-thermostat methodology at a temperature of 300 K for 8 picoseconds (ps) with an increment of 1 femtosecond (fs).

Te Geometric Structure and Stability of CTF/As vdWhs.
To comprehend the electronic properties of the CTF/As vdWhs, the geometrical structure confgurations of both monolayer CTF and As are needed to be optimized frst. Te structure of a monolayer As, which contains a lattice in a hexagonal structure and zigzagging alternative confgurations based on top and side views, is depicted in Figure 1(a), respectively. Te schematic confguration of the monolayer CTF, which has a hexagonal lattice confguration from a top view is described in Figure 1(d). Te parameters of the optimal lattice were 3.629Å for the monolayer As, agreeable with theoretically attained scores of 3.61 reported by Li et al. [34]. Te parameters of the optimal lattice were 7.272Å for the monolayer CTF, agreeable with theoretically and experimentally attained scores of 7.25 and 7.3Å reported by Jiang et al. [35] and Katekomol et al. [8], respectively. Terefore, we built the CTF/As vdW heterostructure using 2 × 2 × 1 supercell for As and one cell for CTF. Te lattice mismatch was defned as follows: where a 1 and a 2 represent the lattice constants of CTF and As, respectively. Te calculated result was only ∼0.2%, indicating that the CTF/As vdW heterostructure could be easily fabricated with very little interfacial stress. Te band structures of the monolayers As and CTF are described in Figures 1 showing that the substitute CTF is a direct semiconductor including a 2.59 eV band-gap, analogous to the similar theoretically obtained score by employing the PBE approach [35]. Figure 1(c) depicts the iso-surfaces of charge density indicating the As's CBM and VBM states that are produced through the As-4p orbitals, while those indicated in Figure 1(f ) present the CTF's CBM and VBM stages that are led by the C/N-2p and N-2s, N/C-2p orbitals, respectively. To fnd the most stable structure, cases A through F, the six potential stacking orders, are employed, as depicted in Figure 2 inset. Te energy comparison indicates that case A is the most stable layout for the heterostructure. To further examine the energy stability, the formation energy (E f ) was calculated by using the following formula [37][38][39]: where E f represents the formation energy of the CTF/As vdW heterostructures, and E CTF/As , E CTF , E As , and n represent the total energy of the CTF/As vdW heterostructures, CTF, As monolayer and the number of atoms in the heterostructure (n � 23), respectively. A simulation called the AIMD is conducted at 300 K for eight ps to validate the thermodynamic frmness of the heterostructure. In order to include as many atoms as possible in the CTF/As vdWhs systems to acquire the statistical efect for temperature and to obtain the interactions among atoms adequately, the supercell of 4 × 4 × 1 is built for the As monolayers and those of 2 × 2 × 1 for the CTF monolayer and CTF/As vdW heterostructure, respectively. Figure 3 presents the complete energy oscillations versus the time increment. Figure 3 depicts the oscillation versus time increment, which is low based on complete energies (∼0.039 eV/atom) for the approaches used. Also, no distortion in the crystal confguration is compiled because of  the CTF/As view after eight ps (see inset of Figure 3). Te outcomes depict the thermal frmness of the CTF/As vdWh under real environmental conditions and at room temperature. Figure 4(a) shows the projected band structures of the CTF/As vdWh. Te heterostructure delineates the type-II BA in which the electronic states of CTF and As produce the CBM and VBM states, respectively. Also, the heterostructure contains a 1.44 eV indirect band-gap with the CBM and VBM condensed at K and Γ points. Te iso-surfaces of charge density refecting the C/N-2p and As-4p orbitals that generate the CBM and VBM states, respectively, are shown in Figure 4(b), endorsing the heterostructure with the type-II BA. To obtain a more detailed delineation of the electronic properties of the CTF/As vdWh, the plane-mean charge density disparity, along with the z-direction normal to the heterostructure, is depicted in Figure 4(c), and is represented by where ρ vdWh (z), ρ CTF (z), and ρ As (z) denote the plane-mean charge densities of the CTF/As vdWh, the original CTF, and the original monolayer As, respectively. Also, the red and blue isosurfaces delineate the depletion and accumulation of charge, respectively. It is concluded that the redistribution of the weak charge occurs in the interface region due to the small vdW interaction between the interfaces. Figure 4(d) delineates the plane-mean electrostatic potential along with the z-direction normal to the surface. It is observed that the potential of As is larger than the CTF layer. Te potential drop (ΔV) across the bilayer is 1.74 eV (see Figure 4(d)). It implies an electrostatic feld across the interface. Te underlined electric feld could greatly have an impact on the carrier dynamics and lead to an excitation behavior of CTF/ As vdWh completely diferent from that of the isolated CTF layer because it could decouple electrons from holes. Moreover, these bandgaps below are the similar ones underestimated by utilizing the HSE approach. Te estimation of the pinpoint inclination for the band properties could be done through a benchmark PBE functional, representing their physical properties. Tus, the electronic properties of the CTF/As vdWhs are obtained by employing the PBE approach while both the external electric feld and strain are employed to mitigate the cost of the computation.

Te Impact of the Vertical External Electric Field.
Both theoretical and experimental results obtained previously designate that the external electric feld could importantly have an impact on the electronic properties of the vdWh [40][41][42]. Tus, the electronic structures of the CTF/As vdWhs are validated while a vertical external electric feld upright to the CTF/As vdWhs is exerted, while CTF to As has a positive direction. Te external electric feld is changed in [−1.4, 2.0] V/Å with an increment of 0.2 V/Å. Figure 5 depicts the impact of the external electric feld on the electronic properties of CTF/As vdWhs. Te CBM is attained from CTF and situated at K points, while the VBM is attained from As and situated at Γ points in [−1.  [40,43]. Afterward, the impact of in-plane biaxial strain on the electronic structures of the CTF/As vdWhs is examined. Te parameters of a crystal lattice are altered to simulate the in-plane biaxial strain on the CTF/As vdWhs computed by where a 0 and a represent the crystal lattice parameters of vdWhs when both unstrained and strained requirements are under consideration. Te [−5% to 5%] interval with a 1% increment was picked for the outside strain. Te stability of CTF/As vdWhs under strain was obtained with the strain energy and was calculated using the following equation [44,45]: where the E s , E strained , E unstrained , and n were the strain energy, the energy of pristine heterostructures, the energy of the strained heterostructures, and the number of atoms in  Advances in Condensed Matter Physics the heterostructure (n � 23), respectively. As shown in Figure 6(b), the strain energies are a quadratic function relative to the strains of [−5% to 5%], indicating that the deformation of the CTF/As vdWhs is in the elasticity limit and the geometrical structures are stable. Figure 7 depicts the impacts of the strain on the electronic confgurations of the CTF/As vdWhs. Te CBM derived from CTF is situated at K points, while the derivation of the VBM based on As is situated at Γ points in [−5%, 1%], indicating an indirect semiconductor including the type-II BA. Te CBM derived from CTF is situated at K points, while the derivation of the VBM based on As is situated on the Γ-M line near the M points and the Γ-K line near the K point for 2%, indicating an indirect semiconductor containing the type-II BA. Both the CBM and VBM acquired from As are situated at Γ points in [3%, 5%], indicating a direct semiconductor including the type-I BA. Figure 6(b) presents their bandgaps. When the strain raised in [−5%, 1%], the band-gap raised similarly, while it decreased once the strain is boosted in [2%, 5%]. Te outcomes imply that the strain can efciently adjust the electronic properties of the CTF/As vdWhs.

Conclusion
Consequently, the electronic properties of the CTF/As vdWhs were assessed by utilizing the frst-principle calculation contingent on both external electric feld and strain. Concluded that the CTF/As vdWhs were the indirect semiconductors including a type-II BA changing in [−1. -4% -3% -2% -1% 1% 2% 3% 4% 5% Figure 7: Band structures of the CTF/As vdWhs when applying the axial strain with a 1% step, and the strains are arranged from −5% to 5% from left to right. 6 Advances in Condensed Matter Physics adjustable band-gap of the CTF/As vdWhs leads to a hopeful perspective for building a substitute nano-electronic and optoelectronic devices.

Data Availability
Te data used to support the fndings of this study are available upon reasonable request from the corresponding authors.

Conflicts of Interest
Te authors declare that there are no conficts of interest.