# Novel Van Der Waals Heterostructures Based on Borophene, Graphene-like GaN and ZnO for Nanoelectronics: A First Principles Study

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{2}and MoSe

_{2}, as well as WS

_{2}and WSe

_{2}[24,25,26,27,28]. Metal oxides, in particular zinc oxide and titanium dioxide, as well as third group semiconductor nitrides, such as gallium, aluminum, and indium nitride, are promising materials for creating UV radiation photodetectors [29]. Among the ways to implement UV radiation sensors, preference is given to detection devices based on photodiodes with a Schottky barrier [30,31,32,33] formed by a metal–semiconductor contact. Such contacts are predominantly fabricated on the basis of van der Waals heterostructures containing graphene. In particular, experimental and theoretical studies have been carried out for such van der Waals heterostructures as graphene/MoS

_{2}[34], graphene/boron nitride [35], graphene/InSe [36], MoTe

_{2}/MoS

_{2}[37], graphene/phosphorene, and heterostructures based on phosphorene and MoSe

_{2}allotropes [38].

_{2}N [45], borophene/MoSe

_{2}, and borophene/WSe

_{2}[46] have already been proposed.

## 2. Methods and Approaches

#### 2.1. Atomistic Models of van der Waals Heterostructures

_{x}= 3.204 Å and L

_{y}= 5.55 Å, and the initial translation vectors of the ZnO unit cell are L

_{x}= 3.205 Å and L

_{y}= 5.5516 Å. Among the allotropic forms of borophene, we chose a triangulated borophene (tr-B) with high energy stability and geometric features that allow it to be combined with GaN and ZnO monolayers [51]. The unit cell of tr-B is originally set by means of atomic positions obtained from the data reported by Peng et al. [52]. The translation vectors of the tr-B unit cell are L

_{x}= 1.613 Å; L

_{y}= 2.864 Å. The close match between the lattice parameters of tr-B and GaN (1.613 Å (3.226 Å) and 3.204 Å, respectively, mismatch ~1%), tr-B and ZnO (1.613 Å (3.226 Å) and 3.205 Å, respectively, mismatch ~1%) makes it possible to create layered heterostructures with minimal mechanical stresses in the plane of the structure. Figure 1 and Figure 2 show the process of overlaying 2D monolayers during the formation of atomistic models of tr-B/GaN and tr-B/ZnO heterostructures with expanded rectangular cells. The original supercell of the tr-B/GaN heterostructure is shown in Figure 1c. It has optimized translation vectors L

_{x}= 3.35 Å and L

_{y}= 6.105 Å. The extended fragment of the tr-B/GaN supercell (see Figure 1a) was obtained by a threefold increase in the vector L

_{x}and twofold increase in the vector L

_{y}of the original supercell. The original supercell of the tr-B/ZnO heterostructure is shown in Figure 2c. Its translation vectors are L

_{x}= 3.28 Å and L

_{y}= 5.83 Å. The extended fragment of the tr-B/ZnO supercell (see Figure 2a) was obtained similarly to an extended fragment of the tr-B/GaN supercell. The distance between the tr-B and GaN monolayers along the Z-axis was 2.91 Å (see Figure 1b), between the tr-B and ZnO monolayers were 2.51 Å (see Figure 2b).

_{b}per atom. The calculation was carried out according to the following equation:

_{tr-B/GaN(ZnO)}is the total energy of the tr-B/GaN (tr-B/ZnO) heterostructure, E

_{tr-B}is the total energy of the isolated layer of triangulated borophene, E

_{GaN(ZnO)}is the total energy of the isolated GaN(ZnO) monolayer, N is the number of atoms in the heterostructure. According to the calculation results, the binding energy for a tr-B/GaN supercell is ~−0.05 eV/atom, and for a tr-B/ZnO supercell, it is ~−0.08 eV/atom. The negative value of the binding energy indicates that the tr-B/GaN and tr-B/ZnO heterostructures are energetically stable and, therefore, can be implemented in practice. In addition, in terms of energy stability (value of binding energy), they are superior to a number of other heterostructures based on GaN and ZnO monolayers, for example, MoSSe-g-GaN and WSSe-g-GaN heterostructures by almost two times [53], and ZnO/g-GeC heterostructures by more than six times [54].

#### 2.2. Calculation Details

_{b}is the bias voltage, e is the electron charge, h is Planck′s constant, f(E-μ

_{L/R}) are the Fermi–Dirac distribution functions for the left (L) and right (R) electrodes, respectively, μ

_{L/R}= E

_{F}± V

_{b}/2 is the chemical potential of the left (L) and right (R) electrodes, which shifted upwards (downwards) relative to the Fermi energy E

_{F}, T(E,V

_{b}) is the quantum mechanical probability of electrons passing through the channel (transmission coefficient), which can be expressed as follows

_{b}), G

^{†}(E,V

_{b}) are the retarded and advanced Green′s functions describing the contact with the electrodes, Γ

_{L}(E), Γ

_{D}(E) are the level broadening matrices for the left (L) and right (R) electrode. Level broadening matrices for each of the electrodes are defined as

_{L/R}are the self-energy matrices of the left (L) and right (R) electrodes. Green′s matrices are calculated as:

_{C}is the overlap matrix of atomic orbitals of the conducting channel, E is the electron energy; H

_{C}is the Hamiltonian of the conducting channel.

## 3. Results and Discussion

#### 3.1. Electronic Structure of tr-B/GaN and tr-B/ZnO Heterostructures

_{x}(Г–X, S–Y, Г–S). A linear dispersion relation is observed along the Г–X, S–Y, and Г–S paths, which is characteristic of triangulated borophene (Figure 4b). Consequently, the GaN monolayer, which plays the role of a kind of substrate for borophene, does not make a decisive contribution to the electronic structure of the tr-B/GaN heterostructure. In the k

_{y}direction (X–S, Y–Г), the energy bands near the top of the valence band and the bottom of the conduction band are flat, which corresponds to a larger effective mass of charge carriers in this direction. Near the top of the valence band in Г–X, S–Y, Г–S paths, the dispersion law is close to isotropic parabolic, which is typical for the energy bands near the top of the valence band of GaN (Figure 4c). On the whole, the presence of band dispersion anisotropy in the electronic structure of tr-B/GaN should be noted.

_{x}direction) and Г–S paths. Interestingly, the linear dispersion relation is typical for borophene in the entire k

_{x}direction (Г–X, S–Y, and Г–S, see Figure 6b), while for the tr-B/ZnO heterostructure it mainly has a place in the G–X path, both near the bottom of the conduction band and near the top of the valence band. In the S–Y and Г–S paths, the linear dispersion relation is observed only at the bottom of the conduction band, while in the valence band there is a tendency to transition from a linear dispersion relation to a parabolic one, and hence to a nonzero effective mass.

#### 3.2. Electrical Properties of tr-B/GaN and tr-B/ZnO Heterostructures

_{12}/MoS

_{2}[46], SeMoS/SMoS, and SMoSe/SMoS [67] van der Waals heterostructures used as a Schottky contact. The comparison results showed that at the same voltages, the current values in the β

_{12}/MoS

_{2}MoS

_{2}/WSe

_{2}/graphene, SeMoS/SMoS, and SMoSe/SMoS heterostructures are no more than a few nanoamperes, while the current values in the tr-B heterostructures/GaN and tr-B/ZnO is measured in tens of microamperes. In addition, the β

_{12}/MoS

_{2}heterostructure in terms of binding energy is two times inferior to the tr-B/GaN heterostructure and three times inferior to the tr-B/ZnO heterostructure. Therefore, it can be predicted that tr-B/GaN and tr-B/ZnO van der Waals heterostructures can also be competitive as Schottky barriers for use in various nano- and optoelectronic devices.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The process of constructing atomistic models of van der Waals tr-B/GaN heterostructure: top view (

**a**) and side view (

**b**) of an extended supercell fragment; the original supercell of tr-B/GaN heterostructure (

**c**) marked with a red box in (

**a**).

**Figure 2.**The process of constructing atomistic models of van der Waals tr-B/ZnO heterostructures: top view (

**a**) and side view (

**b**) of an extended supercell fragment; the original supercell of tr-B/ZnO heterostructure (

**c**) marked with a red box in (

**a**).

**Figure 3.**Schematic representation of a conducting channel (scattering region) enclosed between two electrodes as part of tr-B/GaN and tr-B/ZnO vertical heterostructures for current transfer along the zigzag (

**a**) and armchair directions (

**b**) of GaN/ZnO monolayer.

**Figure 4.**Band structure of the tr-B/GaN van der Waals heterostructure (

**a**) and its constituent monolayers of triangulated borophene tr-B (

**b**) and gallium nitride GaN (

**c**). In (

**a**), the top of the valence band is highlighted in red, and the bottom of the conduction band is highlighted in blue.

**Figure 6.**Band structure of the tr-B/ZnO van der Waals heterostructure (

**a**) and its constituent monolayers of triangulated borophene tr-B (

**b**) and zinc oxide ZnO (

**c**). In (

**a**), the top of the valence band is highlighted in red, and the bottom of the conduction band is highlighted in blue and green.

**Figure 8.**I–V curves of the tr-B/GaN heterostructure for current transfer along the armchair (

**a**) and zigzag (

**b**) edges of a GaN monolayer.

**Figure 9.**I–V curves of the tr-B/ZnO heterostructure for current transfer along the armchair (

**a**) and zigzag (

**b**) edges of a ZnO monolayer.

**Figure 10.**Transmission coefficient T(E) in the cases of current transfer along the zigzag and armchair directions for (

**a**) tr-B/GaN and (

**b**) tr-B/ZnO heterostructures.

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**MDPI and ACS Style**

Slepchenkov, M.M.; Kolosov, D.A.; Glukhova, O.E.
Novel Van Der Waals Heterostructures Based on Borophene, Graphene-like GaN and ZnO for Nanoelectronics: A First Principles Study. *Materials* **2022**, *15*, 4084.
https://doi.org/10.3390/ma15124084

**AMA Style**

Slepchenkov MM, Kolosov DA, Glukhova OE.
Novel Van Der Waals Heterostructures Based on Borophene, Graphene-like GaN and ZnO for Nanoelectronics: A First Principles Study. *Materials*. 2022; 15(12):4084.
https://doi.org/10.3390/ma15124084

**Chicago/Turabian Style**

Slepchenkov, Michael M., Dmitry A. Kolosov, and Olga E. Glukhova.
2022. "Novel Van Der Waals Heterostructures Based on Borophene, Graphene-like GaN and ZnO for Nanoelectronics: A First Principles Study" *Materials* 15, no. 12: 4084.
https://doi.org/10.3390/ma15124084