Tuning the electronic structure and thermodynamic properties of hybrid graphene-hexagonal boron nitride monolayer
Graphical abstract
Introduction
The number of research reports on two-dimensional (2D) materials is on the rise due to their potential applications to the next generation of electronic and energy conversion devices [1], [2], [3], [4]. Graphene, a monolayer of graphite, is the first 2D material to be isolated in 2004 by micromechanical cleavage [5], and one of the most studied due to its fascinating properties. The electronic band structure of graphene shows a linear dispersion relation near the Dirac point [6], which gives rise to many of its unique properties, such as extraordinarily high thermal conductivity and very large charge carrier mobility exceeding those of conventional semiconductors [2]. These features combined with a range of other attractive physical and electronic properties, including high surface area, excellent optical transparency, and high mechanical strength, make graphene a versatile optoelectronic material suitable for numerous applications. However, graphene lacks a band gap [7], an essential component in semiconductors for device control. Consequently, a significant effort in graphene research has been channeled to creating an effective band gap in the system.
The discovery of graphene and characterization of its unique properties have led to vigorous research on other 2D materials [8], [9]. Among them is hexagonal boron nitride (h-BN), a structural analog of graphene with alternating boron (B) and nitrogen (N) atoms in its hexagonal lattice. As it is the case with graphene, h-BN possesses very good mechanical properties [10] and excellent thermal conductivity [11], Furthermore, it remains stable in an inert environment even at 2700 °C and shows good thermal shock resistance to vibrations from the electrical signal [12]. h-BN is resistant to chemical corrosion and wetting and can thus be efficiently used as ultrathin protective coating for corrosion protection of metals. Unlike graphene with its semi-metallic character, h-BN is an insulator with a band gap of 6.0 eV [13]. The large band gap of h-BN limits its direct integration for use as a replacement for silicon in electronic devices.
The existing techniques for creating a band gap in graphene are hydrogenation [14], chemical adsorptions [15], [16], [17], chemical substitution [7], [18], [19], [20], deposition on epitaxial substrates [21], [22], and superstructure fabrication [23], [24]. These approaches adversely affect the inherent properties of graphene. The hydrogenation and chemical adsorption on graphene change its hybridization from sp2 to sp3 leading to buckling and reduction in electrical conductivity of the system. Secondly, a band gap can also be created in graphene when it is deposited on an epitaxial substrate (like SiC [21] or Al2O3 [22]). However, the band gap is not tunable, and structural changes occur due to the significant lattice mismatch between graphene and the underlying substrate. Moreover, with this technique, it is difficult to control the morphology and the surface energy of graphene. Graphene can be made into superstructures such as quantum-dots and nanoribbons to create a finite band gap in it via quantum confinement. Yet, such structures are difficult to make with top-down approaches (like etching and lithography) since their fabrication requires creating uniform widths and edges which are less than 10 nm. Next, chemical substitution (heteroatom doping) is considered an effective approach for creating a finite band gap in graphene. However, carbon is in group IV of the periodic table, and it quite challenging to find elements with the right atomic size to substitute for carbon within the carbon network of the 2D system. Boron and nitrogen are known as suitable heteroatoms for the doping of graphene due to their proximity to carbon in the periodic table. Nevertheless, random doping of graphene with N or B atoms increases its formation energy, and at a high concentration, the doped system becomes unstable. Despite these recent advances, a more robust method for band gap opening in graphene awaits exploration.
Due to the insignificant lattice mismatch (roughly 2% [25]) between graphene and h-BN, there are growing reports on combining directly the two 2D materials to form a lateral heterostructure with controllable domain sizes of h-BN and C phases. It is thought that merging the two extraordinary materials with distinct physical properties could be a promising route for solving a band gap limitation in graphene and h-BN, thereby forming an effective 2D semiconductor for a device application. The earliest attempt to synthesize a graphene/h-BN hybrid system, which consists of h-BN and C phases, was made by Ci et al. [26] They employed chemical vapor deposition (CVD) with a two-step approach, and got a large-scale layer of h-BNC which made up of randomly distributed patches of h-BN and C with compositions extending from pure graphene to h-BN. Levendorf et al. [27] have also recommended “patterned regrowth” synthetic technique which allows for spatial control of the shape and the size of graphene and h-BN domains in the hybrid system. Soon after these studies, there have been several reports on the syntheses and characterization of graphene/h-BN hybrids [28], [29], [30], [31], [32], [33], [34]. It is worth mentioning that the interface between graphene and h-BN domains in the hybrid system is either a zigzag (ZZ) or an arm-chair (AC) type of interface [6], [35]. It has been observed that the former frequently dominates the experimentally grown graphene/h-BN hybrid [31], [36]. These different types of interfaces differently affect the electronic character of the hybrid system. With an AC linking edge, the hybrid forms a semiconductor, whereas with a ZZ linking edge it exhibits semimetallicity [37], [38], [39].
In tandem with the experiments, extensive theoretical studies within the framework of density functional theory, GW, GW plus Bethe-Salpeter equation (BSE), and equilibrium molecular dynamics have been performed to calculate various physical properties of the hybrid system. Electronic [39], [40], [41], [42], [43]. Transport [44], [45], optoelectronic [46], magnetic [47] and thermal [48] properties have all been explored. The electronic properties of graphene doped with patches of boron nitride (BN) have recently been studied. It has been demonstrated that the band gap size is not sensitive to the size of BN domains but rather to their concentration [41]. In another study, the effect of edge structures (ZZ or AC) and of the shape and size of BN domains were investigated [42]. The authors claim that a band gap is opened regardless of the edge structures, and the size of the gap depends on the width of the carbon wall among the neighboring BN quantum dots. Contrary to the aforementioned structure, the electronic properties of graphene nanoribbons with a zigzag edge embedded in a h-BN sheet have been reported to depend on the size of the graphene domains: it has been predicted that a critical width of the ribbon is required for the hybrid system to exhibit semimetallicity [39]. In different studies [43], [47] the effects of the shape, size and the arrays of graphene flakes on the electronic and the magnetic properties were studied. It has been revealed that the electronic gap and the magnetic properties can be altered by controlling the shape and size of the graphene flakes. Similarly, the band gap and the optical absorption spectra of graphene/h-BN lateral heterostructure can also be tuned by the domain size of the graphene [46]. Using molecular dynamics simulations, Kinaci et al. [48] studied the thermal conductivity of BN-graphene stripe superlattices and of the structures composed of BN (graphene) quantum dots embedded in graphene (BN). They demonstrated that the edge structure and spacing of the interface in the material, strongly affect the thermal conductivity. Moreover, for the stripe superlattices, the ZZ interface leads to a higher thermal conductivity (parallel to the interface) than AC structure, whereas the perpendicular conductivity is less susceptible to the edge structure effect. The mechanical and the electronic properties of the stripe superlattices are also sensitive to the interface types and structures. Chen et al. [40] claimed that with an AC or a ZZ type of interface, the tensile strength of the hybrid material nearly equals to that of pure graphene while in the case of the disorientated interface, the tensile strength depends on the disorientation angle. Also, with the tensile strain slightly increased in one direction, the band gap of the system with the ZZ interface remains unchanged, while a non-monotonic change of the band gap is observed with respect to the AC interface. Based on the interface structure effects, Eshkalak et al. [49] have shown that an interface with C-B bonds produces enhanced mechanical strength while C-N bonds at the interface lead to a higher band gap.
All these studies have suggested the possibility of integrating graphene/h-BN hybrid in nano-devices with well-tailored physical properties. However, the research in this hybrid material is far from being exhausted. So far, the effect of graphene domain size on the electronic, magnetic, mechanical, optical and transport properties of the hybrid system has been considered, while the thermodynamic properties have not been explored. It is important to elucidate the effect of graphene domain size on the thermodynamic quantities (such as specific heat capacity at a constant volume, entropy and Helmholtz free energy) since it is a useful parameter to optimize the thermal conductivity of the hybrid system. It is well known that popular versions of density functional theory (DFT) in the form of local density approximation (LDA) and generalized gradient approximation (GGA) intrinsically underestimate the Kohn-Sham band gap of semiconductors. For the accurate description of Kohn-Sham band gaps, hybrid functionals, which describe exchange with a blend of the exact nonlocal HF and GGA, have been formulated. As most of the previous studies on the electronic properties of the hybrid graphene/h-BN system have been done at the level of the generalized gradient approximation (GGA), it appears worth considering to revisit the electronic structure of this material using a higher level of theory (such as hybrid functional), to get a more accurate band gap of the system with respect to the variation of graphene (h-BN) domain size. Therefore, the aims of this study was to investigate the effect of graphene (h-BN) domain size on the electronic and the thermodynamic properties of lateral graphene/h-BN hybrid. By varying the size of graphene domain in the hybrid, we expect the thermodynamic properties to change responsively. Thus, our results would serve as useful guidelines for the future fabrication of the 2D hybrid systems and devices with precisely tailored properties.
Section snippets
Computational methods
First-principles calculations, within the framework of DFT, were performed with the plane-wave self-consistent field (PWSCF) code of the QUANTUM ESPRESSO (QE) package [50]. For the electron–ion interaction, the projected augmented wave (PAW) [51] method was used in all calculations. The local density approximation (LDA) [52] and Perdew, Burke, and Ernzerhof (PBE) of the generalized gradient approximation (GGA) [53] were employed as the exchange–correlation functionals. While the former was
Structural models
The primitive unit cells of both graphene and h-BN contain two atoms (in the case of h-BN it is one B and one N atom) defining two complimentary sublattices. The atoms in the two systems are packed into a hexagonal lattice. Fig. 2 shows the optimized geometry of a 6 × 6 supercell of graphene and that of h-BN. The calculated (PBE) optimized lattice constant and the bond length (C–C) of graphene are 2.46 Å and 1.42 Å, respectively, whereas the corresponding values of 2.50 Å and 1.45 Å (B-N bond)
Conclusions
A first-principles study of the electronic structures, lattice dynamics, structural, and thermodynamic properties of graphene/h-BN hybrid has been presented. The calculations of the electronic structures were done at the level of GGA-PBE and HSE06. The lattice dynamics was done at the level of LDA under the harmonic approximation to obtain the temperature-dependent thermodynamic properties. The results of our calculations of the properties of graphene and h-BN are in good agreement with
CRediT authorship contribution statement
Okikiola Olaniyan: Conceptualization, Software, Investigation, Writing - original draft. Lyudmila Moskaleva: Supervision, Resources, Writing - review & editing. Rabi’atu Mahadi: Investigation. Emmanuel Igumbor: Validation, Writing - review & editing. Abdulhakeem Bello: Visualization, Methodology.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to acknowledge the support and resources from the Center High Performance Computing (CHPC), South Africa.
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