Journal of Nanomaterials

Volume 2019, Article ID 6960787, 8 pages

https://doi.org/10.1155/2019/6960787

## Gap Prediction in Hybrid Graphene-Hexagonal Boron Nitride Nanoflakes Using Artificial Neural Networks

^{1}University of Bucharest Faculty of Physics, Materials, and Devices for Electronics and Optoelectronics Research Center, 077125 Magurele, Ilfov, Romania^{2}Horia Hulubei National Institute for Physics and Nuclear Engineering, 077126 Magurele, Ilfov, Romania^{3}School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik, Iceland

Correspondence should be addressed to G. A. Nemnes; or.cubinu.acizif.dilos@senmen

Received 6 December 2018; Accepted 2 May 2019; Published 16 May 2019

Academic Editor: Bo Tan

Copyright © 2019 G. A. Nemnes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The electronic properties of graphene nanoflakes (GNFs) with embedded hexagonal boron nitride (hBN) domains are investigated by combined ab initio density functional theory calculations and machine-learning techniques. The energy gaps of the quasi-0D graphene-based systems, defined as the differences between LUMO and HOMO energies, depend not only on the sizes of the hBN domains relative to the size of the pristine graphene nanoflake but also on the position of the hBN domain. The range of the energy gaps for different configurations increases as the hBN domains get larger. We develop two artificial neural network (ANN) models able to reproduce the gap energies with high accuracies and investigate the tunability of the energy gap, by considering a set of GNFs with embedded rectangular hBN domains. In one ANN model, the input is in one-to-one correspondence with the atoms in the GNF, while in the second model the inputs account for basic structures in the GNF, allowing potential use in upscaled systems. We perform a statistical analysis over different configurations of ANNs to optimize the network structure. The trained ANNs provide a correlation between the atomic system configuration and the magnitude of the energy gaps, which may be regarded as an efficient tool for optimizing the design of nanostructured graphene-based materials for specific electronic properties.

#### 1. Introduction

The absence of an electronic gap in pristine graphene hinders many of the expected applications based on the field effect. Graphene nanopatterning is one way to tune the electronic and transport properties, and this can be achieved by reducing the dimensionality [1–4], by drilling periodic arrangements of holes [5, 6], by embedding hexagonal boron nitride (hBN) [7–12], or by combining any of these. Graphene nanoribbons (GNRs) and graphene nanoflakes (GNFs), typically passivated with monovalent species like hydrogen or halogen atoms, are two examples of quasi-1D and quasi-0D graphene systems, respectively, which attracted a lot of attention in the past few years. GNRs can have a metallic or semiconducting behavior depending on the lateral width and edge type: armchair or zigzag. In contrast to GNRs, where only the edge states may influence the electronic properties, in GNFs these are markedly influenced by both edge and corner states and, in general, by the different possible shapes [13, 14]. In addition, GNFs may be functionalized, which further extends the range of the electronic, optical and, magnetic properties.

GNFs can be produced by bottom-up approaches, where the synthesis takes place in solution by mechanical extrusion, using magnetic field alignment and thermal annealing [15, 16] or by top-down methods, using techniques like e-beam lithography [17], plasma etching [18], or a cationic surfactant-mediated exfoliation of graphite [19]. Besides the many applications envisioned for nanoelectronics and spintronics [20], more recently, novel applications also indicate the role of GNFs for biological recognition [21]. Therefore, the methods for an efficient investigation of multiple configurations of GNFs and related structures are highly demanded.

In the past few years, machine-learning (ML) techniques are gaining ground in the field of condensed matter. They have been developed to predict the band gaps in solids [22, 23], while they also provide new clues in crystal structure prediction [24, 25]. They can be used to bypass the Kohn-Sham equations by learning energy functionals via examples [26] or predicting DFT Hamiltonians [27]. The generic aim is to develop less expensive and faster methods to calculate the system’s properties. To this end, the methodology contained in PROPhet [28] provides a general framework for coupling machine learning and first-principles methods. ML techniques can also provide more insights about the physical properties of a system. The usefulness as a universal descriptor of grain boundary systems was pointed out [29], potentially indicating which building blocks map to particular physical properties. ML techniques can also achieve high accuracies, the prediction errors of molecular machine-learning models being below that of the hybrid DFT error [30]. High-throughput DFT calculations in connection with ML techniques, as well as some of the problems, challenges, and future perspectives are illustrated in a recent review [31].

Regarding graphene systems, ML techniques have been employed in several studies, e.g., for obtaining an accurate interatomic potential for graphene [32], for searching the most stable structures of doped boron atoms in graphene [33], for investigating the influence of GNF topology [34], and for predicting accuracy differences between different levels of theory [35], as well as for the prediction of interfacial thermal resistance between graphene and hBN [36].

In this paper, we investigate the electronic properties of hybrid graphene-hBN nanoflakes, using combined DFT and ML methods. We construct the distribution of gap energies using ab initio DFT calculations, as LUMO-HOMO differences, which depend on the size and position of the hBN domains within the GNF. Given the large number of possibilities of setting the hBN domains, extensive DFT calculations are typically required, with a significant computational cost. Instead, we develop artificial neural network (ANN) models able to reproduce the energy gaps with high accuracies, which significantly reduce the computational effort. We test our ANN models against reference gap values obtained by DFT and discuss the optimal conditions for the network structure.

#### 2. Model Systems and Computational Methods

We consider GNFs with embedded hBN domains, passivated with hydrogen, as indicated in Figure 1. The hBN domains are rectangular-shaped regions containing an equal number of boron and nitrogen atoms. In this way, the systems retain an intrinsic semiconducting behavior, without a net chemical doping. The embedded rectangular hBN is randomly positioned in the graphene nanoflake. The widths and heights of the rectangular hBN regions are extracted from a flat distribution so that the entire graphene nanoflake can be replaced by BN. The systems analyzed here have a total of 200 atoms, of which atoms are stemming from graphene/hBN and hydrogen atoms. For the investigation of the electronic properties, a number of 900 nonequivalent systems are generated.