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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.

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 [

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 [

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 [

Regarding graphene systems, ML techniques have been employed in several studies, e.g., for obtaining an accurate interatomic potential for graphene [

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.

We consider GNFs with embedded hBN domains, passivated with hydrogen, as indicated in Figure

A typical graphene nanoflake with an embedded rectangular hBN domain. The edges are passivated with hydrogen. Each system contains

The DFT calculations are performed using the SIESTA code [

Based on the DFT results, we implement ANN models able to reproduce the gap energy for similar systems from a new set. The ANNs are standard fully connected backpropagation neural networks implemented using the FANN library [

For training, we employ the iRPROP algorithm of Igel and Husken [

The trained ANNs are tested on a set of 100 new examples and the predicted gaps are compared to the reference values obtained by DFT calculations. We use the

GNFs are quasi-0D systems with a discrete energy spectrum, where the gap energy is typically influenced by their geometry, passivation, and nanopatterning. By embedding hBN in GNFs, which is a wide band-gap isomorph of graphene, it is expected that the gap energy has a strong variation. Particularly in finite systems, the position and shape of the embedded rectangular hBN domain, closer to the edges or at the center of the GNF, significantly influences

We first investigate the variation of

The reference DFT gap vs. the BN fraction

Next, we investigate the accuracies in predicting the energy gaps for the proposed ANN models. In ^{−5} is reached in ∼400 steps. Running the ANN on the test systems, one obtains

Predicted ANN gap vs. reference DFT gap, for typical fully connected networks with three layers: (a)

In the second method, labeled

The final ANN configuration following the training phase depends on the assigned random initial weights. Consequently, the accuracy of the output results obtained by running the test examples is subject to the initialization procedure. In order to see how robust are the obtained results, we construct histograms using an ensemble of 2000 trained ANNs. The results are shown in Figure ^{−6} when training ANNs with

Histograms of

Method 1

Method 2

Comparatively, by employing

Histograms of

The electronic properties of GNFs with embedded hBN domains were investigated using combined DFT and ML techniques. Using DFT calculations, we constructed the energy gap distribution for a set of systems with different rectangular hBN shapes. The collected data was used to train two types of ANNs. In

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was supported by the Romanian Ministry of Research and Innovation under the project PN 19060205/2019 and by the Romania-JINR cooperation project.