First-principles study of the structural and electronic properties of BN-ring doped graphene L. Caputo V.-H. Nguyen and J.-C. Charlier

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First-principles study of the structural and electronic properties

of BN-ring doped graphene

L. Caputo, V.-H. Nguyen and J.-C. Charlier

Institute of Condensed Matter and Nanosciences,

Universit´e catholique de Louvain (UCLouvain),

Chemin des ´etoiles 8, B-1348 Louvain-la-Neuve, Belgium

arXiv:2210.14715v1 [cond-mat.mtrl-sci] 26 Oct 2022

Abstract

Since advanced Silicon-based device components are moderately chemically tunable, doped

graphene has emerged as a promising candidate to replace this semiconducting material in ﬂexible

miniaturized electronic devices. Indeed, heteroatom co-doping (i.e. with boron and/or nitrogen)

is an appealing strategy to tune both its structural and electronic properties, possibly inducing

a band gap in graphene. However, presently synthesized BN-doped carbon-based materials are

randomly doped, leading their electronic properties not to be reproducible. Using ﬁrst-principles

techniques, the present study investigates the periodic doping of graphene with borazine-like rings

in order to search for an entirely new class of BCN hybrid 2D materials exhibiting high stabilities

and optimized band gaps for opto-electronic applications. Ab initio calculations show that BN-

ring doped graphene displays cohesive energies comparable with benchmark ideal periodic BCN

systems (such as BC3, C3N4, BC2N) with a decreasing linear trend toward high concentrations

of BN-rings. Band gaps of BN-ring doped graphene systems are calculated using many-body

perturbation techniques and are found to be sensitive to the doping pattern and to be considerably

larger for high concentration of BN rings exhibiting the same orientation. These predictions suggest

that BN-ring doped graphene materials could be interesting candidates for the next generation of

optoelectronic devices and open new opportunities for their synthesis using chemical bottom-up

approaches.

I. INTRODUCTION

Nowadays, the design of new materials is a fundamental issue driven by the need to

improve existing technology devices for better performance and enhanced safety. Currently,

the majority of opto-electronic devices are based on doped inorganic semiconductors (i.e.

Si) [1]. Their doping allows the systematic tuning of the band alignment at the interface

of semiconductors, increasing its conductivity since substitutional dopant atoms donate

mobile charge carriers. However, Si-based devices have numerous drawbacks, such as

high production cost, stiﬀness, and size limitations that hinder the prospect of current

technology transitioning into ﬂexible and miniaturized devices. Moreover, they exhibit

indirect band gap, low carrier mobility, and are at best only moderately tunable, which

limits the possibility of band alignment. For all of the aforementioned reasons, eﬀorts have

been spent in order to search for new replacing materials [2, 3]. Graphene has emerged

as an excellent candidate for this role thanks to its remarkable properties, such as atomic-

layer thickness, large surface area, high carrier mobility, ﬂexibility, as well as high thermal

and chemical stability [4]. Indeed, its electronic properties are characterized by a band

degeneracy that occurs at the two points (K, K’) at the corners of the hexagonal Brillouin

zone of graphene with a corresponding linear energy dispersion, resulting in the formation of

Dirac cones [5]. This speciﬁc electronic behavior leads to a very small on-oﬀ current ratio that

makes graphene unsuitable for conventional electronic applications. Essentially, exfoliated

graphene exhibits no band-gap [6] thus requiring post-processing to be implemented in

opto-electronic devices and light-triggered applications. Diﬀerent approaches have been

investigated to eﬃciently open a band gap in graphene, such as quantum conﬁnement

within the fabrication of nanoribbons [7] or based on its speciﬁc deposition on diﬀerent

substrates [8, 9]. However, these methodologies do not allow the systematic and controllable

tuning of the electronic properties of graphene. Consequently, fusing sp2-C scaﬀolds with

isoelectronic and isostructural BN-domains has emerged as an appealing strategy to modify

both its electronic and structural properties. Indeed, BN-based materials are chemically

inert and are thus used as dielectric spacer layers in van der Waals heterostructures or

opto-electronic devices [10]. In contrast to graphene, the presence of two diﬀerent atoms

in the two sublattices of h-BN precludes the inversion symmetry, resulting in degeneracy

lifting at the Dirac points in the Brillouin zone. Consequently, BN-based materials are

characterized by large band gaps (around ∼6eV in its pristine form[11]) which strongly

restrain their implementation as semiconductors in electronics.However, doping graphene

with BN domains permits the opening of a band gap. In particular, the honeycomb lattice of

graphene is formed by two Carbon atoms (labeled as A and B, respectively) in its primitive

cell. Each A(B)-type Carbon atom is surrounded by three other B(A)-type ones thus forming

two symmetrical-triangular sublattices. The symmetry between these two sublattices leads

to the gapless character of pristine graphene [12]. Consequently, the incorporation of

Boron and Nitrogen atoms can induce an on-site energy asymmetry in these two sublattices

(i.e. chiral symmetry breaking) that eventually opens a band gap at the Dirac points.

Within this conceptual approach, speciﬁc doping patterns can be used to tune the electronic

properties, thus inducing a wide range of band gaps in BN-doped graphene. Despite the

integrity of each individual phase being maintained, allowing easier fabrication, the current

state-of-the-art is still far from a targeted synthesis of BN-doped 2D materials exhibiting

speciﬁc and controlled properties. In fact, the existing BN-doped carbon-based materials

are not periodically doped, leading to non-reproducible properties [13]. More speciﬁcally,

exploitable materials featuring precise doping patterns of B, N and atoms are particularly

diﬃcult to achieve since atom segregation prevails [14, 15] resulting from the large binding

energy between boron-nitrogen and carbon-carbon atoms. In fact, to our knowledge, only

one example of BN-doped covalent network featuring a regular doping pattern has been

obtained so far through surface-assisted reaction [16]. Consequently, an open challenge in

the fabrication of functional single-layer semiconducting materials is to gain control of their

structural and electronic properties in a controllable and reproducible manner. In order

to achieve this goal, preliminary screening of BN doping patterns is necessary to support

the development of new synthetic strategies for BNC nanomaterials. Using theoretical

modelling, diﬀerent parameters such as the position, the distance of the doping unit, and

even the orientation can be easily tuned in order to investigate the corresponding eﬀect on

the properties of the material. In this work, state-of-the-art DFT calculations are performed

on several BN-doped graphene monolayers using borazine (BN)3doping units in order to

predict the corresponding structural and electronic properties of novel BNC monolayers.

After evaluating the stability of these BN-ring doped graphene when considering diﬀerent

doping parameters, accurate band gap values are predicted using beyond DFT techniques

in order to propose potential candidates to be implemented in optoelectronic nanodevices.

Lastly, the disorder related to ring location and rotation is also investigated to estimate its

eﬀects on the electronic properties of BNC materials.

II. METHODOLOGY

Theoretical modelling was based on density functional theory (DFT) calculations with the

projector-augmented wave method [17] and plane waves basis as implemented in the Vienna

Ab initio Simulation Package (VASP) [18, 19]. The generalized-gradient approximation

of Perdew Burke and Ernzherof [20] has been used for the exchange-correlation density

functional. Convergence threshold for total energy and forces were set to 10−5eV and below

0.03 eV/

A on each atom, respectively. All calculations have been performed using 500 eV as

kinetic energy cut-oﬀ. A k-point sampling of 18x18x1 has been used for pristine graphene.

To sample multiple BN concentrations and patterns, graphene supercells of diﬀerent sizes

have been constructed, with accordingly scaled and converged k-point samplings for every

system. In every model, atomic positions of all atoms have been allowed to relax in the

supercell. Graphene unit cell has been relaxed starting from experimental parameters [21]

using 10

A of vacuum in order to avoid spurious interactions along the z-direction and the

obtained theoretical lattice parameters deviate ∼0.5% from the experimental ones.

Regarding graphene doped with BN segregated islands, a 10x10 supercell has been

considered in order to ensure suﬃcient separation and to avoid spurious coupling between

BN islands. The cohesive energy of each atomistic model has been calculated as follows:

Ecoh =−EBN C +nCEC+nBEB+nNEN

ntot

(1)

where Ecoh is the cohesive energy, EC,EBand ENare the total energies of isolated Carbon,

Boron and Nitrogen atoms respectively while nC, nBand nNrepresent the corresponding

number of atoms in the atomistic model, ntot being the total number of the atoms that form

the BNC system.

In order to predict accurate band gaps and to avoid their usual DFT underestimation,

many-body perturbation theory calculations [22] employing screened Couloumb interaction

were performed without self-consistency in Green’s function (G0W0approximation) using

Quantum Espresso [23] with norm conserving pseudo-potentials [24] and YAMBO code [25].

Plasmon-pole approximation for the dielectric function was used and a truncated Coulomb

potential approach was employed in the z-direction to avoid spurious interactions between

periodically repeated images [26]. Moreover, the Random Integration Method was also used

in order to avoid numerical divergences that could be present in many-body calculations

on low-dimensional systems [25]. Cutoﬀ energies for both exchange and correlation parts

of the self-energy were converged for each model ranging from 50 – 70 Ry and between 10

– 13 Ry respectively. The number of bands used for each calculation was converged using

the Bruneval-Gonze terminator [27], which permits faster convergence with respect to the

number of empty bands.

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First-principlesstudyofthestructuralandelectronicpropertiesofBN-ringdopedgrapheneL.Caputo,V.-H.NguyenandJ.-C.CharlierInstituteofCondensedMatterandNanosciences,UniversitecatholiquedeLouvain(UCLouvain),Chemindesetoiles8,B-1348Louvain-la-Neuve,Belgium1AbstractSinceadvancedSilicon-baseddevicecomponent...

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First-principles study of the structural and electronic properties of BN-ring doped graphene L. Caputo V.-H. Nguyen and J.-C. Charlier

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