PHYSICAL REVIEW B 86, 075421 (2012)
N-rich B-C-N layers: From segregated alloy to solid solution
Jonathan da Rocha Martins
Departamento de F´ ısica, Universidade Federal do Piau´ ı, Campus Ministro Petrˆ onio Portela-Bairro Ininga, 64049-550, Teresina, PI, Brazil
Helio Chacham
*
Departamento de F´ ısica, ICEX, Universidade Federal de Minas Gerais, CP 702, 30123-970, Belo Horizonte, MG, Brazil
(Received 9 February 2012; revised manuscript received 20 July 2012; published 8 August 2012)
We perform a theoretical study of nitrogen-rich B-C-N graphene-type alloys through a combination of Monte
Carlo and ab initio methods. Different from the B/N = 1 limit, where both calculations and experiments indicate
segregation into BN and C regions, the simulations of the N-rich alloys result in solid solution materials, with
isolated carbon substituting boron sites of BN. We show that this is a consequence of the competition between
bond energies. As a result of the solid solution morphology, the electronic structure of N-rich alloys depict a
≈1.5 eV wide, half-filled carbon impurity band that would result in either metallic behavior or disorder-induced
semiconducting behavior with a mobility gap.
DOI: 10.1103/PhysRevB.86.075421 PACS number(s): 61.48.Gh, 73.22.Pr, 73.22.-f
Boron-carbon-nitrogen (B-C-N) layered materials such as
graphene-type single layers,
1,2
multilayers,
3
and nanotubes
4
show electronic and transport properties that range from those
of the large-gap insulating boron nitride to those of the
semimetallic or small-gap carbon nanostructures, depending
on the B-C-N chemical composition. The degree and type of
B-C-N alloying in these materials also depend on chemical
composition. For instance, near the B/N = 1 ratio, the
materials show segregation into either graphene islands in
a planar BN matrix or BN islands in a graphene matrix,
depending on the C/BN ratio.
1,2
This is consistent with
theoretical simulations.
5
In contrast, in N-rich B-C-N materials
there are indications that the carbon atoms are diluted in the
BN matrix.
3
The optical
3
and transport
4
properties are also
strongly dependent not only on the C content, but also on the
B/N ratio.
In the present work we combine the Monte Carlo simulated
annealing and density functional methods to investigate the
effect of composition on structural and electronic properties of
B
x
C
y
N
z
alloys organized on a honeycomb lattice. We consider
carbon contents of less than 25% in the alloy, and nitrogen
contents ranging from a high concentration of 50% down to
the B/N = 1 limit. Different from the B/N = 1 limit, where
calculations
5,6
and experiments
1,2
indicate segregation into BN
and C regions, we find that the N-rich alloys show dilution of
individual carbon atoms within the boron sublattice of BN.
Also in contrast with the B/N = 1 limit, where an insulating
behavior is predicted,
5–9
we find that the N-rich alloys depict a
1.5 eV wide, half-filled carbon impurity band that should result
in either hopping conduction or metallic behavior, consistent
with recent experiments.
4,10
The methodology employed in this work consists of a
combination of Monte Carlo simulated annealing and ab initio
calculations, previously developed by us
5
to be applied to
disordered B-C-N materials. The methodology consists of the
following: For a given B-C-N chemical composition, large unit
cells (of 96 atoms, in the present work) with graphene-type
topology and periodic boundary conditions are subjected to
a Monte Carlo simulated annealing procedure that allows
for first-neighbor atom exchanges.
5
The energy functional
employed in the Monte Carlo annealing is a bond-energy
model
11
where the total energy of a given structure is given by
E
model
=
αβ
n
αβ
ǫ
αβ
, (1)
where α,β = C, B, N, and n
αβ
is the number of α,β bonds
in the structure. The parameters of the model, parametrized
from first-principles calculations,
11
are all the possible first-
neighbor bond energies, namely, ǫ
CB
, ǫ
CN
, ǫ
BN
, ǫ
CC
, ǫ
BB
, ǫ
NN
.
It has been shown that the bond-energy model of Eq. (1) allows
quantitative predictions as compared to first-principles calcula-
tions for small-unit-cell B-C-N structures,
11
as well as for large
unit cell ones.
5
In the case of B-C-N materials with B/N ratio
near unity, the simulated annealing procedure results in low-
energy, partly disordered structures with BN/C segregation,
which is consistent with recent experiments.
1,2
The electronic
structure of the final structures of the simulated annealing
procedure (or even of intermediate ones) are investigated by ab
initio calculations based on density functional theory (DFT)
12
within the generalized gradient approximation (GGA)
13
for
the exchange-correlation functional, as implemented in the
SIESTA method.
14
The geometries are fully optimized using
a conjugate gradient algorithm until all the force components
are smaller than 0.05 eV/
˚
A.
Our present analyses of the structural properties of B-C-N
were based on alloys with six different chemical compositions.
Three alloys depict carbon concentrations of 12.5%, and the
remaining three, 25%. These are consistent with carbon con-
centrations of B-C-N alloys in recent experimental studies.
3,4
Regarding the nitrogen content of the alloys, we considered
two alloys with the ideal B/N = 1 ratio, two N-rich structures
with nitrogen content of 50%, and two with intermediate
nitrogen concentrations. The chemical composition of each
alloy, and the numbers of B, C, and N atoms of the
corresponding unit cells used in the simulations, are shown
in Table I.
Figure 1 shows the atomic configurations of the unit cells
of the six alloys after the optimization using the Monte Carlo
simulated annealing process. The two alloys with the ideal
B/N = 1 ratio, shown in the left column of the figure,
clearly show the formation of segregated carbon and BN
075421-1 1098-0121/2012/86(7)/075421(5) ©2012 American Physical Society