explore various remarkable properties of these structures
experimentally [21,23,24].
In this paper, using first-principles calculations, we inves-
tigate the defect and edge modification effects on the elec-
tronic properties of hexagonal armchair GNFs. More
importantly, based on their novel properties, we propose a
FET model, and find that its ON/OFF ratio can reach 10
5
,
which is a tremendous enhancement as compared with that
less than 10
3
in previous works [15,25]. Meanwhile, we also
design a bipolar field-effect spin-filtering (BFESF) device,
which can provide completely spin-polarized currents with
tunable spin polarizations simply by applying a gate voltage.
Therefore, it is possible to offer an effective manipulation
and detection on the carrier’s spin orientation, which was
considered to be the major challenge of spintronics [26,27].
2. Method
The geometry optimizations and the calculations of elec-
tronic properties are performed by first-principles method
based on the density functional theory (DFT) combined with
the non-equilibrium Green’s function (NEGF) technique
[28,29], which has been confirmed that they are able to give
results agreeing quantitatively well with experiments
[30,31]. All of the calculations are implemented in Atomistix
ToolKit (ATK). The local density approximation (LDA) or local
spin density approximation (LSDA) is used as the exchange–
correlation potential [32], the wave function is expanded by
a single-zeta plus polarization (SZP) basis for H atoms, and
double-zeta plus polarization (DZP) basis for other atoms.
The k-point sampling is 5, 5 and 100 in the x, y, and z direc-
tion, respectively. Here z is the transport direction. At the
same time, 150 Ry was used as the cutoff energy for the grid
integration and the convergence criterion for the total energy
is 10
5
.
For all models studied, a 10 A
˚
vacuum slab is used to elim-
inate interactions between the model and its neighboring
‘‘images’’, and before calculations of electronic properties,
the entire geometry of model is first optimized until all resid-
ual forces on each atom are smaller than 0.05 eV/A
˚
. Once the
convergence in self-consistency calculations is achieved, the
current through a device is computed by the Landauer-like
formula [33,34]. For simplicity, the Fermi level of systems is
set to zero.
3. Results and discussion
The size of the flake is described by the parameter N
a
, and the
N
a
-GNF means that a hexagonal armchair-edged GNF has N
a
hexagonal cells in its each side, Fig. 1(a) shows 4-GNF as an
example. The total number of carbon atoms in a GNF is [18N
a
(N
a
1) + 6], and the length of its side is L =(3N
a
2)a, where
a = 0.142 nm is the C–C bond length. Thus there are 222 carbon
atoms in 4-GNF, and its side length is 10a. To achieve a geomet-
ric stability, carbon atoms at each side have to be passivated by
other chemical species, typically by H atoms, as shown in
Fig. 1(a). We take such a structure as a starting point, firstly,
the comparative studies on its electronic properties and spin
magnetism after different functionalizations are performed,
and based on these findings, then, potential applications for
developing novel nanodevices are explored further.
3.1. Electronic structure of functionalized hexagonal
armchair GNFs
3.1.1. Hexagonal defect effects
The previous woks [35,36] showed that the geometrical
defects have a significant influence on the electronic proper-
ties of 1D GNRs. Therefore, we first consider the geometrical
defect effects on GNFs by taking 4-GNF-H as an example.
Due to much stronger quantum confinement and finite-size
effects in the 0D GNF than that in 1D nanoribbons [37–39],
one can expect that more exceptional electronic and mag-
netic properties can be exhibited in the presence of antidot
defects. As an example, only one hexagonal defect (antidot)
is introduced, as shown in Fig. 1(c). For the convenience of
description, we define the defective 4-GNF-H as the 4-N
r
,
where N
r
= 0, 1, 2, 3, and 4 is the number of carbon-chain rings
removed from the interior of the 4-GNF-H. As displayed in
Fig. 1(a), the red (green, blue, and violet) carbon-chain ring
corresponds to the first (second, third, and fourth) removed
one, which makes the 4-GNF-H become a ring-shape struc-
ture. Its geometrical feature is that outer edges are all arm-
chair-type, while inner edges are all zigzag-type and also
passivated with H atoms, which is an unexplored structure
and expected to have an unusual physical properties. The cal-
culated energy spectra of 4-N
r
at spin-unpolarized non-mag-
netism (NM) state are shown in Fig. 1(b). It can be clearly
seen that the magnitude of the HLG (the highest occupied
molecular orbital (HOMO)-the lowest unoccupied orbital
(LUMO) gap) changes in an obviously oscillatory manner with
the size of the hexagonal defect. How to understand of such a
property? The ring-shaped structure, as shown in Fig. 1(c), has
the 6-fold rotational symmetry and can thus be viewed to be
composed of six arms. Each arm is a quadrilateral flake. For
4-N
r
(N
r
= 0, 1, 2, 3, and 4), the number of carbon atoms N in
each arm is 37, 36, 33, 28, and 21, obviously showing an
odd–even alteration with increasing the ring size. Considering
p electrons, (N 1)/2 degenerate orbitals are fully occupied
and the next higher orbital are half fully occupied when N is
odd, therefore, the Fermi level is located at the centre of this
higher orbital, leading to a metallic property. However, N/2
degenerate orbitals are fully occupied when N is even so that
the Fermi level falls into the gap between N/2 and N/2 + 1 orbi-
tals, resulting in a semiconductoring property. On the other
hand, when six arms are merged to a ring-shaped structure,
there always exist interactions between arms, in particular,
stronger couplings occurs for one site in one arm with other
five equivalent sites. As a result, the degeneracy for energy
levels located at the Fermi level is eliminated and a small
gap occurs. More importantly, there exist 60 turns in the
ring-shaped structure, the propagating direction of electron
waves would be altered in succession when electrons transfer
in a ring, namely, a substantial scattering at the corners
happens, whichof the flake is described by the induces a
larger gap. This effect is combined with ones discussed above
to make larger gaps occur for structures 4–1 and 4–3, and
smaller gaps for others, showing an oscillatory HLG
unambiguously.
CARBON 69 (2014) 142– 150 143