nanomaterials
Article
Computational Predictions for Single Chain
Chalcogenide-Based One-Dimensional Materials
Blair Tuttle 1,2, *, Saeed Alhassan 3 and Sokrates Pantelides 1,4
1
2
3
4
*
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA;
[email protected]
Department of Physics, Penn State Behrend, Erie, PA 16563, USA
Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAE;
[email protected]
Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235, USA
Correspondence: [email protected]; Tel.: +1-814-898-6311
Academic Editor: Ho Won Jang
Received: 9 March 2017; Accepted: 2 May 2017; Published: 17 May 2017
Abstract: Exfoliation of multilayered materials has led to an abundance of new two-dimensional (2D)
materials and to their fabrication by other means. These materials have shown exceptional promise
for many applications. In a similar fashion, we can envision starting with crystalline polymeric
(multichain) materials and exfoliate single-chain, one-dimensional (1D) materials that may also
prove useful. We use electronic structure methods to elucidate the properties of such 1D materials:
individual chains of chalcogens, of silicon dichalcogenides and of sulfur nitrides. The results indicate
reasonable exfoliation energies in the case of polymeric three-dimensional (3D) materials. Quantum
confinement effects lead to large band gaps and large exciton binding energies. The effects of strain
are quantified and heterojunction band offsets are determined. Possible applications would entail 1D
materials on 3D or 2D substrates.
Keywords: nanowires; chalcogenides; ab initio calculations
1. Introduction
Thin films, including few atomic layers and monolayers, grown on substrates have been
studied for decades using methods such as molecular beam epitaxy, pulsed laser deposition, or even
simple oxidation. A breakthrough idea by Novoselov and Geim [1] in 2004 to exfoliate and study
a monolayer from a layered material, namely graphite, led to the explosive growth of new research
into two-dimensional (2D) materials, which now includes free-standing monolayers, bilayers, etc.,
fabricated in a variety of ways, but also monolayers and bilayers on substrates. The number of
2D materials with unique and unusual properties has grown rapidly and has generated enormous
interest from both a basic [2–5] and applied [3,6,7] research perspective. Two-dimensional materials
are promising for electronic [8], optical [9], catalytic [10] and other applications. Given the maturity of
techniques to grow and examine 2D materials and devices [11–14], we turn our attention to analogous
one-dimensional (1D) systems.
Since at least the discovery of carbon nanotubes, there has been great interest in material systems
in which electrons mainly propagate in only one dimension. For carbon nanotubes, semiconducting or
metallic tubes are possible depending on a tube’s bonding topology. Boron-nitride nanotubes [15] and
other nanotubes have been fabricated and studied. Moreover, wires with nanometer scale diameters
have also been grown using Si [16], Se [17] and GaAsSb [18], to name a few. One-dimensional
materials have been used in a variety of two- and three-terminal electrical devices [11,13]. Recently,
Nanomaterials 2017, 7, 115; doi:10.3390/nano7050115
www.mdpi.com/journal/nanomaterials
Nanomaterials 2017, 7, 115
2 of 11
sub-nanometer scale wires were sculpted from 2D monolayer transition-metal dichalcogenides [8].
As scaling proceeds, materials and devices made from single chain 1D systems are becoming realizable.
In chemistry of course, there exist many molecular monomers, which can be combined to form
single chain oligomers or polymers. Indeed, there has been a long history of theoretical studies
of molecular chains, including both finite and infinite systems [19–22]. There is continued interest
in polymer chains and crystalline polymers. For instance, recent studies of crystalline polymers
examined dielectric properties for a large number of carbon-based polymers [23]. Many infinite
chains are known to be stable. Early studies of S and Se chains explored the electronic and structural
properties and provided a fundamental understanding of these 1D systems [21]. Also, early theoretical
studies of polyacene and sulfur nitride infinite chains elucidated the nature of their superconducting
properties [19,24]. Motivated by the emerging possibility of 1D materials for a wide variety of
applications, we present new state-of-the-art theoretical results for chalcogenide-based 1D materials.
In this paper, we apply modern electronic structure methods to calculate a range of properties of
selected 1D materials. Given the recent interest in chalcogenide-based 2D materials [2,25,26], here we
consider chalcogenide-based 1D systems. Specifically, we examine individual chains of chalcogens
(S, Se, Te) and of silicon dichalcogenides (SiS2 and SiSe2 ), all of which are insulating. In addition,
we consider a single strand of SNH, which is insulating, and a strand of S–N, which is metallic.
Finally, for comparison, we include infinite carbon-based chains of polyphenylene (C6 H4 ) [27] and
polyacene (C4 H2 ) [19,20], which can be viewed as a single strand cut from monolayer graphene.
Carbon systems are included since these systems are well understood experimentally and theoretically
and so provide a good benchmark. We find that chalcogenide-based1D materials can in principle be
exfoliated from three-dimensional (3D) polymeric crystals with relative ease (i.e., exfoliation energies
are relatively small). While growth mechanisms are not explicitly calculated, as new 1D materials
are grown, experimentalists can use the present results to understand the fundamental versus the
growth-dependent electrical/mechanical properties. Quantum confinement effects lead to increased
band gaps and larger exciton binding energies when compared to their bulk counterparts. We also
calculate strain moduli and the deformation potentials for electrons and holes of these 1D materials.
Electronic band offsets are reported for select heterojunctions. The properties considered are critical for
applications and the prospects for applications are discussed in the context of the new results. Finally, these
results should help in the selection of materials to be synthesized based on 1D applications of interest.
2. Results
To examine the properties of 1D materials, we begin with unit cells of the corresponding bulk
orthorhombic crystals. The equilibrium lattice constant of an isolated 1D chain is found by allowing
the chain length and atomic positions to relax until a minimum energy structure is found. In Table 1,
the 1D lattice constants (ao ) are reported. The values are close to previously reported values and/or to
the c-axis of the corresponding orthorhombic 3D crystal.
The mechanical strain modulus in one dimension is defined as
Esm =
1 d2 U
L de2
(1)
where L is the periodic length of the one-dimensional material, U is the total energy of the material,
and de = dx/L is the differential strain factor. The strain modulus (Esm ) is a measure of the energy
needed to vary the lattice constant of the material. We have calculated the strain moduli for our
selected 1D materials and report the results in Table 1. The strain modulus results show a clear
trend for materials that contain chalcogens: going down the periodic column, from S to Se to Te,
the strain modulus becomes smaller, indicating weaker covalent bonding as expected. A similar but
less pronounced effect is found comparing SiS2 to SiSe2 results. As expected, the sp3 orbitals of Si
enhance covalent bonding with chalcogenides. The carbon chains considered (C6 H4 , C6 H4 ) have
notably higher strain moduli due to their strongly covalent C–C bonds. It is notable that hydrogenation
Nanomaterials 2017, 7, 115
3 of 11
of S–N results in a lower strain modulus, suggesting that the inclusion of hydrogen weakens the S–N
bonding. Figure 1 reports the iso-surfaces of the electronic charge density for S–N and SNH. Indicative
of a weakening S–N bond, the charge moves from around the S atoms in S–N to between the N and H
7, 115
3 of 11
atoms in Nanomaterials
SNH. To 2017,
be more
quantitative, the charge at the mid-point of a S–N bond is 16%
larger in
1D S–N than
in
1D
SNH.
Finally,
tellurium
is
the
most
ductile
material
considered
here
and
would
be
quantitative, the charge at the mid-point of a S–N bond is 16% larger in 1D S–N than in 1D SNH.
attractiveFinally,
for device
applications
where
strain
is inherently
part
of would
fabrication
and operation.
tellurium
is the most
ductile
material
considered ahere
and
be attractive
for device
applications where strain is inherently a part of fabrication and operation.
Table 1. Results from our calculations for extended one-dimensional (1D) materials. The 1D lattice
Table
1. Results
from our calculations
one-dimensional
materials.
The
constant (a
strain modulus
(Esm ) and for
theextended
exfoliation
energy (Eexf.(1D)
) are
reported
in1D
thelattice
first three
o ), the
(ao), the
strain
modulusenergy
(Esm) andisthe
exfoliationusing:
energyE(Eexf.=
) are reported in the first three
columns.constant
Specifically,
the
exfoliation
calculated
exf. EBulk /NBulk − E1D /N 1D where
the exfoliation energy is calculated using: Eexf. = EBulk/NBulk − E1D/N1D where NBulk
NBulk andcolumns.
N1D areSpecifically,
the number
of atoms in the bulk and 1D calculations, respectively. All the G0 W0
and N1D are the number of atoms in the bulk and 1D calculations, respectively. All the G0W0 band gap
band gap results (Egap ) are reported below. Indirect gaps are reported in parentheses in the two cases
results (Egap) are reported below. Indirect gaps are reported in parentheses in the two cases where the
where theindirect
indirect
gap
is lower
the direct
Thecolumn
last column
the deviation
of the
gap
is lower
thanthan
the direct
gap. gap.
The last
includesincludes
the deviation
of the direct
gap direct
gap versus
strain.
versus
strain.
Material
S
S
Se
Se
Te
Te
SiS
SiS2 2
SiSe
SiSe
22
CC
6H
6H
44
SNH
SNH
SN
SN
C4 H2
C4H2
Material
ao (Å)
Esm (eV/Å) Eexf. (eV/at.)
Eexf. (eV/at.)
Esm (eV/Å)
4.404
6.78
0.08
4.404
6.78
0.08
4.966
4.32
0.20
4.966
4.32
0.20
5.682
2.78
0.27
5.682
2.78
0.27
5.588
10.56
5.588
10.56
0.07 0.07
5.939
5.939
8.19 8.19
0.09 0.09
4.364
31.0731.07
0.12 0.12
4.364
4.700
3.10 3.10
0.14 0.14
4.700
4.556
5.06 5.06
0.05 0.05
4.556
2.468
50.9
0.18
2.468
50.9
0.18
ao (Å)
Egap (eV)
Dgap (eV/%)
Dgap (eV/%)
4.73 (4.60)
−0.13
4.73 (4.60)
−0.13
3.05 (3.00)
−0.06
3.05 (3.00)
−0.06
2.41
−0.05
2.41
−0.05
6.91
(6.34)
−0.02
6.91 (6.34)
−0.02
(4.92)
−0.11
5.255.25
(4.92)
−0.11
2.602.60
+0.11
+0.11
5.145.14
−0.07
−0.07
N/AN/A
N/A
N/A
N/A
N/A
N/A
N/A
Egap (eV)
Figure 1. Atomic and electronic structure for S–N and SNH2 one-dimensional (1D) systems.
Figurerepresent
1. Atomic and
electronic
structure for
S–N and
SNH2 The
one-dimensional
(1D) systems.
Grey is for
Grey regions
surfaces
of constant
charge
density.
charge density
isosurface
regions
represent surfaces
of constant charge density. The charge density isosurface is for 2.3 × 10−4
−
4
3
2.3 × 10 electrons per
Å . Large yellow, small grey and small white spheres represent S, N and
electrons per Å 3. Large yellow, small grey and small white spheres represent S, N and H, respectively.
H, respectively.
In principle, some of the 1D materials considered here can be isolated using the corresponding 3D
materials and
exfoliation
techniques.
Theconsidered
exfoliation energy
is anbe
important
In principle,
some
of the 1D
materials
here can
isolatedquantity
using for
theunderstanding
corresponding 3D
the
physics
of
a
layered
material
[28].
The
exfoliation
energies
has
been
calculated
by
comparing
the
materials and exfoliation techniques. The exfoliation energy is an important quantity for understanding
energy per atom for the single chain to the bulk material. While van der Waals interactions are difficult
the physics of a layered material [28]. The exfoliation energies has been calculated by comparing the
to capture theoretically, the results reported in Table 1 help us understand the trends and electronic
energy per
atom for
the single
chain
bulk material.
While
der
areTe
difficult
structure
of these
materials
(hereto
wethe
consider
a hypothetical
bulkvan
form
of SWaals
similarinteractions
to that of Se and
to capture
the results
in Table 1 form
helpofus3Dunderstand
the trends
electronic
fortheoretically,
comparison purposes
since reported
the room-temperature
S comprises sulfur
rings).and
The pure
systems display
the expected
trends, with
theSlowest
andtoTethat
the of Se
structurechalcogenide
of these materials
(here we
considerexfoliation
a hypothetical
bulkS having
form of
similar
highest
exfoliation
energy.
This
trend
is
expected
since
covalency
decreases
from
S
to
Se
to
Te,
and
and Te for comparison purposes since the room-temperature form of 3D S comprises sulfur rings).
electrons are free to participate in inter-chain bonding. To explore the nature of the interThe puretherefore
chalcogenide
systems display the expected exfoliation trends, with S having the lowest and
chain bonding in the pure chalcogenides, we fix the 1D and 3D coordinates found with van de Waals
Te the highest exfoliation energy. This trend is expected since covalency decreases from S to Se to
interactions and then turn off the van de Waals interaction. The exfoliation energies dramatically
Te, and therefore
to participate
in isinter-chain
explore the
decrease, electrons
suggesting are
the free
inter-chain
interaction
mainly vanbonding.
de Waals To
in character.
Thenature
silicon of the
inter-chain
bonding in the
pure
chalcogenides,
wetrend,
fix the
1Dvalues
and 3D
coordinates
found with
dichalcogenides
exhibit
a similar
but moderate
with
similar
to S. Hydrogenated
S–Nvan de
Waals interactions and then turn off the van de Waals interaction. The exfoliation energies dramatically
decrease, suggesting the inter-chain interaction is mainly van de Waals in character. The silicon
Nanomaterials 2017, 7, 115
4 of 11
dichalcogenides exhibit a similar but moderate trend, with values similar to S. Hydrogenated S–N
has a larger exfoliation energy than pure S–N, which has the lowest exfoliation energy of the systems
considered
here.2017,
Apparently,
the dipole of the N–H bond produces a larger van der Waals effect
Nanomaterials
2017,
7, 115
of than
11
Nanomaterials
7, 115
4 of411
the metallic electrons of the pure S–N. The carbon chains considered (C6 H4 , C6 H4 ) have exfoliation in
aoflarger
exfoliation
energy
than
pure
S–N,
which
has
the
lowest
exfoliation
energy
of the
systems
hashas
a larger
energy
than
pure
S–N,
which
has
theexfoliation
lowest
exfoliation
energy
of the
the middle
theexfoliation
range
found
in the
present
materials.
The
energies
reported
insystems
Table
1 are
considered
here.
Apparently,
the
dipole
of
the
N–H
bond
produces
a
larger
van
der
Waals
effect
than
considered
here.
Apparently,
the
dipole
of
the
N–H
bond
produces
a
larger
van
der
Waals
effect
than
only slightly larger than the value for graphene.
electrons
of the
pure
S–N.
The
carbon
chains
considered
C64H
4) have
exfoliation
thethe
metallic
electrons
of the
pure
S–N.
The
carbon
chains
considered
(C6(C
H64H
, C4,6H
) have
exfoliation
in in
The
Gmetallic
0 W0 band structures have been calculated for our selected 1D chains. We have checked
the
middle
of
the
range
found
in
the
present
materials.
The
exfoliation
energies
reported
in
Table
the middle
the range found
thechain
present
materials.
The
exfoliation
energies
reported
in Table
1 1are
that the
bands of
perpendicular
to in
the
direction
are
flat
indicating
that the
supercell
used
are
only
slightly
larger
than
the
value
for
graphene.
are only slightly larger than the value for graphene.
sufficiently large to eliminate interactions between neighboring chain. The 1D band structures for
The
G00W
0 band
structures
have
been
calculated
selected
chains.
have
checked
that
The
G0W
band
structures
have
been
calculated
forfor
ourour
selected
1D1D
chains.
WeWe
have
checked
that
pure chalcogenides
and the other
insulating
systems
are
reported
in
Figures
2used
andare
3, sufficiently
respectively.
the
bands
perpendicular
to
the
chain
direction
are
flat
indicating
that
the
supercell
the bands perpendicular to the chain direction are flat indicating that the supercell used are sufficiently
The band
gaps
are reported
inbetween
Table
1.neighboring
For
the pure
chalcogens,
the
valence
band
gap
is very flat.
large
to eliminate
interactions
between
neighboring
chain.
The
band
structures
pure
chalcogenides
large
to
eliminate
interactions
chain.
The
1D1D
band
structures
forfor
pure
chalcogenides
Sulfurand
and
selenium
1D
chains
both
have
valence
band
maxima
at
G
which
is
only
0.13
eV
and
0.05 eV,
and
the
other
insulating
systems
are
reported
in
Figures
2
and
3,
respectively.
The
band
gaps
are
reported
the other insulating systems are reported in Figures 2 and 3, respectively. The band gaps are reported
respectively,
higher
than
at
X.
For
all
pure
chalcogenides,
the
conduction
band
minimum
is
at
the X
in Table
1. For
pure
chalcogens,
valence
band
gap
is very
flat.
Sulfur
and
selenium
chains
in Table
1. For
thethe
pure
chalcogens,
thethe
valence
band
gap
is very
flat.
Sulfur
and
selenium
1D1D
chains
both
have
valence
band
maxima
atwhich
G which
is only
0.13
and
0.05
respectively,
higher
than
at For
X. For at
have
valence
band
maxima
at G
is only
0.13
eVeV
and
0.05
eV,eV,
respectively,
higher
than
at X.
point.both
For
the
silicon
dichalcogenides,
the
minimum
gap
is
indirect
with
the valence
band
maximum
all
pure
chalcogenides,
the
conduction
band
is the
at the
Xdirect
point.
For
silicon
dichalcogenides,
pure
chalcogenides,
conduction
band
at
X point.
For
thethe
silicon
dichalcogenides,
Γ andall
the
conduction
bandthe
minimum
near
X. minimum
Inminimum
Table 1,isboth
the
and
indirect
minimum
gaps are
gap
isthe
indirect
with
valence
band
maximum
atand
 and
conduction
band
minimum
thethe
minimum
gap
is indirect
with
thethe
valence
band
maximum
at 
thethe
conduction
band
minimum
reported
inminimum
cases where
minimum
gap
is indirect.
The hydrogenated
chains,
polyphenylene
and
near
X. Table
In Table
1, both
the
direct
and
indirect
minimum
gaps
are
reported
in cases
where
the
minimum
near
X.
In
1,
both
the
direct
and
indirect
minimum
gaps
are
reported
in
cases
where
the
minimum
sulfur nitride, have direct minimum gaps at Γ. The pure chalcogenides are semiconducting with wide
gap
is indirect.
The
hydrogenated
chains,
polyphenylene
and
sulfur
nitride,
have
direct
minimum
gaps
gap
is indirect.
The
hydrogenated
chains,
polyphenylene
and
sulfur
nitride,
have
direct
minimum
gaps
band gaps of 4.73, 3.05 and 2.41 eV for S, Se and Te, respectively. The band gap for the chalcogenides
at The
. The
pure
chalcogenides
semiconducting
with
wide
band
gaps
of 4.73,
3.05
and
2.41
at .
pure
chalcogenides
areare
semiconducting
with
wide
band
gaps
of 4.73,
3.05
and
2.41
eVeV
forfor
S, S,
are lower
as
the materials
covalency
increases.
Polyphenylene
has lower
a gap slightly
larger covalency
than sulfur.
and
respectively.
The
band
gap
chalcogenides
materials
Se Se
and
Te,Te,
respectively.
The
band
gap
forfor
thethe
chalcogenides
areare
lower as as
thethe
materials
covalency
The dichalcogenides
(SiS2 and
and
SNHlarger
are
significantly
more
insulating materials.
Generally,
increases.
Polyphenylene
has
a2 )gap
slightly
larger
than
sulfur.
The
dichalcogenides
(SiS
2 and
SiSe
increases.
Polyphenylene
hasSiSe
a gap
slightly
than
sulfur.
The
dichalcogenides
(SiS
2 and
SiSe
2) 2)
1D chains
have
larger
band gaps
and
lower dielectric
constants
than
their
bulk
counterparts.
The
effect
and
SNH
are
significantly
more
insulating
materials.
Generally,
chains
have
larger
band
gaps
and
and
SNH
are
significantly
more
insulating
materials.
Generally,
1D1D
chains
have
larger
band
gaps
and
lower
dielectric
constants
than
their
bulk
counterparts.
The
effect
is less
dramatic,
however,
is lesslower
dramatic,
however,
forthan
the
more
insulating
materials.
dielectric
constants
their
bulk
counterparts.
The
effect
is less
dramatic,
however,
forfor
thethe
more
insulating
materials.
more
insulating
materials.
Figure 2. Near gap bands are reported for several 1D insulating systems, including S, Se, and Te.
Figure
2. Near
bands
reported
several
insulating
systems,
including
S, Se,
Figure
2. Near
gapgap
bands
areare
reported
forfor
several
1D1D
insulating
systems,
including
S, Se,
andand
Te.Te.
Figure
3.
Near
bands
areare
reported
forforseveral
1D
insulating
systems,
including
SiSe
,C
Figure
3.gap
Near
gap
bands
are
reported
for
several
insulating
systems,
including
SiS
C
Figure
3. Near
gap
bands
reported
several
1D1D
insulating
systems,
including
SiSSiS
2, SiSe
2, C2,62H
46H
22,, SiSe
6 4H4
and SNH
andand
SNH
2. 2.
2 . SNH
Nanomaterials 2017, 7, 115
5 of 11
Nanomaterials 2017, 7, 115
5 of 11
To understand the electronic structure of the materials, we examine the charge densities in
To understand
the 4,
electronic
structure
the materials,
we examine
charge
densities
in a
a couple
cases. In Figure
the charge
density of
isosurfaces
are reported
for thethe
valence
band
maximum
couple
cases. In band
Figureminimum
4, the charge
density
isosurfaces
are charge
reported
for the valence
band for
maximum
and
conduction
states
of Se and
SiSe2 . The
isosurfaces
are similar
Se and
and
conduction
band
minimum
states
of
Se
and
SiSe
2. The charge isosurfaces are similar for Se and
SiSe2 , and these plots are representative of the isosurfaces of the other 1D systems studied here.
SiSe2charge
, and these
plots
are representative
of theband
isosurfaces
of the
other
1D systems
studieddistributes
here. The
The
density
isosurface
for the valence
maximum
state
indicates
that charge
charge densityto isosurface
valencebonding.
band maximum
state
indicates
thatstate
charge
distributes
perpendicular
the plane offor
thethe
Se zig-zag
The valence
band
maximum
is characterized
perpendicular
to
the
plane
of
the
Se
zig-zag
bonding.
The
valence
band
maximum
state
is
characterized
by a non-bonding p-orbital localized on the chalcogen atom. This behavior is natural for chalcogen
by a non-bonding
p-orbital
localized
the chalcogen
atom.
This
is natural
for chalcogen
atoms
with two strong
covalent
bonds.onFigure
4 also shows
that
thebehavior
conduction
band minimum
state
atoms
withlocalization
two strong on
covalent
bonds. Figure
4 also
shows along
that the
conduction
band
state
has
charge
the chalcogen
atom with
p-orbital
x-direction
where
theminimum
bond is along
has
charge
localization
on
the
chalcogen
atom
with
p-orbital
along
x-direction
where
the
bond
is
along
the x–y direction (see Figure 4). In the silicon dicalchogenides, there is also some p-orbital charge
the x–y direction
Figure
4). The
In the
silicon
dicalchogenides,
also
some p-orbital
charge
localization
on the(see
silicon
atom.
charge
localization
reportedthere
hereisare
consistent
with previous
localization
on
the
silicon
atom.
The
charge
localization
reported
here
are
consistent
with
previous
analysis for S and Se chains [21].
analysis for S and Se chains [21].
Figure 4.
4. Atomic
Atomic and
and electronic
electronic structures
structures are
are reported
reported for
for Se
Se (SiSe
(SiSe22)) valence
valence band
band maximum
maximum (VBM)
(VBM)
Figure
and conduction
conduction band
band minimum
minimum (CBM).
and
(CBM). Grey
Grey regions
regions represent
represent surfaces
surfaces of
of constant
constant charge
charge density.
density.
Large dark
dark (blue)
(blue) and
and small
small light
light (green)
(green) spheres
spheresrepresent
representSi
Siand
andSe,
Se,respectively.
respectively.
Large
Applying these chains in opto-electronic devices would require a consideration of the effects of
Applying these chains in opto-electronic devices would require a consideration of the effects of
strain on the electronic properties. The band gap versus lattice strain is reported in Figure 5 for
strain on the electronic properties. The band gap versus lattice strain is reported in Figure 5 for selected
selected chalcogenide-based 1D materials. Here, we focus on direct gap variations, which are more
chalcogenide-based 1D materials. Here, we focus on direct gap variations, which are more important
important for optical applications. We find the variation of gap to strain is linear. Table 1 reports the
for optical applications. We find the variation of gap to strain is linear. Table 1 reports the slope of the
slope of the gap variation with strain. The relative % strain is defined as 100 × Δa/ao where Δa
gap variation with strain. The relative % strain is defined as 100 × ∆a/ao where ∆a difference between
difference between the strained lattice value and ao, the minimum lattice. The band gaps vary by
the strained lattice value and ao , the minimum lattice. The band gaps vary by about 0.1 eV for each 1%
about 0.1 eV for each 1% of lattice strain. For the chalcogens, compressive strain (although difficult
of lattice strain. For the chalcogens, compressive strain (although difficult to realize) would increase
to realize) would increase the band gaps whereas tensile strain would lower the band gaps. We find
the band gaps whereas tensile strain would lower the band gaps. We find most of the band gap change
most of the band gap change is due to the variation in the conduction band minimum. This is
is due to the variation in the conduction band minimum. This is reasonable since the valence band
reasonable since the valence band edge wavefunctions are non-bonding p-orbitals (see Figure 4),
edge wavefunctions are non-bonding p-orbitals (see Figure 4), which are insensitive to variations in the
which are insensitive to variations in the bond lengths. The polyphenylene (C6H4) chains (dashed line)
bond lengths. The polyphenylene (C6 H4 ) chains (dashed line) displays the opposite band gap trend
displays the opposite band gap trend with strain because of its different chemical bonding.
with strain because of its different chemical bonding. Specifically, we find that, for polyphenylene,
Specifically, we find that, for polyphenylene, most of the lattice strain is accommodated by the single
most of the lattice strain is accommodated by the single linkage C–C bond whereas in the other cases
linkage C–C bond whereas in the other cases strain is accommodated symmetrically throughout the
strain is accommodated symmetrically throughout the system. The variation in band edges with strain
system. The variation in band edges with strain would be important when considering heterojunction
would be important when considering heterojunction device applications where significant strain
device applications where significant strain can be expected. Combining the strain moduli results
can be expected. Combining the strain moduli results above and these deformation results, one can
above and these deformation results, one can determine the strain necessary to modify the band
determine the strain necessary to modify the band edges by a desired amount.
edges by a desired amount.
Nanomaterials 2017, 7, 115
Nanomaterials 2017, 7, 115
Nanomaterials 2017, 7, 115
6 of 11
6 of 11
6 of 11
Figure
5. Direct
band
energy
(eV)versus
versusrelative
relative %
% strain,
in in
text.
TheThe
chalcogen-based
Figure
5. Direct
band
gapgap
energy
(eV)
strain,asasdefined
defined
text.
chalcogen-based
systems have positive slopes and are represented by solid lines whereas C6H4 has a negative slope and
systems have positive slopes and are represented by solid lines whereas C6 H4 has a negative slope and
is represented by a dashed line.
is represented by a dashed line.
Recently, 2D graphene nanoribbon heterojunctions have been grown and examined experimentally
Recently,
2D
graphene
heterojunctions
grown
and
examined
[16] while
2D
metal
dichalcogenide
heterojunctions
have
been examined
theoretically
[25].
In Table
2,
Figure
5. Direct
band gapnanoribbon
energy
(eV) versus
relative
% strain,
ashave
defined been
in
text. The
chalcogen-based
experimentally
[16]
2D
metal
dichalcogenide
heterojunctions
been
examined
systems
havewhile
positive
slopes
andoffset
are represented
solid
lines
whereas
C6H4 has
negative
slope and
we report
predictions
for the
band
of Te–Se,by
SiSe
2–SiS
2, and
SN–SNH
1Da have
heterojunctions.
The
represented
by averaged
a dashed
structureisand
the
local potential
ΔV) arefor
reported
in Figure
6 for of
theTe–Se,
Se–Te heterojunction
theoretically
[25].
Inplanar
Table
2, we line.
report
predictions
the band
offset
SiSe2 –SiS2 , and
while
in
Figure
7
we
report
the
interfacial
band
diagram
for
the
Se–Te
heterojunctions.
Se–Te
and
SN–SNH 1D heterojunctions. The structure and the planar averaged local potential The
(∆V)
are reported
Recently, 2D graphene nanoribbon heterojunctions have been grown and examined experimentally
SiS
2–SiSe2 heterojunctions are non-polar. The SN–SNH junction has a polar interface. The local potential
in Figure[16]
6 for the2D
Se–Te
heterojunction
while in Figure
7 we report
the theoretically
interfacial band
diagram
for
metalslope
dichalcogenide
have been
examinedinterfacial
[25]. effect,
In Table
thereforewhile
has a linear
away fromheterojunctions
the interface dipole.
Subtracting
dipole
we2,
the Se–Teweheterojunctions.
The
Se–Te
and
SiS
–SiSe
heterojunctions
are non-polar. The SN–SNH
report
predictionsband
for the
band
offset
of2Table
Te–Se,2.2 SiSe
2, and SN–SNH 1D heterojunctions. The
determine
the SN–SNH
offset
reported
in
The2–SiS
conduction
band offset for SN–SNH is 3.21
junction structure
has a polar
Thelocal
local
potential
therefore
has
a linear
away from the
and theinterface.
planar averaged
potential
ΔV) are
reported in
Figure
6 for theslope
Se–Te heterojunction
eV, which is also the Schottky barrier for this metal–insulator system. While lattice mismatch is a
while
in
Figure
7
we
report
the
interfacial
band
diagram
for
the
Se–Te
heterojunctions.
The
Se–Tereported
and
interface
dipole.
interfacial dipole
effect, we determine
thedoSN–SNH
band
concern
for Subtracting
even 2D heterojunctions
[2], single-chain
1D materials
not suffer
thisoffset
limitation
SiS
2
–SiSe
2
heterojunctions
are
non-polar.
The
SN–SNH
junction
has
a
polar
interface.
The
local
potential
in Table
2. Thejunction
conduction
forinSN–SNH
is 3.21two
eV,chains
whichwhich
is also
thediffering
Schottky
barrier for
although
atoms band
maybeoffset
needed
order to connect
have
bonding
therefore has a linear slope away from the interface dipole. Subtracting interfacial dipole effect, we
this metal–insulator
system.
While
lattice
mismatch
is
a
concern
for
even
2D
heterojunctions
topologies. For instance, phosphorous can be used to connect 1D Se and SiSe2 chains as illustrated in [2],
determine the SN–SNH band offset reported in Table 2. The conduction band offset for SN–SNH is 3.21
single-chain
materials
do not
suffer this limitation
although
atoms
maybe
needed in
Figure 8.1D
One
can use these
heterojunction
band offset
results tojunction
assess the
potential
of extended
1Dorder
eV, which is also the Schottky barrier for this metal–insulator system. While lattice mismatch is a
junctions
for
a variety
of have
applications.
We
find thetopologies.
Se–Te would
notinstance,
be suitable
for semiconductorto connect
two
chains
which
differing
bonding
For
phosphorous
can
be
concern for even 2D heterojunctions [2], single-chain 1D materials do not suffer this limitationused
insulator
because
the
are tooinsmall
but 8.
theOne
interface
of Se–P–SiSe
2 may be useful
to connect
1Dapplications
Se junction
and SiSe
asoffsets
illustrated
Figure
can use
these
2 chains
although
atoms
maybe
needed
in order to
connect
two chains
which
haveheterojunction
differing bondingband
for
electron
quantum
wells.
Overall,
given
the
lack
of
lattice
mismatch
and
their
range
band
gaps,
offset results
to assess
potential
of extended
junctions
for1D
a Se
variety
of 2applications.
We
find
topologies.
For the
instance,
phosphorous
can be1D
used
to connect
and SiSe
chains asofillustrated
in the
1D chalcogenide-based
heterojunctions
are
promising
for
a
variety
of
applications.
Figure
8. be
Onesuitable
can use for
these
heterojunction band offset applications
results to assess
the potential
of extended
Se–Te would
not
semiconductor-insulator
because
the offsets
are too1Dsmall
junctions of
forSe–P–SiSe
a variety of applications.
We for
findelectron
the Se–Tequantum
would notwells.
be suitable
for semiconductorbut the interface
may be useful
Overall,
given the lack of
Table
2. For four 2heterojunctions,
we report
the valence and conduction
band
offsets.
insulator applications because the offsets are too small but the interface of Se–P–SiSe2 may be useful
lattice mismatch and their range of band gaps, 1D chalcogenide-based heterojunctions are promising
for electron quantum wells. Overall,
given the
lack
of lattice
and their range of band gaps,
Material
VBO
(eV)
CBOmismatch
(eV)
for a variety
of applications.
1D chalcogenide-based heterojunctions are promising for a variety of applications.
Te–Se
0.44
0.20
SiSe
2–SiS2
1.00
0.42
Table 2.Table
For four
heterojunctions, we report the valence
and conduction band offsets.
2. For four heterojunctions, we report the valence and conduction band offsets.
SN–SNH2
1.93
3.21
Se–P–SiSe
2
0.13
1.72
Material
VBO
(eV) CBO
CBO
(eV)
Material
VBO
(eV)
(eV)
Te–Se
0.44
0.20
Te–Se
0.44
0.20
SiSe
2–SiS2
1.00
0.42
SiSe
1.00
0.42
2 –SiS2
SN–SNH
2
1.93
3.21
SN–SNH2
1.93
3.21
Se–P–SiSe
0.13
1.72
Se–P–SiSe
0.13
1.72
2 2
Figure 6. Atomic positions and change in local potential (eV) as a function of z-distance, in Å, for Se–Te.
Figure 6.
Atomic positions and change in local potential (eV) as a function of z-distance, in Å for Se–Te.
Figure 6. Atomic positions and change in local potential (eV) as a function of z-distance, in Å, for Se–Te.
Nanomaterials 2017, 7, 115
Nanomaterials 2017, 7, 115
Nanomaterials 2017, 7, 115
7 of 11
7 of 11
7 of 11
Figure
7. Heterojunction
band band
diagram
for the
system.
Figure
7. Heterojunction
diagram
forSe–Te
the Se–Te
system.
Figure 7. Heterojunction band diagram for the Se–Te system.
Figure 8. Atomic positions and change in local potential (eV) as a function of z-distance, in Å for the
Figure 8. Atomic positions and change in local potential (eV) as a function of z-distance, in Å, for the
Se–P–SiSe2 junction.
Figure
8. Atomic
positions and change in local potential (eV) as a function of z-distance, in Å, for the
Se–P–SiSe
2 junction.
Se–P–SiSe2 junction.
3. Discussion
3. Discussion
3. Exfoliation
Discussiontechniques may be used to isolate these chalcogenide-based 1D materials. A procedure
Exfoliation techniques may be used to isolate these chalcogenide-based 1D materials. A procedure
may may
start
fromfrom
the techniques
adhesive
exfoliation
originally
used
to isolate
graphene
[29].1D
This
method
been
Exfoliation
may
be used
tooriginally
isolate
these
chalcogenide-based
materials.
Ahas
procedure
start
the adhesive
exfoliation
used
to isolate
graphene
[29].
This method
has been
optimized
and
applied
to
other
2D
systems
[30].
Once
2D
materials
have
been
isolated,
one
may
be
able
may
start from
the
adhesive
exfoliation
originally
used to
graphene
[29].isolated,
This method
has
been
optimized
and
applied
to other
2D systems
[30]. Once
2Disolate
materials
have been
one may
be able
to use
a
transmission
electron
microscope
(TEM)
to
isolate
an
arbitrary-length
single
strand,
creating
optimized
and applied to
other 2D
systems [30].
Once
materials
have been isolated,
maycreating
be able a
to use a transmission
electron
microscope
(TEM)
to 2D
isolate
an arbitrary-length
singleone
strand,
a 1D
system.
ThisThis
TEM
technique
has has
longlong
has(TEM)
been
used
to create
single-strand
chains
ofstrand,
carbon
atomsatoms
to 1D
usesystem.
a transmission
electron
microscope
to isolate
ancreate
arbitrary-length
single
creating
a
TEM
technique
has been
used
to
single-strand
chains
of carbon
from
graphene
[31].
Another
possibility
may
be
toto
grow
chains
on
using
molecular
1Dfrom
system.
This
TEM
technique
has long
has
been
used
tosingle
create
single-strand
chains
of molecular
carbon
atoms
graphene
[31].
Another
possibility
may
be
growsingle
chains
on surfaces
surfaces
using
beam
beam
epitaxy,
other
growth
techniques,
asbe
has
implemented
tosurfaces
construct
1D molecular
structures
of [32].
from
graphene
[31].
Another
possibility
may
to been
grow
single chains
on
beam
epitaxy,
oror
other
growth
techniques,
as
has
been
implemented
to construct
1D using
structures
of GaAs
GaAs
[32].
epitaxy,Quantum
or other growth
techniques,
been implemented
to construct
1D structures
of 1D
GaAs
[32].
confinement
effects as
arehas
important
for predicting
the electronic
structure of
materials.
Quantum
confinement
effects
are
important
for
predicting
the
electronic
structure
of
1D
materials.
Quantum
confinement
effects
are
important
for
predicting
the
electronic
structure
of
1D
materials.
Selenium is a case in point. In bulk crystalline Se, we calculate the minimum direct band gap to be 1.62
Selenium
is aiscase
point.
crystalline
calculate
the minimum
minimum
direct
band
gaptotobebe
Selenium
a case
in
point.InInbulk
bulk
crystalline
Se,
we
calculate
the
direct
gap
1.62
eV, close
to
theinexperimental
estimate
of 1.8Se,
eVwe
[33].
The diagonal
components
ofband
the dielectric
tensor
1.62
eV,
close
to
the
experimental
estimate
of
1.8
eV
[33].
The
diagonal
components
of
the
dielectric
eV,are
close
theand
experimental
of 1.8
eV [33].constants
The diagonal
components
of the dielectric
tensor ~
εperpto~12
εpara ~ 20. estimate
These large
dielectric
result
in a small exciton
binding
energy
tensor
are
ε~12
~12
and
~20. In
These
large
ingap
a exciton
small
exciton
binding
perp
para
are0.02
εperp
εpara ~εmaterial.
20. These
large
dielectric
result
a small
binding
energy
~
eV
forand
the bulk
contrast,
adielectric
1D constants
chainconstants
of Se
has result
ainband
of 3.05
eV, almost
double
energy
~0.02
eV
the
bulk confined
material.
In contrast,
a in
1Dlarge
Se has
aofband
gapalmost
of For
3.05double
eV,
0.02
for value.
the for
bulk
material.
In contrast,
a 1D result
chain
of
Sechain
hasexcitonic
aofband
gap
3.05systems.
eV,
theeV
bulk
Quantum
electrons
in the
1D
instance,
almost
double
the
bulkexciton
value.confined
Quantum
confined
electrons
result
in the
1D
systems.
the1D
bulk
value.
Quantum
electrons
result
large
excitonic
1D systems.
For
Se has
a large
binding
energy,
~1.7
eV.inFor
1D
Se, in
thelarge
G0in
Wexcitonic
0the
direct
gap
is 3.05
eVinstance,
but when
For1D
instance,
1D
Se
has
a
large
exciton
binding
energy,
~1.7
eV.
For
1D
Se,
the
G
W
direct
gap
0
0
Se has a effects
large exciton
binding
energy,
eV. For 1D
Se, the
0W0 direct 1D
gapSeiswould
3.05 eVmake
but when
excitonic
are included
the
direct ~1.7
gap reduces
to 1.34
eV.GTherefore,
aisgood
3.05
eV
but
when
excitonic
effects
are
included
the
direct
gap
reduces
to
1.34
eV.
Therefore,
1D
Se
excitonic
effects
included
theBy
direct
gap reduces
to we
1.34find
eV. that
Therefore,
1DTe
Se would
would be
make
a good
absorber
in theare
visible
range.
a similar
analysis,
pure 1D
useful
as an
would
make
a
good
absorber
in
the
visible
range.
By
a
similar
analysis,
we
find
that
pure
1D
Te
would
absorber
in
the
visible
range.
By
a
similar
analysis,
we
find
that
pure
1D
Te
would
be
useful
as
an
infra-red (IR) absorber with an optical gap of 0.9 eV. Excitonic effects are smaller for the more
be infra-red
useful
as
an
infra-red
(IR)
absorber
with
an
optical
gap
of
0.9
eV.
Excitonic
effects
are
smaller
for
the
(IR)1Dabsorber
insulating
chains. with an optical gap of 0.9 eV. Excitonic effects are smaller for the more
more
insulating
1D
chains. 1D single-chain materials for applications, we should take a new look at old
insulating
1Dconsidering
chains.
When
When
considering
1D1D
single-chain
materials
for
we
should
take
newlook
look
When
considering
single-chain
materials
forapplications,
applications,
we should
take
aanew
atatold
materials.
For instance,
selenium
has had
a long history
in semiconductor
device
applications.
Selenium
oldmaterials.
materials.
For
instance,
selenium
has
had
a
long
history
in
semiconductor
device
applications.
selenium
has had
a long
history
in semiconductor
device
applications.
Selenium
rectifiersFor
areinstance,
ubiquitous
in antique
radios.
More
recently,
there has been
interest
in the electrical
and
Selenium
rectifiers
areof
ubiquitous
inselenium
antiqueMore
radios.
More
recently,
there
has been
interest
in the
rectifiers
are
ubiquitous
in antique
radios.
recently,
there
interest
in the
electrical
and
optical
properties
amorphous
(a-Se)
thin
films
forhas
usebeen
in photoconductor
devices
[34,35].
electrical
and
opticalof
properties
of
amorphous
selenium
(a-Se)
films
for could
use inalso
photoconductor
optical
properties
amorphous
selenium
(a-Se)
thin films
forthin
use
in photoconductor
devices
One-dimensional
selenium
chains
combined
with
plasmonic
materials
serve as[34,35].
efficient
devices
[34,35].
One-dimensional
selenium
chains
combined
with
plasmonic
materials
also
serve [9].
One-dimensional
chains combined
plasmonic
materials
could
also2could
serveplasmonics
as efficient
photoconductorsselenium
in nano-opto-electric
deviceswith
similar
to the current
use of
2D MoS
with
photoconductors in nano-opto-electric devices similar to the current use of 2D MoS2 with plasmonics [9].
Nanomaterials 2017, 7, 115
8 of 11
as efficient photoconductors in nano-opto-electric devices similar to the current use of 2D MoS2 with
plasmonics [9].
Lasers may also be a promising application of 1D chalcogenide-based materials. The large exciton
binding energies (mentioned above) make these materials good candidates for optically pumped lasers.
Decades ago, one-dimensional GaAs quantum wires were used for laser applications [36]. Over the
years, advances in growth techniques have reduced the diameter of such quantum wire systems [32,37].
The use of carbon nanotubes for lasing systems has also been achieved [38]. Based on the band-offsets
reported here, chalcogenide-based 1D heterojunction systems are promising for optically pumped
single-chain lasers.
4. Methods
We employ density functional theory (DFT) [39,40] and examine the properties of these materials
using the VASP computer code [41,42]. A plane-wave basis with a cutoff energy of ~300 eV was used
based on the standard projected augmented wave (PAW) potentials to treat core electrons [43,44].
Calculations were performed with the generalized-gradient corrected functional of Perdew, Becke and
Ernzerhof (PBE) [45] to treat exchange and correlation. In addition, for bulk calculations, van der Waals
(vdW) interactions were treated in a semi-empirical fashion using the method of Grimme [46].
All atomic coordinates and lattice parameters were relaxed to their equilibrium values at T = 0 K
using a force tolerance of 0.01 eV/Å.
Single strands are isolated using supercells including a vacuum of ~1.0 nm. Tests with
a larger vacuum at ~2 nm found no significant changes to the quantities reported here. We have
calculated the mechanical properties at the PBE level of theory. For electronic structure, we use
the non-self-consistent G0 W0 approximation [47,48] which accounts for the many-body electron
interactions but retains the input PBE wavefunctions. The G0 W0 quasi-particle electronic bands are
calculated for a 75 × 1 × 1 k-point mesh. From the G0 W0 quasi-particle bands, we calculate excitonic
effects with the Bethe–Salpeter equation (BSE) which accounts for the interaction of a quasi-electron
and a quasi-hole. The present calculations employ the Tamm–Dancoff approximation as implemented
in the Vienna Ab initio Simulation Package (VASP) [26]. The four highest valence bands and the
four lowest conduction bands were used as a basis for excitonic eigenstates. Employing the BSE,
we calculate direct excitation energies and intensities, which can be compared with optical absorption
experimental data. Heterojunction offsets are calculated in the standard band alignment method [49,50]
using PBE for the interface potential alignment and, consistent with recent advances [51], we employ
the G0 W0 results for the bulk band edges.
5. Conclusions
Innovation in the growth and design of 2D materials motivated the present exploration of
extended 1D materials. Specifically, there is interest in chalcogenide-based thin films including 2D
materials (e.g., SiSe). Techniques for creating molecular-scale transistors from single nanotubes [38]
and other similar advances also motivates the search for single chain 1D materials that may also be
useful in such applications.
In this study, we calculate the properties of chalcogenide-based 1D materials including S, Se and
Te along with silicon-dichalcogenides (SiS2 and SiSe2 ) and sulfur nitrides (S–N and SNH). The main
results of our study are presented in Table 1 where we report the strain moduli, the exfoliation energies,
band gaps, and gap deformation potentials. Strain moduli and band gaps decrease whereas the
exfoliation energies increase, as we consider chalcogenides going down the periodic column, i.e., S
to Se to Te. Trends found in Table 1 are explained qualitatively in terms of the covalency of bonding.
The covalent bond density is examined specifically in the case of S–N and SNH showing a weakening
S–N covalent bond with the addition of H. The band gaps and excitonic binding energies for the
insulating 1D materials considered here are found to be larger than their respective bulk counterparts.
Nanomaterials 2017, 7, 115
9 of 11
All chalcogenides have negative band deformation potentials. Finally, we consider heterojunction
band offsets for several 1D systems.
We propose that 1D chalcogenide-based materials may be isolated from the corresponding bulk
materials, which are readily available, following the procedure used to successfully isolate graphene
and single chains of carbon from graphene. Nano-opto-electronics is one promising application area for
these materials. Specifically, Se and Te may be good visible and IR absorbers, respectively. Also, the use
of 1D heterojunctions may allow the realization of optically pumped atomic-scale lasers. Overall,
the present calculations provide a view of the properties of several chalcogenide-based single molecular
chain systems, which are promising for electronic, opto-electronic and other applications.
Acknowledgments: This work was supported in part by the Gas Subcommittee Research and Development
under the Abu Dhabi National Oil Company (ADNOC) and by the McMinn Endowment at Va nderbilt University.
Calculations were performed in part on the Penn State Lion X supercomputers.
Author Contributions: All authors conceived and designed the calculations; B.T. performed the main calculations;
all authors contributed to analyzing the results and wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Novoselov, K.S.; Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Zhang, Y.; Dubonos, S.V.;
Grigorieva, I.V.; Firsov, A.A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666–669.
[CrossRef] [PubMed]
Singh, A.K.; Hennig, R.G. Computational prediction of two-dimensional group-IV mono-chalcogenides.
Appl. Phys. Lett. 2014, 105, 042103. [CrossRef]
Liu, H.; Neal, A.T.; Zhu, Z.; Luo, Z.; Xu, X.; Tománek, D.; Ye, P.D. Phosphorene: An Unexplored 2D
Semiconductor with a High Hole Mobility. ACS Nano 2014, 8, 4033–4041. [CrossRef] [PubMed]
Tran, V.; Soklaski, R.; Liang, Y.; Yang, L. Layer-controlled band gap and anisotropic excitons in few-layer
black phosphorus. Phys. Rev. B 2014, 89, 235319. [CrossRef]
Chernikov, A.; Berkelbach, T.C.; Hill, H.M.; Rigosi, A.; Li, Y.; Aslan, O.B.; Reichman, D.R.; Hybertsen, M.S.;
Heinz, T.F. Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer. Phys. Rev. Lett. 2014,
113, 076802. [CrossRef] [PubMed]
Conley, H.J.; Wang, B.; Ziegler, J.I.; Haglund, R.F.; Pantelides, S.T.; Bolotin, K.I. Bandgap Engineering of
Strained Monolayer and Bilayer MoS2 . Nano Lett. 2013, 13, 3626–3630. [CrossRef] [PubMed]
Singh, A.K.; Mathew, K.; Zhuang, H.L.; Hennig, R.G. Computational Screening of 2D Materials for
Photocatalysis. J. Phys. Chem. Lett. 2015, 6, 1087–1098. [CrossRef] [PubMed]
Lin, J.; Cretu, O.; Zhou, W.; Suenaga, K.; Prasai, D.; Bolotin, K.I.; Cuong, N.T.; Otani, M.; Okada, S.;
Lupini, A.R.; et al. Flexible metallic nanowires with self-adaptive contacts to semiconducting transition-metal
dichalcogenide monolayers. Nat. Nano Lett. 2014, 9, 436–442. [CrossRef] [PubMed]
Butun, S.; Tongay, S.; Aydin, K. Enhanced Light Emission from Large-Area Monolayer MoS2 Using Plasmonic
Nanodisc Arrays. Nano Lett. 2015, 15, 2700–2704. [CrossRef] [PubMed]
Zhuang, H.L.; Hennig, R.G. Theoretical perspective of photocatalytic properties of single-layer SnS2 .
Phys. Rev. B 2013, 88, 115314. [CrossRef]
Leonard, F.; Talin, A.A. Electrical contacts to one- and two-dimensional nanomaterials. Nat. Nano 2011, 6,
773–783. [CrossRef] [PubMed]
Bom, N.M.; Soares, G.V.; de Oliveira Junior, M.H.; Lopes, J.M.J.; Riechert, H.; Radtke, C. Water Incorporation
in Graphene Transferred onto SiO2 /Si Investigated by Isotopic Labeling. J. Phys. Chem. C 2016, 120, 201–206.
[CrossRef]
Van’t Erve, O.M.J.; Friedman, A.L.; Li, C.H.; Robinson, J.T.; Connell, J.; Lauhon, L.J.; Jonker, B.T. Spin transport
and Hanle effect in silicon nanowires using graphene tunnel barriers. Nat. Commun. 2015, 6, 7541. [CrossRef]
[PubMed]
Tuttle, B.R.; Alhassan, S.M.; Pantelides, S.T. Large excitonic effects in group-IV sulfide monolayers.
Phys. Rev. B 2015, 92, 235405. [CrossRef]
Nanomaterials 2017, 7, 115
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
10 of 11
Yin, J.; Li, J.; Hang, Y.; Yu, J.; Tai, G.; Li, X.; Zhang, Z.; Guo, W. Boron Nitride Nanostructures: Fabrication,
Functionalization and Applications. Small 2016, 12, 2942–2968. [CrossRef] [PubMed]
Cai, J.; Pignedoli, C.A.; Talirz, L.; Ruffieux, P.; Söde, H.; Liang, L.; Meunier, V.; Berger, R.; Li, R.; Feng, X.; et al.
Graphene nanoribbon heterojunctions. Nat. Nano Lett. 2014, 9, 896–900. [CrossRef] [PubMed]
Bäppler, S.A.; Plasser, F.; Wormit, M.; Dreuw, A. Exciton analysis of many-body wave functions: Bridging
the gap between the quasiparticle and molecular orbital pictures. Phys. Rev. A 2014, 90, 052521. [CrossRef]
Tellurium (Te) Effective Masses. Non-Tetrahedrally Bonded Elements and Binary Compounds I; Madelung, O.,
Rössler, U., Schulz, M., Eds.; Springer: Berlin/Heidelberg, Germany, 1998; pp. 1–6.
Kivelson, S.; Chapman, O.L. Polyacene and a new class of quasi-one-dimensional conductors. Phys. Rev. B
1983, 28, 7236–7243. [CrossRef]
Mishima, A.; Kimura, M. Superconductivity of the quasi-one-dimensional semiconductor—Polyacene.
Synth. Metals 1985, 11, 75–84. [CrossRef]
Springborg, M.; Jones, R.O. Sulfur and selenium helices: Structure and electronic properties. J. Chem. Phys.
1988, 88, 2652–2658. [CrossRef]
Lovinger, A.J.; Padden, F.J., Jr.; Davis, D.D. Structure of poly(p-phenylene sulphide). Polymer 1988, 29,
229–232. [CrossRef]
Sharma, V.; Wang, C.; Lorenzini, R.G.; Ma, R.; Zhu, Q.; Sinkovits, D.W.; Pilania, G.; Oganov, A.R.; Kumar, S.;
Sotzing, G.A.; et al. Rational design of all organic polymer dielectrics. Nat. Commun. 2014, 5, 4845. [CrossRef]
[PubMed]
Seel, M.; Collins, T.C.; Martino, F.; Rai, D.K.; Ladik, J. SNx with hydrogen impurities in the coherent-potential
approximation. Phys. Rev. B 1978, 18, 6460–6464. [CrossRef]
Amin, B.; Singh, N.; Schwingenschlögl, U. Heterostructures of transition metal dichalcogenides. Phys. Rev. B
2015, 92, 075439. [CrossRef]
Ramasubramaniam, A. Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides.
Phys. Rev. B 2012, 86, 115409. [CrossRef]
Viljas, J.K.; Pauly, F.; Cuevas, J.C. Modeling elastic and photoassisted transport in organic molecular wires:
Length dependence and current-voltage characteristics. Phys. Rev. B 2008, 77, 155119. [CrossRef]
Chen, X.; Tian, F.; Persson, C.; Duan, W.; Chen, N.-X. Interlayer interactions in graphites. Sci. Rep. 2013, 3,
3046. [CrossRef] [PubMed]
Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Katsnelson, M.I.; Grigorieva, I.V.; Dubonos, S.V.;
Firsov, A.A. Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005, 438, 197–200.
[CrossRef] [PubMed]
Huang, Y.; Sutter, E.; Shi, N.N.; Zheng, J.; Yang, T.; Englund, D.; Gao, H.-J.; Sutter, P. Reliable Exfoliation
of Large-Area High-Quality Flakes of Graphene and Other Two-Dimensional Materials. ACS Nano 2015, 9,
10612–10620. [CrossRef] [PubMed]
Jin, C.; Lan, H.; Peng, L.; Suenaga, K.; Iijima, S. Deriving Carbon Atomic Chains from Graphene.
Phys. Rev. Lett. 2009, 102, 205501. [CrossRef] [PubMed]
Arbiol, J.; de la Mata, M.; Eickhoff, M.; Morral, A.F.I. Bandgap engineering in a nanowire: Self-assembled 0,
1 and 2D quantum structures. Mater. Today 2013, 16, 213–219. [CrossRef]
Stuke, J. Review of optical and electrical properties of amorphous semiconductors. J. Non-Cryst. Solids 1970,
4, 1–26. [CrossRef]
Tanioka, K.; Yamazaki, J.; Shidara, K.; Taketoshi, K.; Kawamura, T.; Ishioka, S.; Takasaki, Y. An avalanche-mode
amorphous Selenium photoconductive layer for use as a camera tube target. IEEE Electron. Device Lett. 1987,
8, 392–394. [CrossRef]
Frey, J.B.; Belev, G.; Tousignant, O.; Mani, H.; Laperriere, L.; Kasap, S.O. Dark current in multilayer stabilized
amorphous selenium based photoconductive X-ray detectors. J. Appl. Phys. 2012, 112, 014502. [CrossRef]
Wegscheider, W.; Pfeiffer, L.N.; Dignam, M.M.; Pinczuk, A.; West, K.W.; McCall, S.L.; Hull, R. Lasing from
excitons in quantum wires. Phys. Rev. Lett. 1993, 71, 4071–4074. [CrossRef] [PubMed]
Yoshita, M.; Hayamizu, Y.; Akiyama, H.; Pfeiffer, L.N.; West, K.W. Fabrication and microscopic
characterization of a single quantum-wire laser with high uniformity. Phys. E Low-Dimens. Syst. Nanostruct.
2004, 21, 230–235. [CrossRef]
Nanomaterials 2017, 7, 115
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
11 of 11
Ostojic, G.N.; Zaric, S.; Kono, J.; Moore, V.C.; Hauge, R.H.; Smalley, R.E. Stability of High-Density
One-Dimensional Excitons in Carbon Nanotubes under High Laser Excitation. Phys. Rev. Lett. 2005, 94, 097401.
[CrossRef] [PubMed]
Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864–B871. [CrossRef]
Kohn, W.; Sham, L.J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965,
140, A1133–A1138. [CrossRef]
Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave
basis set. Phys. Rev. B 1996, 54, 11169–11186. [CrossRef]
Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors
using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15–50. [CrossRef]
Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953–17979. [CrossRef]
Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B
1999, 59, 1758–1775. [CrossRef]
Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett.
1996, 77, 3865–3868. [CrossRef] [PubMed]
Grimme, S. Semiempirical gga-type density functional constructed with a long-range dispersion correction.
J. Comp. Chem. 2006, 27, 1787. [CrossRef]
Shishkin, M.; Kresse, G. Implementation and performance of the frequency-dependent GW method within
the PAW framework. Phys. Rev. B 2006, 74, 035101. [CrossRef]
Fuchs, F.; Furthmüller, J.; Bechstedt, F.; Shishkin, M.; Kresse, G. Quasiparticle band structure based on
a generalized Kohn-Sham scheme. Phys. Rev. B 2007, 76, 115109. [CrossRef]
Van de Walle, C.G.; Martin, R.M. Theoretical calculations of heterojunction discontinuities in the
Si/Ge system. Phys. Rev. B 1986, 34, 5621–5634. [CrossRef]
Tuttle, B.R. Theoretical investigation of the valence-band offset between Si(001) and SiO2 . Phys. Rev. B 2004,
70, 125322. [CrossRef]
Shaltaf, R.; Rignanese, G.M.; Gonze, X.; Giustino, F.; Pasquarello, A. Band Offsets at the SiSiO2 Interface from
Many-Body Perturbation Theory. Phys. Rev. Lett. 2008, 100, 186401. [CrossRef] [PubMed]
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).