-
Invariant Wide Bandgaps in Honeycomb Monolayer and Single-Walled
Nanotubes ofIIB-VI Semiconductors
Xiaoxuan Ma,1 Jun Hu,1, ∗ and Bicai Pan2, †
1College of Physics, Optoelectronics and Energy, Soochow
University,Suzhou, Jiangsu 215006, People’s Republic of China
2Department of Physics and Hefei National Laboratory for
Physical Sciences at Microscale,University of Science and
Technology of China, Hefei, Anhui 230026, People’s Republic of
China
Search for low-dimensional materials with unique electronic
properties is important for the devel-opment of electronic devices
in nano scale. Through systematic first-principles calculations, we
foundthat the band gaps of the two-dimensional honeycomb monolayers
and one-dimensional single-wallednanotubes of IIB-VI semiconductors
(ZnO, CdO, ZnS and CdS) are nearly chirality-independent andweakly
diameter-dependent. Based on analysis of the electronic structures,
it was found that theconduction band minimum is contributed by the
spherically symmetric s orbitals of cations and thevalence band
maximum is dominated by the in-plane (dxy − py) and (dx2−y2 − px)
hybridizations.These electronic states are robust against radius
curvature, resulting in the invariant feature of theband gaps for
the structures changing from honeycomb monolayer to single-walled
nanotubes. Theband gaps of these materials range from 2.3 eV to 4.7
eV, which is of potential applications inelectronic devices and
optoelectronic devices. Our studies show that searching for and
designingspecific electronic structures can facilitate the process
of exploring novel nanomaterials for futureapplications.
Keywords: Wide Bandgap, Honeycomb Monolayer, Single-Walled
Nanotube, Semiconductor
I. INTRODUCTION
Advances in modern technologies accelerate miniatur-ization of
electronic devices, which drives the endeav-ors for exploring
exotic materials in nano scale. In thelast two decades, a lot of
low-dimensional materials suchas clusters [1], nanotubes [2], and
atomically thin films[3, 4] have been discovered. These
low-dimensional mate-rials exhibit intriguing and abundant physical
properties,ranging from metallic conductor to semiconductor,
whichguarantee them promising wide applications in electronicand
optoelectronic devices in nano scale [5–9].
As the firstly discovered one-dimensional material [2],carbon
single-walled nanotubes (SWNTs) were investi-gated extensively for
the possible applications in newgeneration of electronic devices.
However, the electronicproperties of the carbon SWNTs depend on
their chi-rality and diameter. For example, the (n, m) carbonSWNTs
are metallic when n −m = 3l (l is an integer),while the others are
semiconducting [10–12]. This largelyhinders the application of
carbon SWNTs, because it isdifficult to repeatedly fabricate carbon
SWNTs with ex-actly the same chirality and diameter, so that all
theproducts (i.e. carbon SWNTs) have the same electronicproperty.
Therefore, invariably semiconducting SWNTssuch as boron nitride
(BN) SWNTs are more favorablefor the applications in electronic
devices [13–16]. Inter-estingly, the band gaps of armchair (n, n)
BN SWNTsare almost constant and independent of the diameters,
∗Electronic address: [email protected]†Electronic address:
[email protected]
while those of zigzag (n, 0) BN SWNTs decrease as thediameters
decrease [13, 15]. These electronic features aremainly attributed
to the sp2σ+ppπ hybridizations of thevalence orbitals [12, 16]. The
sp2σ hybridization mainlycontributes the strong in-plane chemical
bonds, while theppπ hybridization contributes the electronic states
nearthe Fermi energy. Therefore, the electronic properties ofthe
carbon and BN SWNTs are mainly dominated by theppπ hybridization.
It is known that the ppπ hybridizationoccurs between the pz
orbitals. Since the spatial distri-bution of the pz orbital is
perpendicular to the cylindersurface of the carbon and BN SWNTs,
the ppπ hybridiza-tion is sensitively affected by the chirality and
diameter ofthe carbon and BN SWNTs. Consequently, the
electronicproperties of the carbon and BN SWNTs are chirality-and
diameter-dependent.
Recently, the SWNTs of wide-bandgap semiconduc-tor ZnO were
studied extensively [17–22]. It was foundthat the band gaps of ZnO
SWNTs are almost insen-sitive to the chirality and diameter, being
significantlydifferent from the carbon and BN SWNTs. However,the
microscopic origin of this feature in ZnO SWNTs isstill unclear.
Furthermore, no SWNTs of wide-bandgapsemiconductor have been
synthesized in experiment sofar. Nevertheless, recent
first-principles calculations pre-dicted that the ultrathin (0001)
surface of wurtzite IIB-VI and III-V semiconductors prefers to
adopt honeycomblattice due to the electrostatic interaction between
cationand anion layers [23]. This prediction was confirmed
byexperiments for the cases of ZnO [24] and GaN [25].These
achievements are the precursors for fabricatingSWNTs of wurtzite
IIB-VI and III-V semiconductors, be-cause the SWNTs are the
transformation of honeycombmonolayer (HM) by rolling up the later
[26]. Therefore,
arX
iv:1
803.
0821
7v1
[co
nd-m
at.m
trl-
sci]
22
Mar
201
8
mailto:[email protected]:[email protected]
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2
the HMs and SWNTs of wurtzite IIB-VI and III-V semi-conductors
may be produced in experiment under propercondition and applied in
electronic devices in the future.Clearly, revealing the electronic
features of the HMs andSWNTs of these semiconductors is useful and
importantfor the design of these materials in electronic
devices.
In this paper, taking ZnO, CdO, ZnS and CdS as theprototypes of
IIB-VI semiconductors, we studied the sta-bilities and electronic
properties of the HMs and SWNTs,by using first-principles
calculations. We found that boththe HMs and SWNTs are structurally
stable, and theirband gaps are insensitive of their chirality and
diameter.The analysis of the electronic structures revealed that
thed orbital of Zn and Cd plays crucial roles in the
electroniccharacteristic.
II. COMPUTATIONAL DETAILS
All calculations were performed by using the first-principles
pseudopotential method based on density func-tional theory (DFT)
within local density approxima-tion (LDA) as implemented in SIESTA
package [27].The pseudopotentials were constructed by the
Troullier-Martins scheme [28]. The Ceperley-Alder
exchange-correlation functional [29] as parameterized by Perdewand
Zunger [30] was employed. In our calculations, thedouble-ζ plus
polarization basis sets were chosen for allatoms. For the HMs and
SWNTs, the 20 × 20 × 1 and1 × 1 × 20 k-grid meshes within the
Monkhorst-Packscheme [31] in the Brillouin zone were considered,
respec-tively. The atomic structures were fully relaxed using
theconjugated gradient method until the Hellman-Feynmanforce on
each atom is smaller than 0.01 eV/Å. The gen-eralized gradient
approximation (GGA) with PBE func-tional [32] within SIESTA package
and B3LYP hybridfunctional [33] within CRYSTAL03 package were
alsoemployed to explore the effect of different functionals onthe
electronic properties. In the B3LYP calculations,
theStuttgart-Dresden effective core pseudopotentials (ECP)[34] were
used.
III. RESULTS AND DISCUSSIONS
A. Wurtzite bulk versus honeycomb monolayer
Most IIB-VI and III-V compounds crystallize wurtzite(WZ)
structure as shown in Fig. 1(a). The cations andanions stack layer
by layer alternatively along the (0001)direction. If we cut a
two-layer slab composed of onecation layer and one anion layer as
indicated by thedashed rectangle in Fig. 1(a), the Coulomb
interactionbetween them transforms the slab into planar honey-comb
structure [23], as shown in Fig 1(b). Therefore,we chose ZnO, CdO,
ZnS and CdS as the prototypes ofwurtzite IIB-VI semiconductors to
investigate the struc-tural and electronic properties of their HMs.
We firstly
Γ Κ Μ Γ0
100
200
300
400
500
600
Wav
e N
umbe
r (cm
-1)
(a)
(b)
(c)
FIG. 1: (Color online) (a) Wurtzite and (b) honeycomb mono-layer
of ZnO. The red and gray spheres stand for O and Znatoms,
respectively. (c) Phonon dispersion curves of honey-comb monolayer
ZnO.
TABLE I: Bond length (in Å) between cations and anions,and
binding energy (Eb, in eV per formula unit), and bandgap (Eg, in
eV) of ZnO, CdO, ZnS and CdS in WZ and HM.∆ is the contraction of
bond lengths in HM compared to thatin WZ. The values in parentheses
are experimental band gaps.
Bond length Eb EgWZ HM ∆(%) WZ HM WZ HM
ZnO 1.99 1.90 4.62 -9.19 -8.26 0.94 (3.44) 2.03CdO 2.18 2.10
3.44 -7.81 -6.82 0.00 (0.84) 0.77ZnS 2.34 2.23 4.95 -7.69 -6.81
2.19 (3.91) 2.79CdS 2.53 2.42 4.46 -6.82 -5.93 0.96 (2.48) 1.64
optimized the atomic structures of ZnO, CdO, ZnS andCdS in WZ
and HM phases. As listed in Table I, the bondlength between cation
and anion in HM phase is shorterby 3% ∼ 5% than that in the
corresponding WZ phase,due to the reduction of dimensions of the
materials. Inaddition, the binding energies of all considered cases
arenegative, indicating that the interaction between cationsand
anions are energetically exothermal. For each com-pound, the
binding energy of the HM phase is higher thanthat of the WZ phase,
which is reasonable because theWZ is the ground state phase. To
further investigate thestability of the HM phase of these
compounds, we cal-culated the phonon dispersions of ZnO HM by using
the“frozen phonon” approach [35]. As shown in Fig. 1(c),the optical
and acoustical branches are well separatedand all branches have
positive frequency. Therefore, theHM phase is a metastable phase of
ZnO, in agreementwith the experimental observation [24]. This
conclusioncan be extended to other compounds considered in
thiswork.
Then we calculated the band gaps of all cases as listedin Table
I. Clearly, the band gap (Eg) of HM phase issignificantly larger
than that of WZ phase for each com-pound. For example, the Eg of
ZnO HM increases by
-
3
-6 -4 -2 0 2 40
2
4
6
8totalZn-3dO-2pZn-4s
-1 0 1 2 30.0
0.1
Μ Γ Κ ΜEn
ergy
(eV
)A Γ M L
-20
-15
-10
-5
0
5
10En
ergy
(eV
)
-6 -4 -2 0 2 40
2
4
6
-1 0 1 2 30.0
0.1
DO
S (s
tate
s/eV
)
E - EF (eV) E - EF (eV)
(a) (b)
(c) (d)
FIG. 2: (Color online) Band structures and density of
states(DOS) of ZnO in WZ phase [(a) and (c)] and HM phase [(b)and
(d)]. The valence band maximum is set to zero pointof energy. The
insets in (b) are the spatial distribution ofthe radial
wavefunctions of the energy levels indicated bythe red arrows at Γ
point. These energy levels correspondto the bonding and
anti-bonding states of (dxy − py) (left)and (dx2−y2 − px) (right)
hybridizations, respectively. Thecutoff of the isosurfaces is 0.1
electrons/Å3. The red andgray spheres stand for O and Zn atoms,
respectively. Thegreen and blue isosurfaces represent positive and
negativewave functions. The gray areas in (c) and (d) are the
totalDOS. The black, red and blue curves are the projected
densityof states of O−2p, Zn−4s and Zn−3d orbitals,
respectively.
about 1.1 eV, from 0.94 eV in WZ ZnO to 2.03 eV. Notethat the Eg
of WZ ZnO from our LDA calculation is muchsmaller than the
experimental value (3.4 eV) [36, 37],because the DFT calculations
usually underestimate theband gaps of semiconductors. It is even
worse for WZCdO of which the calculated Eg is less than 1 meV,
inagreement with previous theoretical reports [38, 39],
butobviously wrong since CdO is a semiconductor with in-direct Eg
of 0.84 eV and direct Eg of 2.28 eV [40]. Thisproblem may be
relieved by using hybrid functional suchas B3LYP [41], which will
be discussed in more detailslater. Nonetheless, the significant
widening of the bandgaps is still qualitatively reasonable, since
it originatesfrom the change of geometric symmetry and
quantumconfinement effect.
To reveal the electronic feature of these HMs, we choseZnO as
prototype and plotted the band structures anddensity of states
(DOS) in WZ and HM phases in Fig.2. From the band structures in
Fig. 2(a) and Fig. 2(b),it can be seen that both WZ and HM ZnO are
direct-band gap semiconductors, with the valence band maxi-mum
(VBM) and conduction band minimum (CBM) at
Γ point. However, the band dispersions are
significantlydifferent. Furthermore, a gap from −5 eV to −4 eV
ap-pear in the band structure of HM phase. From the den-sity of
states (DOS) in Fig. 2(c) and 2(d), the states from−6.5 eV to 5 eV
are mainly contributed from Zn−3d or-bitals, the states ranging −4
∼ 0 eV are from O−2porbitals, and the states near the CBM are from
Zn−4sorbital.
In the WZ structure, any atom locates at the center ofthe
tetrahedron composed of four neighboring atoms ofthe other type of
element. Therefore, the s and p orbitalsof anions adopt the sp3
hybridization and then hybridizewith all components of the d
orbitals of cations. On thecontrary, in the HM phase, the s and p
orbitals of an-ions adopt the sp2 hybridization, and the d orbitals
ofcations split into three group: dz2 , dxz/yz and dxy/x2−y2
.Consequently, hybridizations in HM phase should be sig-nificantly
different from those in WZ phase. To revealthe role of
hybridizations in the electronic properties, wecalculated the
radial wavefunctions of the energy levelsat Γ point. The VBM of ZnO
HM is doubly degenerateand mainly originates from the anti-bonding
states of thein-plane (dxy − py) and (dx2−y2 − px) hybridizations,
asshown in the insets in Fig. 2(b). The correspondingbonding states
are 6.6 eV bellow, manifesting the stronginteractions between
O−2px/y and Zn−3dxy/x2−y2 or-bitals. In addition, the energy level
at −2.3 eV (Γ point)is mainly contributed from O−2pz orbital, mixed
with alittle part of Zn−4pz orbital. This state represents weakppπ
hybridization between O−2pz and Zn−4pz orbitals.The narrow bands
near −5.0 eV are from dz2 and dxz/yzof Zn atom, implying that the
dz2 and dxz/yz orbitalsmaintain atomic orbital feature and do not
hybridize withO−2p orbitals. Therefore, the in-plane (dxy − py)
and(dx2−y2 − px) hybridizations dominate both the chem-ical bonds
and electronic states around the Fermi en-ergy, which is different
from the electronic nature of Cand BN monolayers. The electronic
structures of othercompounds considered in this work have similar
featureas ZnO, but the relative positions of the energy levelsare
different due to the different atomic sizes and bondlengths (see
Table I).
B. Single-walled nanotubes
The atomic structures of the SWNTs of ZnO, ZnS,CdO and CdS are
similar to the BN SWNTs, with cations(Zn and Cd) and anions (O and
S) replacing the B andN atoms, respectively. For all compounds, we
consid-ered zigzag SWNTs from (5, 0) to (21, 0) and armchairSWNTs
from (3, 3) to (12, 12), with the radius varyingfrom 2.9 to 14.5
Å. Both the atomic positions and the ax-ial lattice constants are
optimized. In these SWNTs, thewalls are buckled, with the outer and
inner cylinders com-posed of anions and cations, respectively. From
Fig. 3(a),it can be seen that the amplitudes of the buckling are
de-pendent on the radii of the SWNTs but independent of
-
4
2 4 6 8 10 12 14Radius (Å)
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
Stra
in E
nerg
y (e
V/f.
u.) ZnO-(n,0)ZnO-(n,n)
CdO-(n,0)CdO-(n,n)ZnS-(n,0)ZnS-(n,n)CdS-(n,0)CdS-(n,n)
2 4 6 8 10 12 14
Radius (Å)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Rad
ius
Buc
klin
g (Å
)
ZnO-(n,0)ZnO-(n,n)CdO-(n,0)CdO-(n,n)ZnS-(n,0)ZnS-(n,n)CdS-(n,0)CdS-(n,n)
(a)
(b)
FIG. 3: (Color online) (a) Radius buckling (Ranion −Rcation)and
(b) strain energy of all considered SWNTs. Insets in (a)are top and
side views of (6,0) ZnO SWNT. The red and grayspheres stand for O
and Zn atoms, respectively.
the chirality. For each compound, the smaller the radiusis, the
larger the buckling is. Interestingly, the overall ra-dius buckling
of the oxide SWNTs is much smaller thanthat of the sulfide SWNTs.
The buckling can be as largeas 0.6 Å for small CdS SWNTs [e.g.
(5,0) and (3,3)], andstill be ∼ 0.4 Å for those with radii of ∼ 14
Å. On theother hand, the buckling is only ∼ 0.2 Å for (5,0)
and(3,3) ZnO SWNTs whose radii are smaller than 3 Å, anddecreases
to ∼ 0.05 Å when the radius reaches 11 Å. Thisphenomenon
originates mainly from the different ionicityof oxide and sulfide
compounds. In fact, the ionicity ofoxide compound (ZnO and CdO) is
much stronger thanthat of sulfide compounds (ZnS and CdS).
Therefore, theCoulomb interaction in oxide compounds is stronger
thanthat in sulfide compounds, which results in smaller
radiusbuckling between cation and anion cylinders.
Usually, rolling up a HM to form a SWNT requiresextra energy
which is defined as strain energy (Es) [19],
Es = ESWNT − EHM , (1)
where ESWNT and EHM are the total energies per for-mula unit
(f.u.) of a SWNT and a HM, respectively.Usually, the probability of
the formation of SWNTs de-pends on their strain energies: smaller
strain energy cor-responds to larger probability. As shown in Fig.
3(b), theamplitudes of the strain energies are almost
independent
of the chirality for all the SWNTs. Consequently,
theprobabilities of the formations of zigzag and armchairSWNTs of
the same compound are nearly the same, iftheir diameters are the
same. For the oxide SWNTs, thestrain energies are positive, which
implies that the oxideSWNTs are less stable than the corresponding
HMs. Inaddition, the Es decreases as the radius increases,
andapproaches to zero for large SWNTs. On the contrary,the strain
energies of sulfide SWNTs are negative, whichindicates that the
process of rolling up a sulfide HM is en-ergetically exothermic.
Therefore, a sulfide HM may notexist, it rolls up to form a SWNT
spontaneously. As aconsequence, it may be easier to fabricate
sulfide SWNTsthan oxide SWNTs.
Then we calculated the band structures of all SWNTsand plotted
the band gaps in Fig. 4. Obviously, it canbe seen that all SWNTs
are semiconducting. The bandgaps of CdO, ZnS and CdS SWNTs are
larger than thatof the corresponding HM and decrease as the radii
in-crease. The maximum deviations of the band gaps fromthose of the
HMs are 0.23, 0.20 and 0.42 eV, respectivelyfor CdO, ZnS and CdS
SWNTs. Nonetheless, these de-viations are much smaller than other
kinds of SWNTssuch as BN and SiC SWNTs in literature (about 1 −
3eV) [15, 16, 42, 43]. Furthermore, the band gaps of theseSWNTs are
independent of the chirality. On the con-trary, the band gaps of
ZnO SWNTs with radii smallerthan 6 Å depend on the chirality: the
band gaps of thezigzag SWNTs are smaller than that of the HM
ZnO,whereas the band gaps of the armchair SWNTs are largerthan that
of the HM ZnO. However, the deviations ofthe band gaps from that of
the HM ZnO is quit small,with the maximum difference of only 0.08
eV and theband gaps of the ZnO SWNTs with radii larger than 6Å are
almost the same as that of HM ZnO. We shouldpoint out that the
invariant character of the band gapsof these materials implies that
it is not necessary to ex-actly control the chirality and diameter
of the SWNTsto obtain one-dimensional semiconductors with the
sameband gap. Therefore, opposite to the carbon SWNTswhose
chirality- and diameter-dependent electronic prop-erty hinders
their applications in the electronic devices,the oxide and sulfide
SWNTs considered in this workare very promising for future
applications in electronicdevices, because their particular
electronic property af-fords large flexibility for the process of
producing theseSWNTs as building blocks of electronic devices.
It is known that DFT calculations with conventionalfunctionals
such as LDA and GGA usually underestimatethe band gaps of
semiconductors. Fortunately, hybridfunctional B3LYP can
significantly relieve the band-gapproblem. For example, the Eg of
WZ ZnO from B3LYPcalculation was predicted as 3.41 eV [41] which
repro-duces the experimental measurement [36, 37]. There-fore, we
carried out calculations with B3LYP functionalto obtain more
accurate band gaps and further checkwhether the band gaps are still
invariable. Interestingly,it can be seen from Fig. 4 that the band
gaps of oxide
-
5
0
1
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Band
Gap
(eV
)
5
B3LYP
LDA
GGA(a) ZnO
(c) ZnS
(b) CdO
(d) CdS
0
1
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Ban
d G
ap (e
V)
0
1
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Band
Gap
(eV
)01
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Band
Gap
(eV
)
0
1
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Band
Gap
(eV
)
0
1
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Band
Gap
(eV
)0
1
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Band
Gap
(eV
)
0
1
2
3
4
5
(n,0)(n,n) ( (
(n,0)(n,n)
2 4 6 8 10 12 140
1
2
3
4
5
2 4 6 8 10 12 14
δE = 0.08 eVδE = 0.23 eV
δE = 0.20 eV
δE = 0.42 eV
(a) ZnO (b) CdO
(c) ZnS (d) CdS
Radius (Å)
Band
Gap
(eV
)
FIG. 4: Band gaps of zigzag (open symbols) and armchair(filled
symbols) SWNTs.The circles, diamonds and trianglesare from LDA, GGA
and B3LYP calculations. The horizontaldashed lines represent the
band gaps of the HMs with differentfunctionals.
SWNTs are almost the same as the Eg of the correspond-ing HM,
around 4.7 and 2.3 eV for ZnO SWNTs and CdOSWNTs, respectively. The
band gaps of ZnS are alsosteady but smaller by 0.2 ∼ 0.5 eV than
the Eg of HMZnS (4.3 eV). For the CdS SWNTs, the band gaps
varywithin ±0.4 eV with respective to the Eg of HM CdS (2.9eV). The
larger deviations of the band gaps of the sulfideSWNTs relative to
the oxide SWNTs originate from thelarger radius buckling in the
sulfide SWNTs. Neverthe-less, the band gaps of the sulfide SWNTs
are still quiteclose to those of the corresponding HMs.
Furthermore,we used GGA functional to calculate the band gaps ofthe
HM and SWNTs of ZnO and found that the bandgaps are steadily around
1.7 eV as shown in Fig. 4(a).Therefore, the invariant feature of
the band gaps of theoxide and sulfur SWNTs is predicted by LDA, GGA
andB3LYP calculations.
We emphasize that our findings mentioned above aresignificantly
different from the conventional SWNTs suchas C, BN and SiC SWNTs
where the sp2σ and ppπ hy-bridizations contribute the chemical
bonds and the elec-tronic states near the Fermi energy,
respectively. Thesespecial hybridizations lead to the strongly
chirality- anddiameter-dependent electronic properties. For the
IIB-VI compound SWNTs, however, the electronic propertiesare almost
independent of the chirality and weekly depen-dent on the diameter.
To illustrate the underlying mech-anism, we investigated the
electronic properties of theseSWNTs. Take ZnO SWNTs as examples, we
plotted theband structures of (6, 0) and (5, 5) ZnO SWNTs in Fig.
5.Clearly, these SWNTs are direct-band gap semiconduc-tors, with
their gaps of 1.96 eV and 2.07 eV, respectively,very close to that
of ZnO HM (2.03 eV). In addition, theCBM and VBM of both ZnO SWNTs
locate at Γ point.
5
Γ Κ-4
-3
-2
-1
0
1
2
3
4
5
6
Ener
gy (e
V)
Γ Κ
xy
(a) (b)
FIG. 5: (Color online) Band structures of (a) (6, 0) and (b)
(5,5) ZnO SWNTs. The VBM is set to zero point of energy. Theinsets
show the spatial distribution of the radial wavefunctionsof the
VBM. The cutoff of the isosurfaces is 0.1 electrons/Å3.The red and
gray balls stand for O and Zn atoms respectively.
We found that the CBM is contributed mainly from theZn−4s
orbital, and the VBM characterizes anti-bondingstates of the
(dx2−y2−px) and (dxy − py) hybridizations[Fig. 5]. Obviously, these
states maintain the main elec-tronic nature of HM ZnO [Fig. 2(b)],
even though theZnO HM is rolled up and radius curvature is
induced.Both the spherically symmetric Zn−4s orbital and
thein-plane (dx2−y2−px)
∗ and (dxy − py)∗ hybridizations arerobust against the radius
curvature, which results in theconstant band gaps of ZnO SWNTs.
This mechanismapplies to all the cases considered in this work.
IV. SUMMARY
In summary, we studied the stabilities and electronicproperties
of the HMs and SWNTs of IIB-VI semicon-ductors ZnO, CdO, ZnS and
CdS, through systematicfirst-principles calculations. The sulfide
SWNTs are eas-ier to be fabricated than the oxide SWNTs, because
thestrain energies of the former are lower. Interestingly, theband
gaps of the HMs and SWNTs of all the compoundsare nearly
chirality-independent and weakly diameter-dependent. This feature
is contributed from the specialelectronic character of these
materials. The CBM char-acterizes the s orbitals of cations which
are sphericallysymmetric, and the VBM originates from the
in-plane(dxy − py) and (dx2−y2 − px) hybridizations. The bandgaps
of these materials range from 2.3 eV to 4.7 eV, whichmake them
suitable to be the building-block semiconduc-tors in electronic
devices and optoelectronic devices innano scale.
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6
V. ACKNOWLEDGMENTS
This work is supported by the National Natural Sci-ence
Foundation of China (11574223), the Natural Sci-ence Foundation of
Jiangsu Province (BK20150303) and
the Jiangsu Specially-Appointed Professor Program ofJiangsu
Province. We also acknowledge the NationalSupercomputing Center in
Shenzhen for providing thecomputing resources.
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I IntroductionII Computational detailsIII Results and
discussionsA Wurtzite bulk versus honeycomb monolayerB
Single-walled nanotubes
IV SummaryV Acknowledgments References