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: jhu@suda.edu.cn†Electronic address: bcpan@ustc.edu.cn

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,

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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

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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

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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

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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

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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.

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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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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