Physics Letters A 374 (2010) 1054–1058

Contents lists available at ScienceDirect

Physics Letters A

www.elsevier.com/locate/pla

First-principles study on the structural and electronic propertiesof ultrathin ZnO nanofilms

Jun Kang a,b, Yang Zhang a, Yu-Hua Wen a,∗, Jin-Cheng Zheng a, Zi-Zhong Zhu a

a Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Chinab State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 October 2009Received in revised form 10 December 2009Accepted 10 December 2009Available online 16 December 2009Communicated by R. Wu

Keywords:First-principles calculationsZnO nanofilmsElectronic propertiesQuantum effects

Using first-principles density-functional calculations, we have studied the structural and electronic prop-erties of ultrathin ZnO {0001} nanofilms. The structural parameters, the charge densities, band structuresand density of states have been investigated. The results show that there are remarkable charge transfersfrom Zn to O atoms in the ZnO nanofilms. All the ZnO nanofilms exhibit direct wide band gaps comparedwith bulk counterpart, and the gap decreases with increased thickness of the nanofilms. The decreasedband gap is associated with the weaker ionic bonding within layers and the less localization of electronsin thicker films. A staircase-like density of states occurs at the bottom of conduction band, indicating thetwo-dimensional quantum effects in ZnO nanofilms.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, low-dimensional nanostructures have attracteda great deal of interest because of their potential applicationsin electronic, optoelectronic and electromechanical systems. Whenthe characteristic size goes down to nanoscale level, the structuresand properties of materials are often quite different from bothsingle molecule and bulk. As one of the most important semicon-ductor materials, ZnO possesses a direct wide band gap and largeexciton binding energy, having been used for solar cells, transpar-ent electrodes and blue/ultraviolet light emitting devices. Recently,a great variety of ZnO nanostructures, such as nanosheets [1],nanosprings [2], nanobelts [3], nanorings [4] and nanohelices [5]have been synthesized experimentally and have exhibited a widerange of potential applications in optical devices owing to theirdistinguished performance in electronics, optics and photonics. Ex-perimental progresses have promoted the development of theoret-ical studies to understand the physical properties of ZnO nanos-tructures. For example, the study of Zhang et al. indicates that theYoung’s moduli of ZnO nanofilms increase with decreased size [6].The calculations of the piezoelectricity in ZnO nanofilms show thatthe effective piezoelectric constant increases with increasing filmthickness [7]. Our previous study also shows that a direct to indi-

* Corresponding author. Tel.: +86 (592) 2182248; fax: +86 (592) 2189426.E-mail addresses: yhwen@xmu.edu.cn (Y.-H. Wen), jczheng@xmu.edu.cn

(J.-C. Zheng), zzhu@xmu.edu.cn (Z.-Z. Zhu).

0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.physleta.2009.12.031

rect band gap transition occurs in ultrathin ZnO nanowires underuniaxial compression [8].

More interestingly, many studies show that there might be aphase transformation from wurtzite to a graphitic structure in ZnOnanostructures [8–12]. For two-dimensional (2-D) wurtzite ZnOnanofilms, such a transformation occurs below a thickness of 18layers [11,12]. In the graphitic structure, Zn atoms and O atomsare coplanar. For one-dimensional ZnO nanowires, the graphiticstructure is more stable than the wurtzite structure under a criticaldiameter [13]. ZnO nanoclusters can also transform into graphiticstructure when the number of molecules is less than 38 or so [14].Although there have been many studies to investigate the physicalproperties of ZnO nanostructures, some questions still are unclear.To our best knowledge, there is no detailed investigation on thestructural parameters and associated electronic properties of ZnOnanofilms. The dependence of structural and electronic characteris-tics on film thickness remains unknown. What’s more, for ultrathinZnO nanofilms, quantum effects might have a remarkable influenceon their properties. Up to date, there is no work dedicated to in-vestigate them yet. In this Letter, we will employ first-principlescalculations to investigate the structural and electronic propertiesof ZnO nanofilms and address the effects of film thickness onthem.

2. Computational methods

Our calculations are performed within the framework of density-functional theory (DFT) using the Vienna ab initio simulation pack-

J. Kang et al. / Physics Letters A 374 (2010) 1054–1058 1055

age (VASP) [15] in the projector augmented wave (PAW) represen-tation. The slab model is used to describe graphitic ZnO {0001}nanofilms with a thickness range from single layer to five lay-ers. The unit cell consists of ZnO layers and a vacuum region ofat least 10 Å. The exchange correlation functional is described bythe Perdew–Wang 91 for the generalized gradient approximation(GGA) [16]. The cutoff energy in plane wave expansion is 500 eV.Brillouin-zone integrations are performed by using Gamma grid.The k-point mesh is 11 × 11 × 1 and increases up to 31 × 31 × 1in the calculation of density of states (DOS). The convergence fortotal energy is set to be 10−6 eV. The optimized structures areobtained by relaxing the atomic configurations until the calcu-lated Hellmann–Feynman (H–F) force on each atom is smaller than0.005 eV/Å.

3. Results and discussion

The ZnO nanofilms studied in this work are constructed by aplanar sheet stacking with an ABAB. . . sequence. We perform DFTcalculations of a 10-layer wurtzite ZnO film and find that initialwurtzite structure can transform into the graphitic structure afterfull relaxation. With the layer thickness of wurtzite ZnO film upto 20, we still find that the total energy of graphitic film is slightlylower than that of wurtzite film, indicating that the graphitic struc-ture is more preferable than the wurtzite structure, in generalagreement with the previous reports [11,12].

Fig. 1 shows the fully relaxed structures of graphitic ZnOnanofilms and their binding energies as a function of lattice con-stant. It is found that for the single-layer film, Zn and O atomsremain in the same plane. Whereas for the thicker nanofilms (2–5layers), the surface Zn (O) atoms exhibit slightly inward (outward)expansion. Namely, Zn and O atoms on the surface of the slab ex-hibit a buckling structure, which does not occur in graphitic bulkstructure and single-layer ZnO. The buckling magnitude can becharacterized by the spacing between Zn and O of the same planein the direction perpendicular to the film, denoted as �Z in thiswork. The value of �Z changes with different thickness, as listedin Table 1. The value of �Z for the surface layer reaches a maxi-mum value of 0.067 Å in the two-layer film while it decreases to0.049 Å in the three-layer film. In the 4- and 5-layer films, �Z isabout 0.053 Å. The 10-layer film is also found to have a spacing�Z of about 0.054 Å. These results indicate that the spacing �Zfor the surface layer is independent on thickness when the num-ber of layers is larger than three. Within a given thickness film, the�Z is largest near the surface and reaches zero in the center layer.The calculations of the graphitic bulk ZnO show that there is nospacing �Z between Zn and O atoms, as mentioned above. Thisindicates that the non-zero buckling magnitude in the nanofilm isstrongly associated with surface effects.

Due to the free surface, there are dangling bonds on the surfaceof the 2-D nanofilms. The buckling of the surface atoms reducesthe symmetry of the system, which could lead to a lower energyof the slab and the non-zero spacing �Z . The bond angles in layerare close to 120◦ . So, there is no essential variation of the hexag-onal symmetry with film thickness, which is consistent with theprevious studies [11,12,17]. In Table 1, we have also listed thelattice constant, the average bond length and the average bind-ing energy per ZnO molecule in nanofilm. The lattice constant andaverage bond length within layers increase with increased thick-ness and are gradually close to the values of graphitic ZnO bulk(see Table 1). However, the average bond length between adjacentlayers decreases with increased thickness and is about 20% largerthan that within layers. The reason for this decrease is due to theinteraction between the ZnO layers, which is always attractive innature. The stronger the interaction is, the closer the adjacent lay-ers tend to be.

Fig. 1. (Color online.) The fully relaxed structures and binding energies of {0001}ZnO nanofilms with graphitic structure. (a) Top view, (b)–(f) side views for 1–5 lay-ers along [12̄10] direction, respectively. Spheres in red color denote O atoms, andthose in green color denote Zn atoms. (g) Binding energies of ZnO nanofilms as afunction of lattice constant.

Table 1The structural parameters and binding energies of ZnO nanofilms. The number oflayers N , the optimized lattice constant a (Å), the average bond length within layersR in (Å) and between layers Rout (Å), the spacing between Zn and O planes in surface�Z (Å) and the binding energy Eb (eV/ZnO) are given.

N a R in Rout �Z Eb

1 3.284 1.896 – 0 −7.0322 3.353 1.937 2.360 0.067 −7.1913 3.377 1.950 2.361 0.049 −7.2394 3.392 1.959 2.351 0.053 −7.2685 3.402 1.965 2.344 0.053 −7.285bulk 3.445 1.989 2.305 0 −7.362

To investigate the dependence of the electronic properties onfilm thickness, we have calculated the band structures of ZnOnanofilms with 1–5 layers, as shown in Fig. 2. It is clearly seen thatall the ZnO films are semiconductors with direct band gaps at Γ

point, similar to graphitic bulk ZnO. It is well known that the localdensity approximation (LDA) and GGA in DFT calculations usuallyunderestimate the band gap. For example, the experimental bandgap of bulk wurtzite ZnO is 3.37 eV, while we get a much smallercalculated value of 0.755 eV, close to other DFT calculations [18].However, the DFT calculations are still able to predict the trend ofband gap. In our calculations, the band gaps of ZnO films with1–5 layers are all larger than that of bulk with wurtzite struc-

1056 J. Kang et al. / Physics Letters A 374 (2010) 1054–1058

Fig. 2. (a) Band structures of ZnO nanofilms with 1–5 layers; (b) band structure of bulk ZnO with graphitic structure, only those in {0001} plane are shown for comparisonwith ZnO nanofilms. The valence band maximum is chosen as energy zero; (c) band gap of ZnO nanofilms vs. the number of layers, and that of bulk is also shown.

ture. As the conductivity is associated with band gap, these widegaps indicate the insulating feature in ZnO nanofilms. The bandgap decreases with increased thickness, and will reach 0.967 eV ofgraphitic ZnO bulk when the thickness becomes infinite, as shownin Fig. 2c.

Why does the band gap decrease as the film thickness in-creases? To address this question, we investigate the charge trans-fer in ZnO nanofilms. Fig. 3 shows the charge density differences of1-, 2- and 5-layer ZnO nanofilms in the {12̄10} plane. The chargedensity difference may illustrate the charge transfer from one atomto the others. As shown in Fig. 3, it is clear that there are re-markable charge transfers from cation (Zn) to anion (O), and thecharge transfer occurs mainly within layers with only small por-tion between layers. Therefore, ZnO nanofilms exhibit a strongionic bonding behavior, similar to the bonding characteristic inwurtzite bulk. For further analyses of the ionic bonding changewith thickness, we calculate the average number of charge aroundanion in Wigner–Seitz radius and find that the number of chargedecreases slowly in thicker ZnO films. This suggests that Zn–Obonding within layers becomes stronger with decreased thicknessof nanofilms. Such a bonding characteristic can also be impliedfrom the bond length within layers (see Table 1). Thus, we mayinfer that the decrease of band gap is associated with the weakerionic bonding in thicker film. Besides the charge transfer, there isanother possible reason for this decrease. With the growth of filmthickness, the electrons in the film are less confined. As a result,the confinement effects in the film become weaker, leading to thedecreased band gap.

To further investigate the electronic properties of ZnO nano-films, we present the total DOS and partial DOS in Fig. 4. It canbe seen from Fig. 4(a) that the valence bands between 0 and−4 eV are mainly from the O 2p orbital and Zn 3d orbital, whilethe major contributions to the lower valence bands between −4and −6 eV are originated mainly from Zn 3d orbital with a smallportion from O 2p. Apparently, there is a strong hybridization be-tween Zn 3d and O 2p orbitals in the valence bands. The analysesof the atomic orbital contribution for the valence-band maximum(VBM) show that for both ZnO films and bulk in graphitic struc-ture, the VBM is mainly occupied by the Zn 3d and O 2p states.An analogous occupied mechanism has been reported in the studyof Schleife et al. [19]. It is worth noting that the Zn 3d state along[0001] direction has no contribution to the VBM of graphitic ZnOwhile for wurtzite ZnO, the z-component of Zn 3d states has somenon-neglectable contributions to the VBM. The conduction bandsare mainly contributed by Zn 4s orbital, mixed with some O 2sand 2p states. The contribution of the total DOS and partial DOS isvery similar in all studied films.

Interestingly, we observe that the total and partial DOS arestaircase-like in the conduction bands, as shown in Fig. 4a. Theypresent a typical feature of quantum well states, induced by quan-tum confinement effects in two-dimensional systems. This suggeststhat the behavior of electrons which are stimulated to the conduc-tion bands should be similar to that of 2-D free-electron gas. Sincethe conduction bands come mainly from Zn 4s orbital, we illus-trate the partial DOS of Zn 4s orbital in Fig. 4b. In all the studiedZnO nanofilms, the partial DOS of Zn 4s state is quite different in

J. Kang et al. / Physics Letters A 374 (2010) 1054–1058 1057

Fig. 3. (Color online.) The charge density differences of (a) 1-layer, (b) 2-layer and (c) 5-layer ZnO nanofilms in the {12̄10} plane. The charge density differences of 3- and4-layer films are similar to that of the 5-layer one.

Fig. 4. (Color online.) (a) Total density of states and partial density of states in 5-layer ZnO nanofilm. Inset: zoom near the bottom of conduction band. (b) Partial DOS ofZn 4s states in the 1–5 layers nanofilms. Zn 4s states are staircase-like in the conduction band range of 1–5 eV. The partial DOS in (a) and (b) are normalized to one ZnOpair.

conduction band region. There appears one stair in the partial DOSof Zn 4s unoccupied state of the 1-layer film, two stairs in thatof the 2-layer film, and n stairs in that of the n-layer film. Thestaircase-like effects have been associated with the characteristicsof band gap. The number of staircase is substantially equal to the

number of band between 0 and 5 eV, as shown in Fig. 2a. Thestaircase-like DOS indicates the strong 2-D quantum effects in ZnOnanofilms. It is well known that for free electrons in 2-D structuretheir motions are confined within plane, leading to the formationof quantum states. So, the DOS of free electrons in 2-D structures

1058 J. Kang et al. / Physics Letters A 374 (2010) 1054–1058

is a step-like function. Since Zn is a metal element, the propertiesof Zn 4s orbital in conduction bands are analogous to those of freeelectrons. Therefore, the partial density of Zn 4s states in 2-D filmsis also staircase-like.

4. Conclusions

In summary, we have employed first-principles calculations tostudy the structural and electronic properties of graphitic ZnO{0001} nanofilms with thickness ranging from one layer to five lay-ers. We have investigated the thickness dependence of the struc-tural parameters such as lattice constant, bond length and bucklingspacing in the surface layer. The charge density difference and den-sity of states are also presented. The results show that there areremarkable charge transfers from Zn to O atoms in the nanofilms.The graphitic ZnO nanofilms exhibit direct wide band gaps com-pared with bulk counterpart, and their band gaps decrease withincreased thickness. The decreased band gap is associated withthe weaker ionic bonding within layers and the less localizationof electrons in thicker film. Our study shows that the partial DOSof Zn 4s state presents staircase-like at the bottom of conductionband, indicating the 2-D quantum effects in ZnO nanofilms.

Acknowledgements

The authors gratefully acknowledge financial support from theNational Nature Science Foundation of China (Nos. 10702056 and10774124) and theProgram for New Century Excellent Talents in

Fujian Province University, China (NCETFJ). J.C.Z. is supported bythe Minjiang Scholar Distinguished Professorship Program throughXiamen University of China, Specialized Research Fund for the Doc-toral Program of Higher Education, and the Natural Science Foun-dation of Fujian Province, China (Grant No. 2009J01015).

References

[1] X.H. Huang, G.H. Li, L. Duan, L. Li, X.C. Dou, L.D. Zhang, Scripta Mater. 60 (2009)984.

[2] X.Y. Kong, Z.L. Wang, Nano Lett. 3 (2003) 1625.[3] M.H. Zhao, Z.L. Wang, S.X. Mao, Nano Lett. 4 (2004) 587.[4] X.Y. Kong, Y. Ding, R. Yang, Z.L. Wang, Science 303 (2004) 1348.[5] P.X. Gao, Y. Ding, W. Mai, W.L. Hughes, C. Lao, Z.L. Wang, Science 309 (2005)

1700.[6] L. Zhang, H. Huang, Appl. Phys. Lett. 89 (2006) 183111.[7] C. Li, W. Guo, Y. Kong, H. Gao, Appl. Phys. Lett. 90 (2007) 033108.[8] Y. Zhang, Y.H. Wen, J.C. Zheng, Z.Z. Zhu, Appl. Phys. Lett. 94 (2009) 113114.[9] A.J. Kulkarni, M. Zhou, K. Sarasamak, S. Limpijumnong, Phys. Rev. Lett. 97

(2006) 105502.[10] T.M. Schmidt, R.H. Miwa, Nanotechnology 20 (2009) 215202.[11] F. Claeyssens, C.L. Freeman, N.L. Allan, Y. Sun, M.N.R. Ashfold, J.H. Harding, J.

Mater. Chem. 15 (2005) 139.[12] C.L. Freeman, F. Claeyssens, N.L. Allan, Phys. Rev. Lett. 96 (2006) 066102.[13] L. Zhang, H. Huang, Appl. Phys. Lett. 90 (2007) 023115.[14] B. Wen, R. Melnik, Chem. Phys. Lett. 466 (2008) 84.[15] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15.[16] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244.[17] Z.C. Tu, X. Hu, Phys. Rev. B 74 (2006) 135434.[18] A. Schleife, F. Fuchs, J. Furthmuller, F. Bechstedt, Phys. Rev. B 73 (2006) 245212.[19] A. Schleife, F. Fuchs, C. Rodl, J. Furthmuller, F. Bechstedt, Phys. Status Solidi

B 246 (2009) 2150.