First-principles investigation of the size-dependent structural stability and electronic properties...

First-principles investigation of the size-dependent structural stability and electronicproperties of O-vacancies at the ZnO polar and non-polar surfacesKin Mun Wong, S. M. Alay-e-Abbas, A. Shaukat, Yaoguo Fang, and Yong Lei

Citation: Journal of Applied Physics 113, 014304 (2013); doi: 10.1063/1.4772647 View online: http://dx.doi.org/10.1063/1.4772647 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/113/1?ver=pdfcov Published by the AIP Publishing

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First-principles investigation of the size-dependent structural stability andelectronic properties of O-vacancies at the ZnO polar and non-polar surfaces

Kin Mun Wong,1,a) S. M. Alay-e-Abbas,2,3 A. Shaukat,3 Yaoguo Fang,1 and Yong Lei1,b)1Institut fur Physik & IMN MacroNanoV

R

(ZIK), Technische Universitat Ilmenau, Prof. Schmidt-Str. 26,Ilmenau 98693, Germany2Department of Physics, GC University Faisalabad, Allama Iqbal Road, Faisalabad 38000, Pakistan3Department of Physics, University of Sargodha, 40100 Sargodha, Pakistan

(Received 11 November 2012; accepted 29 November 2012; published online 3 January 2013)

In this paper, all electron full-potential linearized augmented plane wave plus local orbitals method

has been used to investigate the structural and electronic properties of polar (0001) and non-polar

(1010) surfaces of ZnO in terms of the defect formation energy (DFE), charge density, andelectronic band structure with the supercell-slab (SS) models. Our calculations support the size-

dependent structural phase transformation of wurzite lattice to graphite-like structure which is a

result of the termination of hexagonal ZnO at the (0001) basal plane, when the stacking of ZnO

primitive cell along the hexagonal principle c-axis is less than 16 atomic layers of Zn and O atoms.

This structural phase transformation has been studied in terms of Coulomb energy, nature of the

bond, energy due to macroscopic electric field in the [0001] direction, and the surface to volume

ratio for the smaller SS. We show that the size-dependent phase transformation is completely

absent for surfaces with a non-basal plane termination, and the resulting structure is less stable.

Similarly, elimination of this size-dependent graphite-like structural phase transformation also

occurs on the creation of O-vacancy which is investigated in terms of Coulomb attraction at the

surface. Furthermore, the DFE at the (1010)/(1010) and (0001)/(0001) surfaces is correlated withthe slab-like structures elongation in the hexagonal a- and c-axis. Electronic structure of the neutral

O-vacancy at the (0001)/(0001) surfaces has been calculated and the effect of charge transferbetween the two sides of the polar surfaces (0001)/(0001) on the mixing of conduction bandthrough the 4s orbitals of the surface Zn atoms is elaborated. An insulating band structure profilefor the non-polar (1010)/(1010) surfaces and for the smaller polar (0001)/(0001) SS withoutO-vacancy is also discussed. The results in this paper will be useful for the tuning of the structural

and electronic properties of the (0001) and (1010) ZnO nanosheets by varying their size. VC 2013American Institute of Physics. [http://dx.doi.org/10.1063/1.4772647]

I. INTRODUCTION

Zinc oxide (ZnO) is crystallographically a wurtzite

structure with the Zn and O ionic planes stacked alternatively

along the principal axis (cHex) of hexagonal symmetry. As it

is a wide band gap (3.37 eV) semiconducting oxide havinga large exciton binding energy of 60meV at room tempera-

ture which is chemically stable, biocompatible, with high

thermal stability, and environmentally friendly, hence ZnO

has been frequently utilized in thin films and in low-

dimensional nanostructures.1,2 The assemble of functional

nanostructures by various techniques,24 in particular, the

use of ZnO as a fundamental nanoscale building block has

led to the increase in the packing density of the thin films

and nanostructures for potential applications in nanosensors,5

ultra-violet lasers,6 and solar cells.7 In the process of imple-

menting ZnO for device integration in these applications,

ZnO has been grown in many different configurations such

as nanowires, nanodots, and nanosheets (ultra thin films).8

Growth of the ZnO nanosheets along the [0001] direc-

tion9,10 or where the nanosheets are enclosed entirely by the

(0001) facets11 have been achieved by a number of different

techniques such as the pulsed laser deposition method10 or

by a thermal decomposition and reduction process of the ini-

tial ZnS powder followed by a simple oxidation process.11 It

is also well known that the ZnO polar surfaces (0001)/(0001)formed by repeating the wurtzite primitive unit cell along the

c-axis leads to a macroscopic electric field perpendicular to

the (0001) surface due to the non-zero dipole moment, thus,

resulting in electrostatic instability.12 In spite of this, the low

Miller indexed surfaces (1010) and (0001) of ZnO are espe-cially important as they usually appear as the dominate surfa-

ces in the synthesized two-dimensional (2D) nanosheets and

one-dimensional (1D) nanostructures.13 For example, the

growth of highly crystalline ZnO nanorods with the micro-

wave assisted hydrothermal method result in a predomi-

nately hexagonal phase along the (1010) plane.14 Inaddition, synthesis of uniform hexagonal prismatic ZnO

whiskers, highly crystalline hexagonal ZnO quantum dots or

particles, as well as some of the sides of the hexagonal col-

umns of the ZnO powder particles are also primarily made

up of these (1010) facets and surfaces.1517 Conversely,

a)Electronic addresses: [email protected] and km2002wong

@yahoo.com.sg.b)Electronic mail: [email protected].

0021-8979/2013/113(1)/014304/11/$30.00 VC 2013 American Institute of Physics113, 014304-1

JOURNAL OF APPLIED PHYSICS 113, 014304 (2013)


according to the models of the idealized growth mechanism

of the ZnO prismatic crystals, the outlook of the crystallite is

related to the relative growth rate of the different crystal fac-

ets where the growth rate along the [0001] direction is almost

twice as compared to the other directions.15 In a recent ex-

perimental work, we had also shown that the predominate

growth direction of ZnO nanowires is along the [0001]

direction18 which agrees with other studies reported in the

literature and is shown to be energetically favourable. In

addition, some of the synthesized ZnO nanosheets are

observed to be enclosed entirely by the (0001) facets.10

Consequently, there are some stabilization mechanisms of

the oxide polar surfaces such as the creation of surface

states by the intrinsic charge transfer of negative charges

from the O-terminated to the Zn-terminate surface, adsorp-

tion of the charged species (e.g., H) as well as the modifi-cation of the surface stoichiometry from the creation of

vacancies (e.g., O-vacancies).1921

The feasibility of single-walled ZnO nanotubes had

been demonstrated with the deposition of ultra-thin ZnO

(0001) films on Ag (111) where the Zn and O atoms are

arranged in planar sheets.22 Importantly, the demonstration

that ZnO can be grown in a sheet-like form having either

(1010) or (0001) termination or are entirely enclosed by the(0001) surfaces10 makes it worth investigating for spin-

tronics, electronics, and other important technological appli-

cations.23,24 This is also due to the well defined geometry of

the 2D ZnO nanosheets and their ease of assembly which

render them as useful materials for the synthesis of nanode-

vices. These ultra-thin ZnO nanosheets have a large surface

to volume ratio, therefore, the electrical, optical, and mag-

netic properties as well as their performance in device appli-

cations are intimately related and are strongly affected by the

presence of surface defects such as oxygen vacancies.25

Hence it is important to investigate the formation energy of

the oxygen vacancies in the ZnO (1010) and (0001) surfaceswith different sizes.

Due to the nanometer size of the ZnO nanosheets, there

are many difficulties related with present experimental tech-

niques to elucidate physical properties associated with the

causes and effects of the surface defects. Moreover, the

functionalization of ZnO nanosheets requires a thorough

understanding of the electronic structure of the ZnO surfa-

ces. In this paper, theoretical investigations involving the

first-principles full-potential linearized augmented plane

wave plus local orbitals (FP-LAPW lo) method have beencarried out for a deeper understanding of the size-dependent

structural and electronic properties of the (1010) and (0001)ZnO surfaces with and without the surface O-vacancy.

Comparison of our results with earlier theoretical studies

carried out using different ab-initio methods and variousstructural models provide unambiguous evidence of the

suitability of computationally accurate FP-LAPW lo andthe supercell-slab (SS) models. Therefore, we hope to

provide a further insight into the size-dependent structural

and electronic properties of the (1010) and (0001) ZnOsurfaces pertaining to the physical mechanisms behind the

geometrical distortions and structural phase transformation

of, especially, the (0001) SS. In addition, our results pro-

vide useful and better understanding in tailoring the

structural and electronic properties of ZnO surfaces or

nanosheets by controlling their size for important device

application.

II. CALCULATIONAL DETAILS AND STRUCTURALMODELS

The properties of all the ZnO SSs in an artificial symmetry

have been calculated using the density functional theory

(DFT) based WIEN2K computer program.26 The exchange-

correlation potential has been treated by utilizing the PBEsol

generalized gradient approximation (GGA) parametrization

scheme as this functional is known to provide good results for

solids and their surfaces as compared to hybrid DFT functional

which are 2 to 3 orders more expansive computationally.27

The SSs for imitating (0001)/(0001) polar surface havebeen constructed by stacking ZnO primitive unit cells and a

vacuum region of several A along the c-axis of hexagonal lat-

tice. In this case we represent different lengths of SS as

1 1 2, 1 1 3, 1 1 4, and 1 1 5 (1 1N)which contain 8, 12, 16, and 20 atoms, respectively. In order

to verify stability of a 1 1 surface unit cell of the (0001) and(0001) surfaces that represents correct cleavage of a hexagonallattice at the basal plane, we consider two possible SS which

are labeled as type-A and type-B, respectively, and both SS

belong to trigonal space group # 156 (P3m1). In case of type-

A SSs, the bulk unit cell of wurtzite ZnO was stacked along

the c-axis followed by a vacuum region of about 10 A that

resulted in the 1 1 3 type-A SS shown in Fig. 1(a). A sim-ple stacking of the bulk unit cell along the c-axis results in the

(0001) surface being terminated with an O atom, while the

(0001) surface is terminated by a Zn atom which is contradic-tory to the required termination of the wurtzite structure at the

basal plane.19,20 The type-B 1 1 2 SS shown in Fig. 1(b)can be obtained by constructing a 1 1 3 type-A SS andthen clipping off Zn and O atoms at both ends of the slab to

obtain a 1 1 2 type-B SS with the Zn (O) atom layer termi-nating at the basal plane along [0001] ([0001]) directions. Sim-ilar procedure was adopted for obtaining the type-B 1 1 3,1 1 4, and 1 1 5 SSs. In Fig. 1(c), the 1 1 surfaceunit cell of ZnO (0001) surface is shown (Tasker Type-III12).

The non-polar (1010)/(1010) surface terminations havebeen modeled by stacking six, eight, and ten primitive unit

cells of wurtzite ZnO along the a-axis of hexagonal lattice

followed by a vacuum region of several A to decouple the

interactions between SSs. We represent these SSs as

6 1 1, 8 1 1, and 10 1 1 (in general, N 1 1,where N is the number of ZnO primitive unit cells stacked

along the a-axis of the hexagonal lattice) which contain 24,

32, and 40 atoms, respectively. The N 1 1 SSs obtainedin this way belong to triclinic space group # 1 (P1) and have

equal number of Zn and O atoms on the surface (Tasker

Type-I12) and consists of rows of ZnO dimmers along

the [1010]/[1010] direction as shown in Fig. 2. Wewould like to stress that our N 1 1 SSs are repeated infin-itely both along the b- and c-axis whereas the 1 1N SSsare repeated infinitely along a- and b-axis of hexagonal

lattice.

014304-2 Wong et al. J. Appl. Phys. 113, 014304 (2013)


In the FP-LAPW lo method implemented in this work,the core states have been treated fully relativistically relaxed

in the spherical approximation, while the valence states have

been treated scalar-relativistically. For all the SS calculations,

the parameter RO x Kmax 7.0 for the plane wave basis setexpansion was applied, where RO 0.79 A is muffin-tin radiusof O atom and Kmax is the maximal reciprocal lattice vector.For the first Brillouin zone integration, a (9 5 1) Mon-khorst-Pack28 k-point mesh has been used for the N 1 1SSs in the P1 structure, while a (14 14 1) k-point meshhas been used for 1 1N SSs in the P3m1 structure. Subse-quently, the k-point mesh was increased to 10 6 1 and17 17 1 for the N 1 1 and 1 1N SS, respectively,as a test of the convergence where same results were obtained.

Both Kmax and the number of k-points were found to be suffi-cient to achieve a self-consistent minimum total energy below

0.1 mRy, and hence, our calculations are credible.

III. RESULTS AND DISCUSSIONS

A. Perfect polar (0001)/(0001) surfaces

In both the type-A and type-B 1 1N SS, the Zn andO atoms were initially located at their bulk positions which

were then fully relaxed by minimizing the atom forces to 1

mRy/a.u. The type-A and type-B 1 1N SS shown in Fig.3 deform along the c-axis after optimization of internal ge-

ometry. The structural data of the four type-A and type-B SS

are tabulated in Table I where it can be clearly seen that the

% volume collapse (LDLD2

LD2 x100, where L is the length of

the SS along c-axis, DL is the length contraction, and D isthe width which is same for all 1 1N SSs since the slabsare infinite along a- and b-axis), in type-A SS do not follow a

trend on going from smaller structure to the larger ones

which provide a first evidence regarding the non-suitability

of type-A SS for the (0001) surfaces. On the other hand, for

FIG. 1. (a) Side view of the 1 1 3type-A supercell-slab and (b) 1 1 2type-B supercell-slab in the trigonal

P3m1 setting. d1, d2, and d3 are the firstthree interlayer distances from the

(0001) surface. (c) The top view of

the Zn-terminated (0001) surface of

1 1 2 type-B supercell-slab showinga 1 1 surface unit cell. In case of1 1N SS, the hexagonal c-axis isparallel to the trigonal c-axis as shown

in (a) and (b). The O, Zn and surface

O-vacancy atoms are represented by the

large red, small grey, and crossed yellow

spheres, respectively.

FIG. 2. 6 1 1 supercell-slab in tri-clinic P1 setting showing the (1010) and(1010) non-polar surfaces consisting of aZnO pair at the surface. The hexagonal

a-axis is shown along which the

O-vacancy has been studied. b.l1, b.l2, and

b.l3 are the bond lengths between surface

O atom and Zn atoms bonded to it, while

U1 and U2 are the surface OZnO bondangles at the (1010) and (1010) surfaces.The O, Zn, and surface O-vacancy atoms

are represented by the large red,

small grey, and crossed yellow spheres,

respectively.



the type-B SS the contraction in length is maximum

(14.48%) in the case of 1 1 2 SS and reduces with theincreasing length of the structure which should be expected

as increase in the length of SS along the c-axis results in a

bulk like environment. The volume collapses in the

1 1N SS are a direct consequence of the vacuum regionbetween successive slabs that vanishes the outwards electric

attraction for the surface atoms. We stress here again that for

the perfect type-A and type-B structures we have not used

any non-stoichiometric SSs which may result in a false stabi-

lizing mechanism. For a complete graphical representation

of the deformation along the c-axis corresponding to the type

B 1 1N SS before and after minimization, please referto Figs. S1 and S2 in the supplementary information.44

In order to provide a further insight into the stability of

different lengths of the SS, the heat of formation (Hf ) valueshave been computed using29

Hf Ept =n EZnbulk EO: (1)

In Eq. (1), Ept is the minimum total energies of the perfect(stoichiometric) ZnO SS, EZnbulk is the energy of hexago-nal Zn and EO EO2=2, where the energy of gas-phaseO2 has been computed by placing two O atoms at a distance

of 1.21 A in artificial periodic conditions in a cubic box of

side 10 A and n is the number of formula units in a 1 1NSS. Our calculated value of Hf for bulk ZnO obtained usingthe PBEsol27 functional is 3.14 eV which is in good agree-ment with theoretical as well as experimental values.29 This

benchmark test of the PBEsol functional for the bulk ZnO

verifies the suitability of this functional for the subsequent

calculation performed for any of the 1 1N and N 1 1SS in this work. The heat of formation values tabulated in

Table I further strengthen the suitability of type-B SS for

imitating the polar (0001) surface of ZnO.

The three interlayer spacing at the (0001) surface

depicted in Figs. 1(a) and 1(b) are designated as d1, d2, andd3 for the type-A and type-B SS, respectively. From previoustheoretical accounts, it is well established that the interlayer

separations d1 and d3 contract, while d2 expand along the[0001] direction and approach their bulk values with increas-

ing length.19,30,31 For the case of type-A SS, d1 and d3increase with the increasing length of the structure approach-

ing the bulk value of 1.99 A, whereas the d2 decrease toequal the bulk value of 0.62 A which provides further evi-

dence that the type-A SS do not imitate a polar surface and

mimic only the local environment of wurtzite ZnO.32 In con-

trast, the small negative d1 values for type-B 1 1 2 and1 1 3 SS imply a surprising slight crossover between sur-face layers at the Zn-terminated (0001) surface, while all the

positive d1 (for the 1 1 4 and 1 1 5 SS), d2 and d3values indicate that there is a contraction or expansion of

interlayer spacing which is never accompanied by a cross-

over. Importantly, d2 values for the type-B SS approach thebulk values (1.99 A), when the length of the SS increases

from 1 1 2 to 1 1 5. The d1 and d3 values alsoapproach their bulk value (0.62 A) on going from smaller

type-B 1 1N SS to larger ones except for 1 1 3 SS.This non-linear behavior hints at the competition between

bonding energy and the electrostatic energy that finally

FIG. 3. (a) 1 1 3 type-A SS beforerelaxation, (b) 1 1 3 type-A SS afterrelaxation, (c) 1 1 3 type-B SSbefore relaxation, and (d) 1 1 3 type-B SS after relaxation in the trigonal

P3m1 setting. The hexagonal c-axis is

also shown which is parallel to the trigo-

nal c-axis. The O and Zn atoms are rep-

resented by the large red and small grey

spheres, respectively.

TABLE I. Structural data for the type-A and type-B 1 1N SS along with the heat of formation (eV) computed using the PBEsol functional. The interlayerdistances depicted in Figs. 1(a) and 1(b) and the surface ZnO bond lengths are presented.

1 1N SS% Volume

collapse

Interlayer

distance d1 (A)

Interlayer

distance d2 (A)

Interlayer

distance d3 (A)

Surface ZnO bond lengths (A)

Hf (eV)Zn-term O-term

1 1 2 Type-A 0.534 1.960 0.662 1.937 1.960 1.831 1.3211 1 3 Type-A 0.429 1.972 0.644 1.949 1.972 1.833 1.8291 1 4 Type-A 0.449 1.985 0.632 1.956 1.985 1.830 2.0851 1 5 Type-A 0.646 1.992 0.620 1.964 1.992 1.830 2.2391 1 2 Type-B 14.487 0.066 2.423 0.024 1.882 1.882 2.5841 1 3 Type-B 12.272 0.070 2.416 0.010 1.882 1.882 2.5951 1 4 Type-B 3.853 0.269 2.162 0.466 1.900 1.904 2.6231 1 5 Type-B 3.551 0.3112 2.125 0.504 1.907 1.906 2.668



triggers a structural phase transformation after a certain

threshold length during the growth of wurtzite ZnO along

the [0001] direction. In spite of the fact that relaxed non-

polar type-B 1 1 2 and 1 1 3 SS have the same sur-face bond lengths (Table I), a larger stacking of the 1 1 3SS have significant effects related to the non-linear behavior

of defect formation energy (DFE) in Table II and the band

structure profiles after the creation of O-vacancy at the Zn-

terminated (0001) surface which are discussed in Sec. III B.

Unlike the type-A SS, the most striking feature of the

type-B SS is the difference in the structural deformation

when the atomic layers of Zn and O atoms is less than 16. In

the case of type-B 1 1 2 and 1 1 3 SS, the structuresflatten after geometry optimization (Fig. 3) resulting in a

graphite-like ZnO. As mentioned previously, the volume col-

lapse in type-B 1 1N SS decreases as the stacking ofbulk ZnO unit cell along the c-axis is increased from 2 to 5

(Table I) which is a direct consequence of the surface to vol-

ume ratio (D2=LD2 1=L) that is larger in the case of thetype-B 1 1 2 and 1 1 3 SSs as compared to all othertype-A and type-B structures. Since the extreme surface Zn

and O atoms of the 1 1 2 and 1 1 3 SS have alreadylost one of the four bonds due to the surface termination as

compared to bulk ZnO, a larger surface to volume ratio for

these SS ensures that they are unable to compensate for these

broken surface bonds which together with the stronger Cou-

lombs attraction from the interior atomic layers then trigger a

collapse of surface atomic layers towards the interior of SS

resulting in flattening of the atomic layers. Since this could

have been a consequence of insufficient vacuum region

between the SS, we verified our results by varying the vacuum

region from 7 to 13 A for both type-A and type-B SS and

found the same volume collapse for all the 1 1N SSs.In case of type-B 1 1 4 and 1 1 5 SS, a smaller

surface to volume ratio for these structures does compensate

for the broken surface bonds, and thus, is able to retain the

wurtzite structure for these SS. These results are consistent

with earlier theoretical reports on AlN, GaN, and ZnO,31,33

however, unlike Ref. 31 our results clearly show that the

transformation from wurtzite to graphite-like ZnO structure

occurs for

bond lengths and the bonding nature at the (0001) surfaces.

Therefore, we predict here that the competition between the

bond energy, the Coulomb energy, and the energy originat-

ing from the macroscopic electric field of the dipole surface

must be responsible for the non-linear variation in the DFE

for O-vacancy at the Zn-terminated (0001) surface. On the

other hand, the smaller values of DFE for the O-terminated

(0001) surface indicates that an O-vacancy can be easily pro-duced as compared to the (0001) surface.

From Table I, it can be easily observed that the surface

ZnO bond lengths for type-B 1 1N SS increases ongoing from 1 1 3 to 1 1 5 SS which is an indicationof stronger bond energy for the 1 1 5 SS and decrease inthe Coulombs energy. This bonding nature is supported by

charge density plots in the (1120) and (0001) planes asshown in Figs. 4 and 5, respectively. For the charge density

plots in the (0001) plane, please refer to Fig. S3 in the sup-plementary information/material.44

From the above figures, the transformation of the

smaller 1 1 2 and 1 1 3 SS to graphite-like structureis also visible. In the case of 1 1 2 and 1 1 3 SS, afterrelaxation, the bond lengths of the surface Zn and O atoms

are 1.882 A which signify a stronger Coulombs energy over

the 1 1 4 and 1 1 5 SS. Importantly, the creation ofsurface O-vacancy as depicted in Fig. 1 results in the re-

moval of the stronger Coulombs attraction at the terminated

surface and thus eliminates the graphite-like structure for the

defective SS. However, the effect of the removal of the O

atom at the (0001) surface for these SS is different. This dif-

ference in the charge density distribution at the surface of de-

fective type-B 1 1 2 SS gives it a band structure profileentirely different from the rest of the type-B SSs which are

presented later in Fig. 6. Finally, the smaller Coulomb

energy results in smaller values of the defect formation

energy for the larger structures. It should also be mentioned

that due to the phase transformation of the 1 1 2 and1 1 3 SS to graphite-like, the trend for the DFE at the Znand O-terminated surface could be different from the

1 1 4 and 1 1 5 SS. The values computed for thesetwo surfaces in the case of 1 1 2 SS are the same, whilefor 1 1 3 SS, the DFE value on both surfaces are differ-ent which is indicative of the fact that upon creation of va-

cancy the 1 1 3 SS starts to retain its wurtzite phase.In bulk wurtzite ZnO, large charge transfer from Zn

to O atom is expected due to the large electronegativity

FIG. 4. The charge density plots of the relaxed type-B 1 1N SSs alongthe (1120) plane (top panel) without an O-vacancy (perfect) and (bottompanel) with a shallow O-vacancy. (a) 1 1 2, (b) 1 1 3, (c) 1 1 4,and (d) 1 1 5 SS.

FIG. 5. The charge density plots of the

relaxed type-B 1 1N SSs along the(0001) plane (top panel) without an

O-vacancy (perfect) and (bottom panel)

with a shallow O-vacancy. (a) 1 1 2,(b) 1 1 3, (c) 1 1 4 and (d)1 1 5 SS.



differences of 1.79 on the Pauling scale between the Zn and

O atom,37 which results in the bulk ZnO having ionic and

covalent bond simultaneously with about 55% ionic charac-

ter. In the middle of the charge density plots for the larger

type-B SSs as shown in Fig. 4, a mixed ionic and covalent

character is seen which is maintained at the surface region

also. At the Zn-terminated and O-terminated surfaces, charge

accumulation and charge depletion, respectively, is also

clearly seen which is consistent with other studies38 for the

(0001) and (0001) surfaces. Fig. 5 shows the charge densityplots for the type-B SS without and with the removal of an O

atom below the Zn-terminated (0001) surface. Comparison

of the two panels shows that the charge accumulation is

larger for the case of vacancy SS. This should be expected as

the ZnZn bond is created at the surface and the charges

become highly delocalized which is characteristic of shallow

O-vacancy. Moreover, the graphite-like nature of the charge

density at the (0001) surface of the 1 1 3 SS transformsit back to the wurtzite charge distribution with the creation

of vacancy which has already been discussed. In addition,

the (0001) and (0001) surfaces for the type-B 1 1 2 and1 1 3 SS show almost similar charge density profilewhich is a direct consequence of the flattening of the polar

surfaces that gives rise to an insulating band structures for

these two SS as shown in Fig. 6.

Fig. 6 shows the electronic band structure for the perfect

and defective type-B SS where it is clearly observed that the

1 1 2 and 1 1 3 SS are insulating with a band gap of1.25 eV and 1.15 eV, respectively. These band gaps are

larger as compared to our computed band gap (0.75 eV) for

bulk ZnO at the gamma point (C) which can be attributed tothe quantum size confinement effect.39 The band structure

diagrams for perfect SS show no sign of the Fermi level

being shifted into the conduction or valence band for the

1 1 2 and 1 1 3 SS. This is due to the structuraltransformation of the 1 1 2 and 1 1 3 SS intographite-like structure that eliminates the macroscopic elec-

tric field along the c-axis inside these structures. Conversely,

the band structures of the 1 1 4 and 1 1 5 SS do haveclear evidence of the electric field along the c-axis causing

FIG. 6. The electronic band structure of the type-B 1 1N SS (top panel) without, (middle panel) with an O-vacancy at the (0001) surface, respectively.(Bottom panel) With an O-vacancy at the (0001) surface. (a) 1 1 2, (b) 1 1 3, (c) 1 1 4, and (d) 1 1 5 SS.



the valence band to move above the Fermi level. Moreover,

a mixing of conduction and valence band states at the Cpoint leading to surface metallization is observable. This sur-

face metallization results from the charge transfer to the Zn-

terminated surface from the O-terminated surface, which

leads to strongly dispersing 4s orbitals of the Zn atom on thesurface, hence leaving almost no occupancy of the 4s statesin the subsurface layers.19 From the band structures of the

defective 1 1N SS, it can be seen that the removal of anO atom below the Zn-terminated surface have different

effects on the different sizes of the slabs. It is clearly observ-

able from the figure that the creation of vacancy results in a

band structure with no band gap for all the type B 1 1NSS. This could have been possibly a result of the metallic

ZnZn bond at the surface due to the creation of the

O-vacancy which enhances the surface metallization.

C. Perfect non-polar (1010)/(1010) surfaces

In order to understand the effects of O-vacancy at non-

polar (1010)/(1010) surfaces, we present the bond lengths ofthe O atom with its neighbouring Zn atoms at the surface

(labelled as b:l1, b:l2, and b:l3 in Fig. 2) in Table III alongwith other structural properties of the N 1 1 SS. Fromthe decreasing volume collapse and increasing Hf values, itis evident that the SS become more and more stable with

increasing length along the hexagonal a-axis. The bond

lengths listed in Table III together with the charge density

centered at the surface Zn atom at the (1010) and (1010)

surface as shown in Fig. 7 are helpful in understanding the

bonding nature of the surface O atoms. The increasing value

of the b:l1 between the surface O and Zn indicates a tendencyof becoming more covalent as the length of the N 1 1 SSincreases. For example, the charge density contours for the

1 1N SS which encompass both the O and Zn atom in a8-like shape for the 6 1 1 SS (see Fig. 7) appears to splitfor the 10 1 1 SS. This is a clear indication of reducedcharge transfer (reduced Coulomb energy) between the sur-

face ZnO dimer in larger SS, hence making the bonding na-

ture more covalent in the 10 1 1 SS. This is furtherconfirmed by the charge density contours around the Zn

atom in the 10 1 1 SS above the O2 atom, which appearto be slightly more non-spherical as compared to the

8 1 1 and 6 1 1 SS. Furthermore, in the case of6 1 1 SS, the charge density around the Zn atom abovethe O2 and O11 atoms at the (1010) and (1010) surfaces,respectively, show similar trends from which we can predict

that the DFE for these atoms will be approximately equal.

On the other hand, for the 8 1 1 (10 1 1) supercell-slab comparison of charge densities around the Zn atom

above the O2 and O15 (O19) atoms clearly show different

bonding natures. The O2 atoms at the (1010) surface appearsto have stronger covalent bond as compared to the surface O

atoms at the (1010) surface from which one can infer thatthe O15 (O19) atoms will have larger DFE.

From Table III, the bond lengths between the O2 and

O11, O15 or O19 atom with its neighbouring Zn atoms gen-

erally increases on going from 6 1 1 to 10 1 1 SS,

TABLE III. The volume collapse and Hf of the relaxed N 1 1 SS after running the minimization program. The bond lengths and the bond angles at the(1010) and (1010) surfaces.

At the (1010) surface At the (1010) surface

N 1 1 SS % Volume collapse b.l1 (A) b.l2 (A) b.l3 (A) U1 (deg) b.l1 (A) b.l2 (A) b.l3 (A) U2 (deg) Hf (eV)

6 1 1 1.744 1.846 1.913 1.913 118.751 1.845 1.913 1.912 118.782 2.6888 1 1 1.681 1.849 1.912 1.912 118.563 1.847 1.913 1.912 118.631 2.73210 1 1 1.651 1.852 1.912 1.912 118.654 1.844 1.911 1.911 118.778 2.758

FIG. 7. The charge density plot centered

around the surface Zn atom at the (top

panel) (1010) surface and (bottom panel)(1010) surface. (a) 6 1 1, (b) 8 1 1, and (c) 10 1 1 SS.



thus, confirming the above mentioned more ionic nature of

the 6 1 1 surface ZnO dimmer. However, the bondlengths are not sufficient to present a clear picture of the

trend in the DFE of the prospective neutral O-vacancy at

the (1010)/(1010) surfaces. For this reason, we also presentthe OZnO bond angle (U1/U2) in Table III which is consti-tuted between the two outermost ZnO dimers at the (1010)/(1010) surfaces.

For the unrelaxed N 1 1 SS shown in Fig. 2 (andalso in our optimized ZnO bulk unit cell), these angles are

108.243. Upon geometry optimization, the surface OZnObond angle tilts by an amount x1/x2 at the (1010)/(1010)surfaces resulting in a larger U1/U2 value as compared to thebulk. This tilt angle is a consequence of the outward move-

ment of surface O atom and the relative movements of the

internal layers of the atoms below the (1010)/(1010) surfa-ces. Earlier theoretical studies carried out using local density

approximation,40 B3LYP,30 Perdew-Wang GGA,31 and all

electron Hartree-Fock method41 predict a tilt angle 3.59,2.13, 9, and 2.48, respectively, which are much smallerthan the strong tilt angles (11.56 5) observed in low-energy-electron diffraction (ELEED) experiments for the

(1010) surfaces dimers of wurtzite structures.42 Our com-puted tilt angles ranging between 10.2 and 10.6 again pro-vide evidence of the excellent performance of the PBEsol

functional for surface studies.

All in all, a close inspection of the bond lengths and the

bond angles for the surface O atoms listed in Table III show

no particular trends on going from smaller SS to larger ones

as was observed in the case of the polar surfaces. Therefore,

the trendy competition between the bond energy and the

Coulomb energy as seen in Fig. 7 that controls the DFE val-

ues of the neutral surface O-vacancy presented in Sec. III D

are a complex interplay between the bond lengths and bond

angles listed in Table III.

D. Neutral O-vacancy at non-polar (1010)/(1010)surfaces

The DFE due to a neutral surface O-vacancy at the

(1010) and (1010) surface was computed by removing the Oatom highlighted by a yellow cross in Fig. 2. Our computed

DFE values for the O-vacancy (Table IV) reduce with

increasing length of the SS along the hexagonal a-axis which

are in good agreement with earlier works.39 However, in the

case of 8 1 1 and 10 1 1 SS, the DFE values at the(1010) surface are slightly higher than the DFE values at

the (1010) surface. This is clearly due to the smaller bondlengths and larger tilt angles (Table III) of the O15 and O19

atoms corresponding to the 8 1 1 and 10 1 1 SS,respectively, as discussed in Sec. III C.

From a comparison between Tables II and IV, it can be

observed that the DFE for the 1 1N SS are larger thanthe N 1 1 SS which was due to the extra energy originat-ing from the macroscopic electric field along the [0001]

direction as the centers of the positive and negative charges

do not coincide at the surface for the 1 1N SS. The pres-ence of this electrostatic field in the perfect type-B 1 1NSS results in scaling the DFE to higher values as compared

to the N 1 1 SS. However, from the charge density plots(Figs. 5 and 7), we can easily deduce that the decreasing

value of DFE on going from smaller supercells to larger ones

is controlled by the decreasing Coulomb energy.

The charge density plots with the creation of the

O-vacancy at the (1010) and (1010) surface of the 6 1 1,8 1 1, and 10 1 1 SS clearly shows a charge delocali-zation on the surfaces which is a characteristic of surface

O-vacancy. For further information about the charge density

plots and the corresponding electronic band structures of the

surface O-vacancy for the N 1 1 SS at the (1010) sur-face, please refer to Figs. S4 and S5 in the supplementary in-

formation/material.44 The O-vacancy DFE values obtained

using the SS model in this work is in good agreement with

the more complicated structure of similar cross-sectional

width at 16.4 A,39 which validates the suitability of the SS

(considered in this work) that require a fraction of the exten-

sive computational time required for the more complicated

structure.

Finally we discuss the effects of surface O-vacancy on

the electronic band structures of the N 1 1 SS which areshown in Fig. 8. The C symmetry point direct band gap of6 1 1, 8 1 1, and 10 1 1 SS are 0.78 eV, 0.71 and0.68 eV, respectively. Thus, all the perfect SS show insulat-

ing nature and the band gap increase with decreasing length

of the structure in the hexagonal a-axis which is due to the

quantum confinement effect. The conduction band is pre-

dominantly made up of the empty Zn 4s-orbitals,19 while thevalence band is made up of the occupied O 2p-orbitals43 andthe band gap is created due to the repulsion between the con-

duction band states and the valence band states. For the

entire perfect N 1 1 SS, the Fermi level is located insidethe valence band which is due to the fact that both surfaces

of the relaxed N 1 1 SS are made up of the O atoms thatresults in the shifting of the O 2p-states above the Fermilevel and therefore giving these materials (without any O-va-

cancy) a p-type semiconducting character.

A band gap for all the horizontal N 1 1 SS alsoshows that there is no charge transfer between the (1010)and (1010) surfaces as compared to the polar 1 1N type-B SS, which is primarily due to the equal number of similar

atoms on both the non-polar (1010)/(1010) surface. Aftercreation of the O vacancy (O2 and O11, O15 or O19 atom),

one of the bands made up of Zn 4s-orbitals in the perfectN 1 1 SS split from the conduction band and movesdownwards on the energy scale making it an occupied state.

The difference in the energy positioning of this vacancy state

TABLE IV. O-vacancy DFE for the N 1 1 SSs at the (1010) and (1010)surfaces in both the O-poor and O-rich conditions.

SS defect formation

energy (eV) at the (1010)

surface

SS defect formation

energy (eV) at the (1010)

surface

SS Vo (O-poor) Vo (O-rich) Vo (O-poor) Vo (O-rich)

6 1 1 0.546 3.233 0.546 3.2338 1 1 0.261 2.991 0.487 3.21710 1 1 0.208 2.965 0.467 3.224



with the bottom of the conduction band give rise to a band

gap. This bandgap is symmetric for both the (1010) and(1010) surface and decreases from 0.78 eV to 0.42 eV corre-sponding to the 6 1 1 and 10 1 1 SS, respectively. Inaddition, the bandgap for the N 1 1 SS with the surfaceO-vacancy is smaller as compared to the bandgap for the per-

fect N 1 1 SS. With the creation of surface O-vacancy,the semiconducting nature of the defective N 1 1 SSbecomes n-type. The shift of the Fermi level into the conduc-

tion band is a consequence of the O-vacancy that results in

the creation of a broken ZnO bond which leads to a ZnZn

metallic bond on the surface. The free electrons as a result of

the creation of the O-vacancy do not lead to the mixing of

the conduction and valence bands as observed in the vertical

1 1N SS.

IV. CONCLUSION

In this study, the polar (0001) and non-polar (1010)surfaces of ZnO have been modelled as supercell-slabs to

investigate the effects of O-vacancy at these surfaces. For

the two perfect polar (0001) SSs, type-A and -B 1 1N

SS with a non-basal and basal plane termination, respec-

tively, a wurtzite to graphite-like phase transformation is

observed only for the more stable type-B SS. Our results

show a clear evidence that the competition between the

bonding nature, the Coulomb energy, energy originating

from the macroscopic electric field of the dipole and the

larger surface to volume ratio for the type-B 1 1 2 and1 1 3 SS triggers a structural phase transformation fromthe wurtzite structure to graphite-like structure below a

certain threshold length (

Zn-terminated surface from the O-terminated surface. Impor-

tantly, a good correlation is observed in the type-B SS

between the longer bond lengths which is associated with a

smaller/larger Coulomb/bond energy that yields smaller val-

ues of the defect formation energy for the larger structures.

The higher values of DFE at the polar (0001) surfaces as

compared to the non-polar surface are a consequence of the

extra energy originating from the macroscopic electric field

along the [0001] direction in the polar SS.

On the contrary, for the non-polar (1010) and (1010)surfaces, the computed DFE values for O-vacancy of the

N 1 1 SS reduce with increasing length of the SS alongthe hexagonal a-axis and appears to be dependent on the

ionic and covalent nature of the surface ZnO bonds. How-

ever, the bond lengths and the bond angles for the surface O

atoms show no particular trends on going from the smaller

SS to larger ones. Therefore, the competition between the

bond energy and the Coulomb energy that controls the DFE

values of the neutral surface O-vacancy are a complex inter-

play of the ZnO bond lengths and the OZnO bond angles.

Importantly, the O-vacancy DFE values, the tilt angle, and

the interlayer spacing obtained using the SS model and the

PBEsol functional in this work are in good agreement with

the computationally more demanding calculations reported

in earlier studies. Importantly, our findings open up the pos-

sibility of tuning the structural and electronic properties of

ZnO polar and non-polar surfaces by controlling their size

which is essential for technological application.

ACKNOWLEDGMENTS

Financial support from the European Research Council

Grant (ThreeDSurface), Volkswagen Stiftung, and BMBF

(ZIK: 3DNano-Device) is gratefully acknowledged.

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of the surface O-vacancy for the N 1 1 SS.



First-principles investigation of the size-dependent structural stability and electronic properties...

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