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Size-induced structural transition in ZnO prismatic nanoparticles ,1
Vu Ngoc Tuoc* and Tran Doan Huan
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Phys. Status Solidi B 249, No. 3, 535–543 (2012) / DOI 10.1002/pssb.201147356
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basic solid state physics
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1
Department of Theoretical Physics, International Center for Computational Materials Science (ICCMS), Hanoi University of Science and Technology (HUST), 1 Dai Co Viet Road, Hanoi, Vietnam 2 Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland 3 Institute of Engineering Physics, Hanoi University of Science and Technology (HUST), 1 Dai Co Viet Road, Hanoi, Vietnam Received 18 July 2011, revised 12 September 2011, accepted 19 September 2011 Published online 14 October 2011 Keywords density functional theory, structural transition, zinc oxide nanoparticles * Corresponding
author: e-mail
[email protected], Phone: þ84-4-38692801, Fax: þ84-4-38693498
We report a first-principles study on several series of zinc oxide prismatic nanoparticles (NPs) with triangular and hexagonal cross-section geometries and various diameters up to 2.4 nm. Structural and electronic properties of the NPs are calculated using density functional theory, focusing on the effects induced by the surfaces reconstruction and the quantum sizes of the structures. We have observed a transition from the rocksalt structure for short NPs to the wurtzite structure for long NPs. These two structures are found to correspond to two mechanisms
of surface stabilization, which are also observed in short and long NPs. For short NPs, the surfaces are stabilized by merging two polar facets of each layer into one while for long NPs, an ‘‘effective charge transfer’’ between two outer base surfaces is the key mechanism for surface stabilization. Effects of sizes and surfaces on electronic properties of the structures, e.g., the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap, are examined to support the discussion of the structural transition and the polar surface stability.
ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction Current interest in zinc oxide (ZnO), a wide band gap semiconductor material, is fueled by the unique properties, which allow ZnO-based devices to have distinguished performance in optoelectronics, sensors, transducers, and biomedical sciences [1–4]. A direct wide band gap (3.37 eV 375 nm at 300 K), the polar surfaces and the high exciton binding energy (60 meV) are promising for high efficient light emitting nanodevices (blue light emitting diode (LED), nanoscale ultraviolet (UV) laser) and photodetectors [1]. The transparent conductivity of ZnO may find applications in flat panel displays and thin film solar cells [1]. The strong piezoelectric and pyroelectric properties, which are resulted from the lack of a center of symmetry and a large electromechanical coupling of ZnO material, are useful in surface acoustic wave devices for communication and sensing applications [1]. Diluted magnetic semiconductors obtained by doping ZnO with transition metals are promising materials for spintronic [1]. Moreover, ZnO nanoparticles can be used for some biomedical applications, e.g., selective destruction of tumor cells and drug delivery [4]. While physical properties of bulk semiconductor structures are size independent, major physicochemical
properties of semiconductor structures of nano sizes, e.g., nanoparticles (NPs), are essentially different and are strongly size/shape-dependent [3, 5, 6]. For NPs, surfaceto-volume ratio of the atom involving species is frequently used to characterize the quantum size effects. This ratio is about 15% for a 5-nm NP while it is about 0% for bulk structures. As the surface-to-volume ratio increases, the quantum size effects are expected to be of major importance in determining the physical properties of the nanostructures. Interesting quantum size effects on properties of ZnO nano structures have recently been discussed, e.g., structural phases [5], acoustic phonon spectrum [6], optical blue shift [2, 3, 6–8], surface stabilization [9], piezoelectricity [10], and exciton binding energy [11, 12]. We present in this paper a first-principles study on structural and electronic properties of several series of freestanding ZnO hexagonal- and triangular-cross-sectional prismatic NPs, emphasizing the effects of the sizes and the surfaces on the structural properties of the structures. The size and the shape of the NPs considered in this work are chosen to be connected with the symmetry of the lattice and the existing experimental studies. The electronic ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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properties of the NPs and the quantum size effects on the physical properties of the NPs are then discussed. 2 Computational methods Density functional theory (DFT) [13, 14] is widely used in computational materials science (see Refs. [9, 15–21] for few examples) because of its accuracy and predictive capability. However, it is still not easy to use DFT for simulations of large structures, e.g., those of thousands atoms, because the computational demand generally grows much faster than the structure size. Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA), an electronic structure code that relies on DFT and implements linear-scaling methods for gaped systems [22, 23], is a well designed tool for simulations of quantum-mechanical models of several hundreds atoms. Therefore, computational work presented in this work is performed by the version of DFT implemented in SIESTA while some figures are prepared by XCrySDen [24]. Our DFT calculations are carried out using optimized Troullier–Martins nonlocal pseudopotentials with partial core corrections. The flexible localized numerical doublezeta plus polarization (DZP) basis set is used, allowing for arbitrary angular momenta, multiple radial functions per angular momentum, as well as polarized and off-site orbitals [22]. The exchange-correlation energy is evaluated using the widely used generalized gradient approximation developed by Perdew et al. [25]. In our pseudopotential approach, the Zn-3d electron states are treated as valence states so that the hybridization between the Zn-3d and O-2s orbital is taken into account. Consequently, the valence electron configurations taken for oxygen and zinc atoms were 2s22p4, and 4s23d10, respectively. The pseudopotential radii employed for s, p, d, and f orbitals of the oxygen atoms are all 1.14 a.u., while the radii for those of the zinc atoms are 2.09, 2.09, 1.89, and 2.09 a.u., respectively. 3 ZnO nanoparticle structures For preparing the ZnO NP structures to be studied, we first design series of prismatic unsaturated (vacancy-free) wurtzite NPs by cropping corresponding unrelaxed wurtzite ZnO nanowires (NWs), and then relax them to the optimized geometry. Because of the symmetry of the wurtzite crystal structure and motivated by experimental works [1–3, 6, 26], we consider in this paper a series of three triangular and two series of four hexagonal prismatic NPs of which the prismatic axes, taken to be the z axis, are parallel to the c axis on the [0001] direction of the wurtzite lattice. A double facet layer of atoms on the xy plane, simply referred to as a ‘‘layer’’ in what follow, is the building block of a series, of which the NPs are different in the number of layers but share the same layer geometry (see Fig. 1 for an illustration). We label the series of triangular NPs as triangular (TR) and two series of hexagonal NPs as HA and HB. An NP in a series is referred to by one of the numbers 1, 2, 3, or 4 following the series label so that the larger the number is, the longer the NP is. ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 1 (online color at: www.pss-b.com) Optimized geometries of three series of NPs labeled by TR, HA, and HB, from the top to the bottom. For each series, the geometry of the prism’s base surface is shown, followed by the side geometries of the NPs in the series, from the left to the right. The oxygen atoms are colored by red while the Zn atoms by light cyan. The numbers of atoms in a (double facet) layer are n ¼ 33 for TR, n ¼ 54 for HA, and n ¼ 96 for HB. The total number of atoms of a given NP is determined by the number of layers multiplying with the corresponding number of atoms in a layer. For example, the NP HA-3 has six layers so the number of atoms on the NP is 324 ¼ 6 54. On the figures of the side surfaces, the O-terminated facets are on the left while the Zn-terminated facets are on the right. See Table 1 for more information on the NPs.
The longest distance between an atom on the bottom base surface to another atom on the top base surface is defined as the length L of a NP. The diameter D of a NP is defined as the diameter of the circle that encloses an equivalent area of the base facet. Since the volume and/or the area of a molecular or a finite cluster structure is not well defined, we determine the area of the base facet by multiplying the area per atom s of the bulk ZnO material with the number of atoms n/2 in the facet D
4n s p2
1=2
4n ¼ p2
pffiffiffi 1=2 3 2 a ; 2
(1)
where a is the lattice parameter of the wurtzite lattice structure of ZnO. Values for the diameter D of the NPs determined by Eq. (1) are shown in Table 1. 4 Results and discussions The NPs geometries are optimized by minimizing the interatomic forces using selectively the conjugate gradient and the modified Broyden methods [27]. The ground state energies and optimized geometries of all NPs were carefully tested for convergence with respect to the size of the localized basis set and the dimensions of the supercell. The energy shift parameter related to the cutoff radii of the localized atomic orbitals is chosen to be 200 meV in order to have an optimizer theoretical wurtzite lattice parameter as ˚ and c ¼ 5.26 A ˚ , closed enough to the experimena ¼ 3.23 A ˚ and tal lattice parameters of real ZnO (a(expr) ¼ 3.25 A www.pss-b.com
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Table 1 Summary of the ZnO NPs structures studied in this work. There are three series of NPs, one with triangular cross-section and two with hexagonal cross-section, labeled by TR, HA, and HB. Relaxed prismatic length is defined as the longest distance between an atom on the bottom side surface to another atom on the top side surface while the diameter D of the NPs is defined by Eq. (1). series of NPs
number of atoms ˚) relaxed length L (A ˚ diameter D (A) HOMO level
triangular (TR)
hexagonal A (HA)
1
2
3
1
2
3
4
1
2
3
4
132 7.4 13.8 594
198 11.3 13.8 891
264 18.9 13.8 1188
162 4.84 17.6 729
216 7.4 17.6 972
324 11.2 17.6 1458
432 18.9 17.6 1944
288 4.86 23.5 1296
384 8.4 23.5 1728
480 9.1 23.5 2160
576 14.9 23.5 2592
˚ ). The convergences are assumed when the c(expr) ¼ 5.20 A ˚ . The relaxed length forces on the ions are less than 0.01 eV/A L of the NPs is shown in the Table 1. 4.1 Geometrical structure 4.1.1 Surface reconstruction description and mechanisms The optimized geometrical NPs of three series TR, HA, and HB, of which detailed parameters can be found in Table 1, are shown in Fig. 1. For each series, the base surfaces and the side surfaces of all the NPs are given. For more information, Fig. 2 sketches the atomic displacements in HA-2 and HA-4, visualizing the reconstructions of the NPs. Figures 1 and 2 indicate that for a given series of NPs, as the lengths L of the prismatic NPs increases, both the side and the base surfaces of the structures are dramatically reconstructed. In particular, the surfaces of the NPs are compressed and shrunk in such a way that depends on L and D. It is worth noting that when dangling bonds are not saturated, the surface relaxation occurs inevitably in comparing to that taken from its stress-free bulk counterparts.
Figure 2 (online color at: www.pss-b.com) Displacements of the atoms of HA-2 (top row) and HA-4 (bottom row), both from the top (left) and from the side (right) views. Similar to the convention in Fig. 1, oxygen atoms are colored by red while Zn atoms by cyan. The magnitude and direction of an arrow indicate the displacement of the atom located at the same site with the arrow. www.pss-b.com
hexagonal B (HB)
In the case of NWs, i.e., one dimension (1D) infinite structures, this relaxation may initially deform the nanowires without any applied loads, leading to the shrinkage of the nanowire outermost surface layer and the elongation of the nanowire along the wire axes [16]. Situations are even more complicated for the NPs case because the relaxation can occurs on both the base and side surfaces. The O-terminated ð0001Þ-O and the Zn-terminated (0001)-Zn surfaces, two basal planes of w–ZnO, are examples of ‘‘Tasker type 3’’, a class of polar surfaces formed by placing alternately layers of oppositely charged ions [28, 29]. Because ZnO is not centrosymmetric, any slabs representing the polar ZnO surfaces are inevitably O terminated on one side and Zn terminated on the other side. Adopting a simple assumption of the purely ionic model in which ions are in formal bulk oxidation states, such a stacking sequence creates a nonzero dipole moment which is perpendicular to the base surfaces and diverges with structure length L. Also by simple electrostatic arguments, the surface energy has been shown [29] to diverge with sample size, implying that there should exist certain mechanisms, which are responsible for the surface stabilization. With the existence of these stabilization mechanisms, ZnO polar surfaces are indeed remarkably stable [17–20]. We have observed in this work two competing mechanisms for the NPs surface stabilization, one is of major importance for short NPs while the other dominates the surface stabilization of NPs with larger L. For short NPs, pairs of Zn and O facets on each constituent layer have a tendency to merge into a single facet layer, thus canceling the internal dipole moment along the prismatic axis. Consequently, short NPs are closely described by the rocksalt-like structure, known to be the relevant structural phase of ZnO at high pressure. Indeed, Fig. 1 clearly shows that the surface of TR-1, TR-2, HA-1, HA-2, HB-1, and HB-2 are relatively flat, implying the important role of ‘‘facet merging’’, the dominated surface reconstruction mechanism for short NPs. In the literature, similar behavior has also been reported by Li et al. [17] for ZnO structures with less than 100 atoms. In the other limit, i.e., when the length L of a NP is larger (long), two base surfaces are inversely reconstructed so that two outer-most facets become rough and bi-concave (Figs. 1 ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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and 2). This behavior is consistent with that reported by Combe et al. [9], sketching bi-concave facets on the xy planes and convex side surface along the z direction. In addition, from the optimized structures reported here, we argue that the Zn-terminated facets are much more distorted in comparing with those on the O-terminated facets. The reconstruction of the prismatic NPs side surfaces can also be observed in Figs. 1 and 2. In particular, the Zn atoms move more deeply into the structures in comparing to the O atoms on the same layer. However, the side surface reconstruction is weaker than that of the base surfaces. Moreover, the side surface reconstruction dependence on the diameter D is less extensive than that on the length L. The surface reconstruction mechanism for long NPs is different from that for short NPs. When the length L of a NP is large enough, the wurtzite symmetry starts to be conserved, i.e., small clusters with wurtzite structure are formed, probably near the NPs center layers. Consequently, the internal dipole moment cannot be canceled out by merging Zn and O facets as discussed above. Instead, the major mechanism for stabilizing the surfaces in the case of long NPs is the so-called ‘‘metallization of polar surfaces’’, similar to the polar surface stabilization mechanism proposed by Meyer and Marx [18] for 2D ZnO structures. In particular, a small portion d of negative charge is considered to be ‘‘effectively’’ transferred from the outermost O facet to the other outer-most Zn facet, raising an external dipole moment between the two outer-most facet (see Section 4.2.1 for a detailed discussion of the ‘‘effective charge transfer’’). The additional dipole moment, which also depends on the structure length L, partly cancels out the internal dipole moment and consequently, stabilize the side surfaces of the NPs. Previous ab initio studies [19, 20] argues that the effective charge transfer, up to 0.17e (here e is the electron charge) [19], plays a key role in the stabilization in ZnO finite polar surfaces. We have observed in this work an amount of effective charge transfer of about 0.14e by a Mulliken population analysis, discussed in Section 4.2.1. The mechanism of metallization can be described in the language of electronic structures. In particular, the electric field originated from the internal dipole ‘‘tilt’’ the band structure of the NPs and raises the valence band maximum (VBM). When the VBM is higher in energy than the conduction band minimum (CBM), electrons can be effectively transferred from the VBM (mostly located at the O-terminated facet) to the CBM (located at the Znterminated facet). For a more detailed discussion on this picture, readers are referred to Ref. [18]. 4.1.2 Structural transition The difference in the structures of NPs with different L implies that there should exist a certain size-induced transition between two competing phases, the rocksalt phase (six-coordinates) and the wurtzite phase (four-coordinates), the former is relevant to short NPs while the latter corresponds to long NPs. Qualitatively speaking, for a NP with given diameter D, there should exist a threshold for the length L which ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
characterizes the rocksalt-to-wurtzite transition. This threshold, moreover, also characterizes the transition between two mechanisms of the surface reconstruction, one is facet merging for short NPs and the other is metalization of polar surfaces for long NPs. The size-induced rocksalt-to-wurtzite transition from short NPs to long NPs observed in this work can be considered to connect with the similar transition of ZnO material induced by pressure, which has been observed elsewhere, e.g., in Ref. [21] for bulk ZnO material. In the short NPs, because of its small volume, the internal pressure induced by base polar surface interaction is higher than the internal pressure of long NPs, which have larger volume. The structure of short NPs, therefore, is rocksalt while that of long NPs is wurtzite. Consequently, the rocksalt-to-wurtzite transition described in this work can also be considered as a pressure-induced structural transition. The rocksalt-to-wurtzite transition in the NP structures, although driven by pressure, is observed in this work to be characterized by the length L given that the diameter D of the NPs is fixed. The role of L in this transition is twofold. On one hand, when L is large enough, there is enough space for clusters of wurtzite structure to be grown. On the other hand, the internal pressure induced by the base surface interaction for larger L is smaller, also allowing the wurtzite structure of the NPs to be realized. 4.1.3 Bond analysis We have done an analysis of Zn–O–Zn angle in the NP structures because the result can help in clarifying the rocksalt-to-wurtzite transition discussed above. In Fig. 3, the normalized distributions of the Zn–O–Zn angles of HA-2/HA-4 and HB-2/HB-4 are shown. The angle distribution of HA-2 and HB-2, two short NPs, is characterized by two pronounced peaks around 908 and 1208, the former corresponds to the interlayer angle while the latter corresponds to the intralayer angles of the hexagons of the NPs. Comparing to that of the short NPs, the angle distribution of two long NPs (HA-4 and HB-4) has a new
Figure 3 (online color at: www.pss-b.com) Normalized distribution of the Zn–O–Zn angles of HA-2/HA-4 and HB-2/HB-4. Solid lines are for NPs of HA while dashed lines are for NPs of HB. Legends for particular NPs are given in the figure. www.pss-b.com
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intermediate peak locating between 1008 and 1128, implying the existence of clusters in which layers split into two (Znand O-) facets, i.e., the wurtzite structure, in HA-4/HB-4, of which the characteristic angle is 1098. It can also be observed from Fig. 3 that a considerable portion of the interlayer angles (908) are enlarged thus contributes to the formation of the new intermediate peak, demonstrating a transition from the rocksalt structure to the wurtzite structure. The smearing out of the angle distribution indicates the slight distortion of the wurtzite structure in HA-4/HB-4 because the internal pressure induced by the interaction of the base polar surfaces of this NP is still not small. As a concluding remark, the Zn–O–Zn angle distribution of the NPs is a visual signature of the rocksalt-to-wurtzite transition. 4.1.4 Structural stability To estimate the NPs stability, the binding energies per particles Ebinding of the optimized configuration is calculated as Ebinding ¼
Etotal nZn EZn nO EO ; nZn þ nO
(2)
where nZn and nO are the number of zinc and oxygen atoms, Etotal, EZn, and EO are the total energies of the NP and isolated atom Zn and O atoms, respectively. Results for binding energy is shown in Fig. 4. The binding energy of series HA and HB is much lower than that of series TR, implying that hexagonal NPs are more stable than the triangular NPs. For short NPs, the surface-induced effects on the binding energy are dominated by the base surfaces. This is however not the case for long NPs where the roles of the base and side surfaces are comparable. Figure 4 also reveals that the binding energy
Figure 4 (online color at: www.pss-b.com) Binding energy of three series TR, HA, and HB as a function of the ratio L/D of the NPs. Data for the binding energy are given by symbols while lines are for guiding the eyes.
of HA and HB series are non-monotonic, implying the existence of an optimal value of the ratio D/L with the given value of D or L for the structural stability. 4.2 Electronic structure From the optimized geometry of the NPs, we have calculated some electronic properties of the NPs, which allow for further discussions on the structural transition and related concepts of NPs. 4.2.1 Mulliken population analysis For a detailed discussion on the surface stabilization mechanisms for NPs, we have performed a Mulliken population analysis. Figure 5
Figure 5 Charge transfer data from the Mulliken population analysis for HA-2 (left) and HB-4 (right) on the planes passing the prismatic axes of the NPs. Filled/dark circles represent Zn atoms and open/light circles are for O atoms. The number attached to an atom represents the charge associated with this atom. For any NP, the O-terminated facet is on the left while the Zn-terminated facet is on the right. www.pss-b.com
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shows two cut planes along the prismatic axis of HA-2 and HB-4, it clearly indicates the positions of the atoms on the planes passing the prismatic axes of the NPs in association with the charge transfer Dq between atoms of different species. Precisely, charge transfer Dq is the difference between the valence pseudocharge density and the atomic valence pseudocharge density in association with particular sites. In other words, this quantity demonstrates the amount of charge an atom receives from other atoms of different species as a consequence of polar bonding. In Fig. 5, number attached to an atom shows the amount of charge transfer in unit of jej. For example, the amount of charge Dq an oxygen/zinc atom inside the NPs receives is about 0:7jej=0:7jej, which may vary depending on the locations of the atoms. Interestingly, the charge transfer associated with surface atoms may be strongly deviated from the mentioned value of 0:7jej=0:7jej. The concept of effective charge transfer (not to confuse with the charge transfer from the Mulliken analysis), which is proposed for the first time by Meyer and Marx [18] for the 2D structures, can now be discussed in NPs, i.e., in 0D structures. It can be observed from Fig. 5 that for HB-4, the charge transfer associated with atoms on the base surfaces is generally smaller in magnitude than that for atoms inside the NPs. Specifically, the charge transfer of the zinc atom at the right-most site of HB-4 is 0.56jej, implying that the Znterminated facet’s zinc atom is less positive an amount of d ¼ 0.14jej than the zinc atoms residing deeply inside the NP, whose charges are 0:70jej. The similar charge difference can also be observed between the oxygen atom at the leftmost site on the O-terminated facet (the left side of the view for HB-4 in Fig. 5) and the oxygen atoms residing deeply inside the NP. These charge differences can be considered as an effective process in which an amount d is transferred from the O-terminated facet to the Zn-terminated facet. Consequently, there is an amount of 2d charge difference between the facets, raising an additional dipole moment that partially cancels out the internal dipole moment, thus stabilizing the NPs surfaces as discussed in Section 4.1. The effective charge transfer amount d ¼ 0.14jej found in our work is consistent with the amount of 0.17jej reported in Ref. [19]. Effective charge transfer is also observed from the prismatic side surfaces of HB-4 but with a smaller amount (d 0:02 0:05jej), because of the reconstruction of the dangling bonds on the surfaces. The large amount of effective charge transfer observed on HB-4 can be interpreted as an observation for the important role of the effective charge transfer mechanism in stabilizing the surfaces of HB-4, i.e., a long NP. For short NPs, as discussed in Section 4.1, merging two facets of a given layer is the main mechanism for stabilizing the NPs surfaces. This mechanism can also be seen in Fig. 5 where the relatively flat surfaces of HA-2, i.e., a short NP, are shown. The charge transfer for this NP is generally uniform throughout the structure, thus the effective charge transfer between the two outer-most facets is considerably small.
ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Consequently, the effective charge transfer is of minor role in stabilizing the surfaces of HA-2. 4.2.2 Charge difference distribution Electronic charge difference (ECD) is useful in recognizing the nature of the charge transfer Dq analyzed in Section 4.2.1. ECD, by definition, describes the distribution of the charge transfer as a consequence of bonding in the structure: drðrÞ ¼ rðrÞ ratm ðrÞ;
(3)
where r(r) is the valence pseudocharge density and ratm ðrÞ the sum of atomic valence pseudocharge densities. In Fig. 6, the ECD profile is shown for HA-2 and HA-4. For each NP, cuts on xy and yz planes are chosen to clearly demonstrate the ECD distribution around the atoms lying on the planes. The region of high magnitude ECD is colored red (negative) and magenta (positive) while the low magnitude ECD regions are colored green (negative) and cyan (positive). Figure 6 reveals that for a layer, the zinc facet is positively charged and the oxygen facet is negatively charged. On a given layer, because of the alternative arrangement of zinc and oxygen atoms on the xy plane, the dipole moment on the plane is vanishing. There is, however, non-zero dipole moment along the z direction because charges of different signs on the layer are still separated in this direction. For outer layers, the surface reconstruction can merge the two facets but it is not the case for layers inside the NPs. Consequences of the dipole moments has been discussed in Section 4.1. The localization of ECD around the zinc atoms (light cyan) and O (red) inside the structures demonstrates the
Figure 6 (online color at: www.pss-b.com) Electronic charge difference distribution drðrÞ for two NPs, HA-2 on the top row and HA-4 on the bottom row. In each row, views from the base surfaces are given on the left while views from the side surfaces are on the right. Oxygen and zinc atoms are colored red and light cyan.
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highly ionic characteristic of these atoms. The ECD distribution of surface atoms is, however, more delocalized, visualizing the presence of dangling bonds. Also, the surface states are mainly located at oxygen sites, while at the zinc sites, they are less extended. From Fig. 6 for the ECD distribution of HA-2 and HA-4, we may draw some comparative comments. First, we note that from the hexagonal base view, comparing to the ECD density around the inside atoms, the ECD density around the atoms on side surface are more broadly extended because of the dangling bonds that certainly exist for the atoms. Next, similar behavior can also be observed from the side view with a note that the most extended ECD densities belong to the edge atoms. Finally, the side views in Fig. 6 reveals that the ECD density on the base surfaces of HA-4 is smaller than the ECD density on the base surface of HA-2. In other words, the effective charge transfer in HA-4 is more than that in HA2, implying the difference in the surface stabilization mechanisms in the two NPs. 4.2.3 Dipole moment An examination of the dipole moment m of the NPs is clearly desirable because m, or more precisely, the z-component mz of m, plays the key role in the polar surface stabilization mechanisms of both short and long NPs, as discussed in Section 4.1.1. From the Mulliken charge data obtained, the dipole moment m of the NPs is determined by [30] m¼
X
Dqi ri ;
(4)
i
where Dqi is the Mulliken charge transfer at site i located at the coordinate ri. Results for the dipole moment m per Zn-O pair (bond) calculated from Eq. 4 indicate that mx and my, i.e., the x- and y- components of m are closed to zero, i.e., at least two orders smaller than mz, due to the symmetry of the NPs. It is also found that the dipole moment mz for optimized NPs is smaller by one to three orders than the corresponding value of bulk ˚ ), emphasizing the key role wurtzite ZnO material (0.687jej A of mz reduction in stabilizing the NPs polar surfaces. In Fig. 7, the dipole moment mz per Zn–O bond is shown for the optimized NPs of TR, HA, and HB. The figure reveals that for long NPs, i.e., those with large L/D, the dipole moment mz becomes very large (although this value is still much smaller, about ten times, than that of the bulk wurtzite ˚ ), signaling the wurtzite order in the long ZnO, i.e., 0.687jej A NPs. For short NPs, i.e., those with small L/D, the dipole moment is nearly vanished, implying the existence of the rocksalt order in the structures. Figure 7 also indicates a D-dependent optimal ratio L/D, which is about 0.6 for HA and 0.4 for HB. The values are consistent with the optimal value of L/D for the binding energy shown in Fig. 4, again, implying the direct role of the dipole moment mz on the structural stability. Consequently, the optimal L/D indicated in Figs. 4 and 7 can be regarded as an estimation of the rocksalt-to-wurtzite transition. www.pss-b.com
Figure 7 (online color at: www.pss-b.com) The z-component dipole moment mz of the NPs in three series TR, HA, HB. Data are given by symbols while the lines are guides for the eyes.
4.2.4 HOMO–LUMO gap The suppression of HOMO–LUMO gap at large L is useful for a discussion of ‘‘metallization of polar surfaces’’, the key reconstruction mechanism of long NPs. The HOMO–LUMO gap, by the way it is named, is calculated as the energy difference between LUMO and HOMO levels. Although DFT systematically underestimates the gap, one can still examine the trend of this quantity at large L. The dependence of the gap on the NPs length L is sketched in Fig. 8, showing a general tendency of reducing the gap as the NPs get longer. For NPs with not large L and/or D, e.g., HA-2 and HB-2, the gap is larger than the corresponding theoretical bulk value, certifying the quantum confinement effects. As L and/or D become larger, the structures are shifted from the semiconductor character to the metallic character where the gap can be sufficient small, enabling the key role of ‘‘metallization of polar surfaces’’ in long NPs, as discussed in Section 1. 4.2.5 Projected density of states One of the major reasons for the HOMO–LUMO suppression at large L is the
Figure 8 (online color at: www.pss-b.com) HOMO–LUMO gap at large L of the NPs in three series TR, HA, and HB. Data for the NPs are given by symbols while the lines are guides for the eyes. ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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60
20 0 100
(b) HA−2
75
25
Projected DOS (a. u.)
0 4.0
(c) HA−2, site PDOS
3.0
10 0 −2
0 −2
(d) HA−3
0 200
(e) HA−4
150
50 0 3.0
(f) Bulk
1.0 0.0
−3
−2
−1
1
2
−1
0
1
2
−1
0
1
2
−1
0
1
2
−1
0
1
2
10 0 −2
20 10 0 −2
0.2
O−2p O−2s Zn−4s Zn−4p Zn−3d
2.0
0
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O−2p O−2s Zn−4s Zn−4p Zn−3d
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O−2p O−2s Zn−4s Zn−4p Zn−3d
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2
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1
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O−10 O−26 O−75 Zn
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O−2p O−2s Zn−4s Zn−4p Zn−3d
50
the oxygen 2s orbitals. By examining a detailed report of contributions from particular atom sites, we found that states near the conduction band edges are formed by the hybridization of the states arising from the s orbitals of zinc atoms on the surface and the p orbitals of oxygen atoms inside the NPs. Figure 9(c) provides identification information of the atoms that significantly contribute to the valence and the conduction band edges. Three facet’s oxygen atoms at sites 10, 26, and 75 dominate the valence band edge while the conduction band edge is formed by all the zinc atoms with comparable contributions. We therefore can conclude that the dangling bonds of surface atoms give rise to the majority of the localized in-gap states residing at the top of valence band and the bottom of conduction band. The surface reconstruction during the relaxation of the NPs, as observed in Fig. 1, introduces in-gap states. Most of them are located near the VBM while the others in the vicinity of the CBM. The states near the VBM are acceptor levels while the others, residing near the CBM, are donor levels. The existence of the levels results in the DOS peaks, which can be seen in Fig. 9(c) for the partial DOS contributed by particular sites.
20
O−2p O−2s Zn−4s Zn−4p Zn−3d
(a) ZnO NW
40
0.1 0.0 −2
0
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2
3
Energy (eV)
Figure 9 (online color at: www.pss-b.com) Orbital PDOS of (a) ZnO nanowire (NW), (b) HA-2, (d) HA-3, (e) HA-4, and (f) bulk wurzite ZnO structures. Specifically for HA-2, (c) is for the site PDOS, namely the DOS contributed by particular atoms in the NP. Legends are shown on the corresponding sub-figures. Inset for a sub-figure provides a closer look to the vicinity of the HOMO–LUMO energy gap.
appearance of some in-gap states, mainly distributed near the VBM. Therefore, we examine the partial density of states (PDOS), i.e., the density of states projected on particular orbitals or atomic sites, of the NPs for a more detailed discussion on the contributions to the valence and conduction band edges. The PDOS for the NPs from the series HA are shown in Fig. 9 together with the PDOS of a ZnO nanowire and a ZnO bulk structure serving as references. For each NP, the PDOS from the atomic orbitals 2s, 2p of oxygen atoms and the atomic orbitals 4s, 4p, and 3d of zinc atoms are plotted separately. The orbital projected DOS for HA-2, HA-3, and HA-4 are shown in Fig. 9(b), (d), and (e), respectively. It is clearly observed from these figures that the HOMO states of the NPs are predominantly p-like symmetric and the valence band edge are mainly formed by surface oxygen atoms, i.e. the base dangling oxygen 2p orbitals. Small contributions from the zinc 3d and 4p (semicore) orbitals also present deeply inside the valence band. The LUMO states are essentially slike symmetric and the conduction band edge arises from the surface zinc atoms residing at the side and the base facets, i.e., the dangling Zn-4s orbitals. Smaller contributions to the conduction band also come from the oxygen 2p and possibly ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
5 Conclusions We have performed in this work firstprinciples calculations on several series of ZnO NPs of hexagonal and triangular cross-section shape with different lengths and diameters. The structural and electronic properties of the NPs are found to be strongly affected by the NPs size, shape, and the reconstruction of NPs surfaces, especially the base surfaces. We have observed a transition from the rocksalt structure for short NPs to the wurtzite structure for long NPs. These structures are consequences of the surface stabilization mechanism, which depends on L, the length of the NPs. For short NPs, surface reconstruction stabilizes the surfaces by merging two facets into one flat facet in each layer. For long NPs, there is an effective charge transfer process between the two outer-most facets, partially canceling out the internal dipole moment interaction, thus stabilizing the surfaces. This suggests that for the NPs of given diameter D, these exists a threshold for the length L that characterizes the rocksalt-towurtzite transition. From the analysis of the projection of the density of states on the atomic orbitals, we found that both HOMO and LUMO involve atoms located at the surfaces, particularly the base surfaces. While the HOMO–LUMO gap is of semiconductor type for short NPs, that for long NPs is strongly suppressed, enabling the surface metallization process, which may be the origin of the surface instability. The Mulliken population analysis and the electronic charge density analysis reveal some ‘‘effective charge’’ transfer between the outer-most facets of the NPs, supporting the polar surface stabilization mechanism for long NPs. The dipole moment of the NPs is also derived from the Mulliken charge, clarifying the key role of dipole moment reduction in stabilizing the polar surfaces of the NPs. www.pss-b.com
Original Paper Phys. Status Solidi B 249, No. 3 (2012)
Acknowledgements Part of this work (by V. N. T.) is supported by the Vietnamese NAFOSTED program No. 103.02.100.09.
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