and Surface-dependent Stability, Electronic Properties, and Potential

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Size- and Surface-dependent Stability, Electronic Properties, and Potential as Chemical Sensors: Computational Studies on One-dimensional ZnO Nanostructures Zhen Zhou,†,* Yafei Li,† Lu Liu,† Yongsheng Chen,‡ S. B. Zhang,§ and Zhongfang Chen§,|,* Institute of New Energy Material Chemistry, Institute of Scientific Computing, Tianjin Key Laboratory of EnVironmental Remediation and Pollution Control, Nankai UniVersity, Tianjin 300071, P. R. China, Department of CiVil and EnVironmental Engineering, Arizona State UniVersity, Arizona 85287, USA, and Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA; Department of Chemistry, UniVersity of Puerto Rico, Rio Piedras Campus, San Juan, PR 00931-3346 ReceiVed: April 15, 2008; ReVised Manuscript ReceiVed: June 19, 2008

The structures and electronic properties of zinc oxide (ZnO) one-dimensional (1D) nanostructures, including nanowires with hexagonal or triangular cross sections, faceted nanotubes, and conventional single-walled nanotubes, were investigated using density functional theory. The binding energies and band gaps of ZnO 1D nanostructures are determined by surface atom ratios and sizes. Hydrogen passivation preserves semiconducting characteristics and further enhances the band gap of ZnO nanowires. ZnO nanowires are potential chemical sensors for dioxin. 1. Introduction Zinc oxide (ZnO) has attracted a great deal of interest from researchers due to its direct, wide band gap (Eg) 3.3 eV at 300 K) and thus its potential technological applications. Moreover, ZnO exhibits advantages over other wide-band gap semiconductors such as GaN, including a large exciton binding energy (60 meV), the availability of fairly high-quality single crystals, and simpler crystal-growth technology. These characteristics make ZnO a good candidate for low-cost devices.1 In particular, onedimensional (1D) ZnO nanostructures (nanowires, nanorods, nanotubes, etc.2-16) have unique physical and chemical properties arising from surface and quantum confinement effects, and thus can be utilized as fundamental building blocks for fieldeffect transistors, gas sensors, resonators, transducers, actuators, cantilevers, and field emitters.1 ZnO nanowires usually grow along the (0001) direction and have a hexagonal or triangular cross section.17 Since Iijima’s structural elucidation in 1991,18 the synthesis of tubular nanostructures has been actively explored. Many layered compounds, such as the metal dichalcogenidessMoS2,19 ZrS2, and HfS2s,20 NiCl2,21 and boron nitride (BN),22 were folded into nanotubes. Interestingly, some nonlayered materials, such as GaN23 and AlN,24 also exhibit tubular morphologies, although they resemble their bulk wurtzite phase rather than single-walled nanotubes.25 Considerable efforts have also been made to fabricate ZnO nanotubes.26-33 ZnO nanotubes are faceted and can be regarded as nanowires with hollow interior centers that preserve the bulk-like configuration. Recently, many theoretical and computational investigations have focused on ZnO nanostructures34-47 such as nanowire, nanofilm, nanoplate, graphitic planar sheet, and single-walled nanotubes (SWNTs). However, it is still necessary to compare the energetics and electronic properties of various 1D ZnO nanostructures at the * Corresponding author e-mail: [email protected] (ZZ) and chenz4@ rpi.edu (ZC). † Nankai University. ‡ Arizona State University. § Rensselaer Polytechnic Institute. | University of Puerto Rico.

Figure 1. Models of ZnO 1D nanostructures: (a) nanowires with hexagonal cross sections, (b) nanowires with triangular cross sections, (c) faceted nanotubes, and (d) conventional SWNTs. Red and gray balls denote O and Zn atoms, respectively.

same theoretical level, and to enhance understanding of the structural and electronic properties of these nanostructures. Therefore, models of ZnO 1D nanostructures, including faceted nanotubes, crystalline nanowires with hexagonal and triangular cross sections, and SWNTs, were considered in the present computational investigation. Also, the possibility of utilizing ZnO nanostructures as adsorbents or as sensors of toxic chemicals was explored. 2. Computational Method In this work, ZnO crystalline nanowires and faceted nanotubes of various sizes were compared with conventional single-walled nanotubes. ZnO usually exhibits a typical wurtzite structure (space group P63mc) with two zinc and two oxygen atoms in a tetrahedral coordination per unit cell. The experimentally obtained lattice parameters are as follows: a ) b ) 3.2465 Å, c ) 5.203 Å, and u ) 0.3812.48 To create the models, a large 10 × 10 × 1 ZnO supercell was first constructed based on the above experimental wurtzite structure. The supercell was cut with cylinders of various diameters to create the initial models of several crystalline nanowires and faceted nanotubes of different sizes. The atoms outside the cylinders were removed to achieve crystalline nanowires with hexagonal (Figure 1a) or triangular (Figure 1b) cross sections of different diameters. The atoms outside a large cylinder and inside a small cylinder were removed to obtain faceted nanotubes (Figure 1c) with different

10.1021/jp803273r CCC: $40.75  2008 American Chemical Society Published on Web 08/13/2008

Computational Studies on 1D ZnO Nanostructures outer and inner diameters. ZnO nanowires and faceted nanotubes have infinite length along the (0001) direction (c axis) and are enclosed by (101j0) surfaces. The conventional single-walled ZnO nanotube models (Figure 1d) were created in analogy with single-walled BN nanotubes. Zigzag nanotubes were studied here, because they have atomic arrangements much closer to wurtzite ZnO and are more stable than armchair ones.42a All of the above structures were placed in a periodically repeating tetragonal supercell, separated by a vacuum region of >10 Å in the x and y directions, so that the interaction between the tubes/wires and their nearest images is negligible. The geometric optimizations of infinitely long (rather than truncated) 1D systems were performed with periodic boundary conditions (PBC) along the tube/wire axis. Our density functional theory (DFT) computations were performed using the plane-wave pseudopotential technique implemented in the Vienna ab initio simulation package (VASP).49 Throughout the computations, the generalized gradient approximation (GGA) with the PW91 functional50 and a 360 eV cutoff for the plane-wave basis set were used. For all the systems studied, the coordinates of the atoms within the supercell were fully relaxed during geometry optimizations; the lattice constant, c, was also optimized to minimize the total energy along the tube/wire axis. A 1 × 1 × 5 k-point Monkhorst-Pack51 mesh was used for sampling the 1D Brillouin zone along the tube/wire axis, and the convergence thresholds were set at 10-4 eV for energy and 10-3 eV/Å for force. On the basis of the equilibrium structures, a 1 × 1 × 21 k-point Monkhorst-Pack mesh was used to obtain band structures. The adsorption of dioxin on ZnO nanowires was investigated using all-electron DFT computations within the GGA with the PW91 functional50 and the double numerical plus polarization (DNP) basis set as implemented in the DMol3 package.52 3. Results and Discussion 3.1. Geometric Structures of ZnO 1D Nanostructures. First, the bulk ZnO model was optimized. The optimized lattice parameters of wurtzite ZnO (a ) b ) 3.236 Å, c ) 5.182 Å, and u ) 0.381) are very close to the experimental values48 and previous DFT computational results.34-44 ZnO 1D nanostructures (see Figure 1) were then fully relaxed without any symmetry constraints. The interatomic topology and the wurtzite structure are retained in the ZnO nanowires, although the bond lengths and angles change in the lateral surface. For example, for the nanowire in Figure 1a, the lengths of Zn-O bonds in the surface parallel to the wire axis are 1.880 Å, and the zigzag Zn-O bond lengths are about 1.890 and 1.965 Å, respectively. In comparison, the corresponding Zn-O bond lengths in bulk ZnO are 1.974, 1.968, and 1.968 Å. The Zn-O-Zn and O-Zn-O bond angles are ∼103.7 and 118.5°, respectively, in the nanowire, whereas in bulk ZnO they are 108.3° and 110.6°. The surface Zn and O atoms are all 3-fold coordinated, and the large surface strain induces structural distortions. The surface atoms exhibit apparent shrinkage, but the atoms in the core region are accordingly expanded, so the lengths of the Zn-O bonds parallel to the wire axis in the inner core are elongated to 2.017 Å. In addition, the optimized lattice constant c of the nanowire unit cell is longer than that of the bulk ZnO unit cell (5.27 vs 5.182 Å). Similar structural distortions also occur in ZnO nanowires with triangular cross sections (Figure 1b), as well as on the outer and inner lateral surfaces in faceted ZnO nanotubes (Figure 1c). The faceted nanotubes can be regarded as nanocrystals that

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Figure 2. Variation of binding energies with surface atom ratios for various 1D ZnO nanostructures. The inset shows binding energy as a function of diameter for the nanowires with hexagonal cross sections.

preserve the bulk-like configuration but possess a hollow interior defect. Single-walled ZnO nanotube models, however, retain regular, smooth walls (Figure 1d) after full relaxation, like single-walled carbon nanotubes (SWCNTs). The bulk configuration is completely lost; Zn and O atoms are all 3-fold coordinated and adopt hexagonal configurations. The Zn-O bond length (∼1.89 Å) and bond angles (118-120°), characterize a structure very different from bulk ZnO. 3.2. Stability of Various ZnO 1D Nanostructures. Figure 2 summarizes the binding energies of various 1D ZnO nanostructures. The binding energy (Eb), defined as Eb ) (nEZn + nEO - EZnnOn)/n, measures the stability of different structures; those with larger binding energies are more stable. The binding energies of nanowires with hexagonal cross sections clearly increase with wire diameter (see the inset in Figure 2) (the wire diameter is defined as the largest lateral distance between atoms). This increase in binding energy indicates high stability for large nanowires. The binding energies of ZnO nanowires do not increase linearly with wire diameter. However, they do satisfy a linear relationship with the surface atom ratio (Rs), Eb ) 7.62 - 0.91Rs (Figure 2) (Rs is defined as the number of unsaturated Zn and O atoms in the surface divided by the total number of Zn and O atoms in the system). The largest nanowire studied, H3, which is 2.3 nm in diameter and has 25% surface atoms, exhibits the largest binding energy, 7.4 eV, 97.2% of that of bulk ZnO. For ZnO nanowires with hexagonal cross sections, Fan et al. also found linear behavior for binding energy versus surface atom ratio, and relaxations on the facet surfaces play an important role in stabilizing the nanowires.36 The linear relationship of Eb versus Rs is also found in ZnO nanowires with triangular cross sections (T1-T3). Interestingly, the binding energies of various faceted ZnO nanotubes are also linearly related to the ratios of surface atoms, but not to tube sizes. For example, among the faceted nanotubes, F1-F3, F2, and F3 have the same tube diameters, and F1 and F3 have the same surface atom ratios; however, F1 and F3 exhibit almost the same binding energies, 7.20 eV. Accordingly, the stabilities of these 1D ZnO nanostructures are determined directly by the ratios of unsaturated surface atoms. Because conventional SWNTs lose the wurtzite characteristics, even though their atoms are all in the surface and have the same surface atom ratio (100%) as that of the smallest nanowire with

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Figure 3. Structure evolution of a ZnO single-walled faceted nanotube and a wurtzite single layer after full relaxation.

hexagonal cross section (H0), their binding energies are far from the above line for nanowires and faceted nanotubes. A series of (n,0) zigzag ZnO SWNTs (n ) 8, 10, 12, 15, and 20) are optimized as well as a single ZnO graphitic layer, which can be regarded as the SWNT with the largest tube diameter. The binding energies of these structures are in the range of 7.10-7.17 eV, slightly larger than those of the ultrathin nanowires with high surface atom ratios, such as H0 and T1, but much lower than those of the nanowires and faceted nanotubes with lower surface atom ratios. Thus, it is understandable that although the existence of ZnO SWNTs has been predicted theoretically,44 they have not been observed in experiments. Experimentally prepared ZnO nanowires are all rather large in diameter, and the ultrathin nanowires are also impractical under the present experimental conditions. ZnO adopts intrinsically more stable configurations during formation. Specific experimental conditions, such as template confinement, may favor the retention of nanostructures with bulk-like configurations such as faceted nanotubes. However, ZnO SWNTs do not adopt the energetically favorable configuration, their synthesis would be extremely challenging. When surface atom ratios are high, on the other hand, the situation changes completely. Small nanowires such as H0 and T1 that preserve the wurtzite configuration exhibit much lower binding energies than ZnO SWNTs. As surface atom ratio increases, the strain in the system also increases dramatically. If the surface atom ratio is too high, surface restructuring alone is not enough to eliminate the large strain, so ZnO SWNTs are energetically more preferable. When a ZnO single layer with a wurtzite configuration is fully relaxed, the buckled layer completely changes into a planar and smooth one (Figure 3). Similarly, the thinnest faceted ZnO nanotube, F0, with one ZnO wurtzite wall, also quits the initial configuration and adopts the conventional SWCNT-like form after full relaxation. In these structures, all atoms are in the surface and are 3-fold coordinated with sp2 hybridization. The high stability of ZnO SWNTs can be explained by the diminishing dipole, similar to the case in ZnO graphitic layers.38 Similar results are reported for the stabilities of various nanowires and nanotubes of other wurtzite compounds, such as AlN,25 GaN,53 and ZnS.54 For zero-dimensional (0D) ZnO clusters, a shape-driven phase transition from the four-coordinate wurtzite to the six-coordinate

Zhou et al. rocksalt structure was theoretically found in a ZnO cluster with 48 atoms.37 Wang et al. also found some tube configurations in their search for the most stable or metastable structures of (ZnO)n (n ) 9-18) clusters.40 Their DFT computations also show that the graphitic planar structure and single-walled nanotubes of ZnO are experimentally accessible under certain conditions.42 For example, ZnO thin films less than three Zn-O layers thick remove the dipole by adopting a planar, graphitelike structure rather than the wurtzite structure.35,38 Single-walled ZnO nanotubes can exist in principle, and fabrication through the solid-vapor phase process with carbon nanotubes as templates has been proposed.35 Zhang and Huang also found that infinitely large ZnO nanoplates and infinitely long ZnO nanowires transform from wurtzite to graphitic structures below a critical thickness or diameter.41 For ultrasmall ZnO 1D nanostructures (e38 atoms per unit cell), SWNTs are energetically more favorable than crystal-like nanowires.43 Experimentally, the most exciting finding is that, in a novel nonpolar structure of two monolayer (ML) ZnO (0001) films grown on Ag (111), Zn and O atoms are arranged in planar sheets such as in the hexagonal BN prototype structure, and the transition to the bulk wurtzite structure occurs in the 3-4 ML coverage range.55 3.3. Electronic Structures of ZnO 1D Nanostructures. Electronic band structures were computed based on the equilibrium ZnO 1D nanostructures. Figure 4 shows the typical band structures for the ZnO nanowires with hexagonal cross section H2 and triangular cross section T2, the faceted nanotube F1, and the (12,0) SWNT. Figure 5 compares the band gaps of all the 1D nanostructures. A direct band gap of 0.72 eV is computed for the ZnO wurtzite solid at the Γ point along the Γ f Z direction in reciprocal spaces, which is close to previous GGA35 and LDA39 results but is much lower than the experimental band gap (3.437 eV at 2 K). This is due to the well-known fact that GGA and LDA approaches underestimate band gaps.56 However, the trends elucidated by the computational results at the same level of theory for various 1D nanostructures (Figure 5) should still be valid. The band gaps of all the ZnO 1D nanostructures are larger than that of bulk ZnO (Figure 5). Generally the quantum size effect enlarges the band gaps; however, the band gap change due to quantum confinement effects is also related to the surface effect (surface atom ratio) and diameter. It has been reported that AlN25b,c and GaN57 nanowires exhibit smaller band gaps than those of bulk solids because surface effects dominate in determining the band gaps of these 1D nanostructures. The surface states generate new energy levels at both valence and conduction band edges, which narrow the band gaps significantly. Similarly, the surface effects are also very important in determining the band gaps of ZnO 1D nanostructures; the band gaps exhibit a good linear relationship with surface atom ratios with the exception of the (12,0) ZnO SWNT (Figure 5). However, unlike AlN and GaN nanowires, the band gaps of ZnO nanostructures are also linearly related to wire diameters (the inset of Figure 5), which agrees well with the scaling observed in previous density functional calculations of the quantum size effect in ZnO quantum wires by Li and Wang,46 thus the surface effects are not the only dominant factor in the band gaps of ZnO nanostructures. Therefore, although the surface effects decrease the band gaps of ZnO nanostructures, they cannot counteract the quantum size effect, and the overall effect is the wider band gaps of ZnO nanostructures than that of bulk ZnO.

Computational Studies on 1D ZnO Nanostructures

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Figure 4. Electronic band structures of various ZnO 1D nanostructures. The dashed lines denote the positions of the Fermi levels.

Figure 5. Variation of band gaps with surface atom ratios for various 1D ZnO nanostructures. The inset shows the band gap as a function of diameter for the 1D nanostructures.

Surface effects have a larger influence on the band gaps of faceted ZnO nanotubes than the size (diameter) effects. F1 and F3, which have the same surface atom ratios, exhibit close band gaps; F2 and F3, on the other hand, have different band gaps despite their similar diameters. With an atomic configuration significantly different from bulk wurtzite crystal, the band structure of the ZnO SWNT is similar to those of other nanostructures, but the band gap is very different from the linear relationships of other systems. As reported by Wang and co-workers,42a the calculated band gaps of ZnO SWNTs are relatively uniform and are almost independent of diameter and chirality. 3.4. Hydrogen-passivated ZnO Nanowires. The H1 ZnO nanowire was used as a model system to investigate hydrogen saturation. The surface Zn and O atoms with dangling bonds are all saturated with H atoms, and the H-passivated nanowire is fully relaxed. In the relaxed H1 nanowire, the surface atoms show almost the same structural features as atoms in the core region of ZnO nanowires; for example, the Zn-O bond lengths are all about 2.0 Å. Therefore, hydrogen saturation eliminates surface strain, and the size effect is dominant in H-passivated ZnO nanowires. The electronic structure of this nanowire was also investigated. Figure 6 presents the band structures of H1 ZnO nanowires without and with H saturation. The H-passivated ZnO nanowire exhibits similar band structures as the pristine H1

Figure 6. Electronic band structures for H1 ZnO nanowires without (left) and with (right) hydrogen saturation. The red dashed lines indicate the position of Fermi levels.

ZnO nanowire, but the band gap is widened from 1.57 to 2.54 eV due to the elimination of surface states. The saturation of AlN nanowires with H25b or NH319c and of silicon nanowires with -H, -OH or -NH258 has been reported to result in various modifications to band gaps. Hu et al. 34 and Wang et al.59 found that the band gap of ZnO nanowires with triangular cross sections can be tuned by passivation with hydrogen; bare and completely passivated wires are semiconducting, whereas wires with intermediate hydrogen passivation exhibit metallic behavior. 3.5. Adsorption of Dioxin on ZnO Nanowires. The electronic properties of ZnO nanostructures are susceptive to surface states, which means that they have great potential as chemical sensors. The viability of ZnO nanostructures as sensors with high sensitivity and fast response time has been demonstrated for many molecules, including H2,60 O2,61 CO,62 ethanol,63 and glucose.64 Dioxin (C12H4O2Cl4), a compound consisting of two benzene rings that have four attached chlorine atoms and are linked by two oxygen atoms, is a common environmental pollutant with serious toxicity. Dioxin is a carcinogen and affects the human immune system65 and can be generated by the burning of organic compounds, especially the open burning of electronic wastes. Recent research has shown that the dioxin body burden of a woman of childbearing age at an electronicwaste recycling site is much higher than that at other sites.66 Thus, developing devices that can remove or monitor dioxin is of particular importance. Carbon materials, such as activated carbon,67 graphene sheets,68 and carbon nanotubes,68,69 have

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Figure 7. Stable configuration of dioxin adsorbed on a H1 ZnO nanowire (a), density of states (DOS) of a clean H1 ZnO nanowire (b), and DOS of a dioxin-adsorbed H1 ZnO nanowire (c). The red dotted lines denote the position of Fermi levels, and the pink dashed lines show the partial DOS of dioxin.

been found to be excellent dioxin sorbents. However, these carbon materials are not sensitive enough for dioxin monitoring. Here we explore the potential for ZnO nanostructures to serve as dioxin sensors using the H1 ZnO nanowire as a model absorption system. Figure 7 presents the most stable configuration and associated adsorption energy (Eads), defined as Eads ) EZnO-dioxin - EZnO - Edioxin, where EZnO-dioxin, EZnO, and Edioxin stand for the total energy of the dioxin adsorbed ZnO nanowire, the clean ZnO nanowire, and the dioxin molecule, respectively. As shown in the figure, the dioxin molecule adsorbs above the faceted surface of the ZnO nanowire. After the geometric optimization, the initial planar shape of the dioxin molecule becomes slightly folded. The nearest distance between dioxin and the ZnO nanowire is about 3.0 Å, and only negligible charge transfer (0.04 |e|) occurs from the ZnO nanowire to the dioxin molecule. Both of these characteristics indicate that the exothermic adsorption energy (-0.52 eV) is primarily derived from electrostatic and exchange-induced interactions.70 The dioxin adsorption strongly affects the electronic properties of ZnO nanowires. Compared with the clean H1 ZnO nanowire (Figure 7b), the density of states (DOS) of a dioxin absorbed nanowire (Figure 7c) was considerably modified; the most pronounced feature is that a new peak appears at ∼0.2 eV below the Fermi level above the valence bands. This peak is attributed to the highest occupied molecule orbital (HOMO) of dioxin. Hence, the conductance and luminescence of ZnO nanowires change upon dioxin adsorption, which can be used to detect dioxin. Moreover, the moderate adsorption energy (-0.52 eV) makes ZnO nanowires feasible for dioxin sensors with short recovery time. Very recently, An et al. have explored the potential application of (6,0) ZnO SWNT with oxygen vacancy as sensors for O2, H2, CO, NH3, and NO2.71 Experimentally available ZnO nanowires are more practical for chemical sensor applications. 4. Conclusion In summary, we investigated several 1D ZnO nanostructures, including nanowires with hexagonal and triangular cross sections, faceted nanotubes, and conventional SWNT analougs by

density functional theory computations. Despite having structural distortions on the surfaces, large-diameter nanowires and faceted nanotubes preserving the bulk-like wurtzite structure are energetically favorable because they have low ratios of surface atoms, and these nanostructures have been obtained experimentally; in comparison, with high surface ratios, single-walled ZnO nanotubes have larger binding energies than the ultrathin nanowires; however, both the SWNTs and ultrathin wires are much higher in energy than the large nanowires and faceted nanotubes, and their syntheses remain big challenges. The band gaps of all the ZnO 1D nanostructures are significantly larger than that of bulk ZnO and are related to surface atom ratios as well as tube/wire diameters. H-saturated ZnO nanowires preserve semiconducting characteristics, but the band gaps increase due to hydrogen passivation. The adsorption of dioxin also modifies the band structures of ZnO nanowires, suggesting potential applications for ZnO nanowires as chemical sensors. Acknowledgment. This study was supported in China by the SRF for ROCS, State Education Ministry, and NSFC (50502021); and in the United States by NSF Grant CHE-0716718, the US Environmental Protection Agency (EPA grant No. RD83385601) and the Institute for Functional Nanomaterials (NSF Grant 0701525). We also thank the referees for valuable suggestions. References and Notes ¨ zgu¨r, U ¨ .; Alivov, (1) See recent reviews and references therein. (a) O Y. I.; Liu, C.; Teke, A.; Reshchikov, M. A.; Dogˇan, S.; Avrutin, V.; Cho, S.-J.; Morkoc¸, H. J. Appl. Phys. 2005, 98, 041301. (b) Klingshirn, C. Chem. Phys. Chem. 2007, 8, 782. (c) Schmidt-Mende, L.; MacManus-Driscoll, J. L. Mater. Today 2007, 10, 40. (2) (a) Wang, Z. L. Mater. Today 2004, 7, 26. (b) Pan, Z. W.; Dai, Z. R.; Wang, Z. L. Science 2001, 291, 1947. (c) Kong, X. Y.; Ding, Y.; Yang, R.; Wang, Z. L. Science 2004, 303, 1348. (3) Duan, X.; Huang, Y.; Cui, Y.; Wang, J.; Lieber, C. M. Nature 2001, 409, 66. (4) Huang, M. H.; Mao, S.; Feick, H.; Yan, H. Q.; Wu, Y. Y.; Kind, H.; Weber, E.; Russo, R.; Yang, P. D. Science 2001, 292, 1897. (5) Gao, X. P.; Zheng, Z. F.; Zhu, H. Y.; Pan, G. L.; Bao, J. L.; Wu, F.; Song, D. Y. Chem. Commun. 2004, 1428. (6) Roy, V. A. L.; Djurisic, A. B.; Chan, W. K.; Gao, J.; Lui, H. F.; Surya, C. Appl. Phys. Lett. 2003, 83, 141.

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