Surface and Quantum Confinement Effects in ZnO Nanocrystals

J. Phys. Chem. C 2010, 114, 18293–18297

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Surface and Quantum Confinement Effects in ZnO Nanocrystals Aline L. Schoenhalz,† Jeverson T. Arantes,‡ Adalberto Fazzio,§ and Gustavo M. Dalpian*,† Centro de Cieˆncias Naturais e Humanas, UniVersidade Federal do ABC, Santo Andre´, SP, Brazil, Centro de Engenharia, Modelagem e Cieˆncias Sociais Aplicadas, UniVersidade Federal do ABC, Santo Andre´, SP, Brazil, and Instituto de Fı´sica, UniVersidade de Sa˜o Paulo, Sa˜o Paulo, SP, Brazil ReceiVed: April 26, 2010; ReVised Manuscript ReceiVed: September 10, 2010

ZnO nanocrystals are studied using theoretical calculations based on the density functional theory. The two main effects related to the reduced size of the nanocrystals are investigated: quantum confinement and a large surface:volume ratio. The effects of quantum confinement are studied by saturating the surface dangling bonds of the nanocrystals with hypothetical H atoms. To understand the effects of the surfaces of the nanocrystals, all saturation is removed and the system is relaxed to its minimum energy position. Several different surface motifs are reported, which should be observed experimentally. Spin-polarized calculations are performed in the nonsaturated nanocrystals, leading to different magnetic moments. We propose that this magnetic moment can be responsible for the intrinsic magnetism observed in ZnO nanostructures. Introduction In the last 30 years, we have seen an extraordinary experimental advance on the techniques to produce, in a controlled way, smaller and smaller structures, even in atomic scale.1 Parallel to these achievements, characterization techniques have also matured in order to better understand the properties of these materials.2,3 Altogether, these factors are responsible for the rising of nanoscience and nanotechnology. When materials are reduced to nanoscale, novel phenomena that are not present in the crystal, appear. One of these effects is related to quantum confinement, which appears due to the fact that the size of the studied particles is in the range of nanometers. Quantum confinement effects can be observed, for example, as an increase in the energy gap of insulators as a particle’s size decreases.4 Besides this effect, when the size of a material is reduced, the surface:volume ratio increases. For structures in the nanometric scale, this becomes even more important because the majority of the atoms might be on the surface. Considering this, the surface plays an important role in the material’s properties, and its correct understanding is sometimes as important as the quantum confinement effects. A relevant class of nanomaterials include semiconductor nanostructures, which have a fundamental role in modern technologies. Recent advances in this area include the miniaturization of devices, reaching the nanoscale. Semiconductor nanocrystals (NCs) have been widely studied, including almost all types of semiconductors.5-7 In this context, zinc oxide (ZnO) rises as a great promise due to the wide variety of its potential applications. ZnO is a direct wide energy gap semiconductor belonging to the II-VI group of binary compounds. The experimental measured energy gap is ∼3.4 eV, having very interesting optical properties.8 Compared with other semiconductors, ZnO is attracting a lot of interest in the scientific community due to its differentiated properties.9,10 Besides being * To whom correspondence should be addressed. E-mail: gustavo.dalpian@ ufabc.edu.br. † Centro de Cieˆncias Naturais e Humanas, Universidade Federal do ABC. ‡ Centro de Engenharia, Modelagem e Cieˆncias Sociais Aplicadas, Universidade Federal do ABC. § Universidade de Sa˜o Paulo.

abundant and nontoxic, its properties include piezoelectricity,11,12 chemical stability and biocompatibility,13 optical absorption/ emission,14 and catalytic activity.15 In addition, possible applications of ZnO-based materials include light-emitting diodes,16 UV detectors,17 gas sensors,18 diluted magnetic semiconductors,19 cosmetics, and biomaterials.20 Although a lot of work has been done on these nanostructures, from both theoretical and experimental perspectives, there are still a lot of challenges to be overcome. Most of the studies focus on the quantum confinement properties of these nanostructures, and very little is known about their surface structure. Theoretically, this is a difficult task due to the limited number of experimental papers reporting on the structure of these surfaces. Experimentally, this is complex due to the intricate nature of the interaction between the nanocrystals and their saturating molecules. In this paper, we study the quantum confinement and surface properties of ZnO nanocrystals. For this purpose, ab initio methods based on the density functional theory are used. We have separately quantified surface and quantum confinement effects and observed their main contributions to the properties of the nanocrystals. We have initially studied quantum confinement effects by passivating the nanocrystals with hydrogen atoms. The hydrogen atoms are then removed, and surface effects appear by the reconstruction of the surfaces and by the formation of levels in the energy gap of the nanocrystals. We report a variety of different surface motifs for the reconstruction of the surfaces, including the formation of flat surfaces, dimers, and other more complex structures. Some of these nonsaturated nanocrystals show unusual magnetic properties, presenting a spontaneous magnetization without the inclusion of magnetic impurities. Methodology To study ZnO nanoparticles, we used density functional theory (DFT)21,22 with the local density approximation (LDA)23 to the exchange-correlation energy term. The calculations were performed by using the Vienna Ab-initio Package (VASP), employing the projected augmented wave method (PAW)24 and using a plane-wave basis set. The vacuum between a nanoparticle and its periodic images was set to a value of 0.6 nm. The

10.1021/jp103768v  2010 American Chemical Society Published on Web 10/07/2010

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simulations were done by allowing the structures to relax until the forces in each Cartesian coordinate were less than 25 meV/ Å, and the convergence criterion in the total energy was fixed as 1 × 10-5 eV. To exploit the polytipism that occurs in ZnO-based materials, we analyzed both wurtzite (WZ) and zinc blende (ZB) types of nanocrystals.25 These structures correspond to hexagonal and cubic structures, respectively, and the preferential structure will depend on growth conditions, such as pressure, precursor concentrations, temperature, and substrate. The nanoparticles were generated by cutting an approximately spheric part of bulk ZnO with a defined radius and center. The spheres cut from crystal can have different diameters, which enables the study of several nanocrystals. Besides the diameter and geometry, different centers for the nanocrystals can be defined. We looked at atom-centered and bond-centered nanocrystals,7 in both zinc blende and wurtzite structures. Thus, we analyzed more than 20 different nanocrystals. As a first step to understanding these nanocrystals, the dangling bonds of the surface atoms were saturated with partially charged hydrogen atoms.26 This procedure was done to avoid surface states in the energy gap and allowed us to separate quantum confinement effects from those originated from surface effects. The objective of these hypothetical H atoms is simply to eliminate the surface states from the energy gap. The study of nanocrystals’ surfaces is very complex because there are not many experimental results reporting on the structure of these surfaces or the structure of the interface between the nanocrystal and its capping molecules. Recent results report on the structure of the solvent of a gold nanocrystal, although they do not give direct evidence of its surface.27 Our model for the nanocrystal’s surface structure is obtained by removing all hydrogen atoms used to saturated them and letting all atoms go to their minimum energy configurations.

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Figure 1. Saturated nanocrystals with (a) 79, (b) 174, (c) 431, (d) 247, (e) 163, (f) 71, (g) 76, (h) 162, (i) 408, (j) 396, (k) 164, and (l) 80 atoms. The green, red, and white spheres represent zinc, oxygen, and hydrogen atoms, respectively.

Results Saturated Nanocrystals. To build our structural models for the nanoparticles, we used atom-centered (AC) and bondcentered (BC) nanocrystals.7 The main difference between AC and BC nanocrystals is that the latter ones are always stoichiometric, whereas the former ones are not. For ZB nanocrystals, the symmetry of the structure is also reduced from AC to BC. After choosing the structure and the center, we defined the radius of the nanocrystal. All atoms located outside the sphere defined by this radius and the respective center were removed. For each structure and center, we have three different sizes for the nanocrystals, which we classify as small, medium, and large, having diameters varying from 0.9 nm to approximately 1.8 nm. Several experimental studies have reported the synthesis of nanoparticles with diameters of this order of magnitude.1,28 As discussed before, after generating the nanocrystals, we saturated all surface dangling bonds in order to remove surfaces states from the energy gap of the nanocrystal. This is done by inserting fictitious H atoms in such a way that each surface atom (either Zn or O) will have four bonds, following the octet rule, as in bulk ZnO. This enables us understand quantum confinement effects separately from surface effects. Figure 1 shows some of the saturated studied particles. The first six belong to AC and the last six to BC. Both sets were generated in wurtzite (Figure 1a-c,g-i) and zinc blende (Figure 1d-f,j-l) structures. When the system is confined, an increase of the HOMOLUMO energy gap occurs. Previous studies show the energy gap dependence with the nanoparticles’ diameter.29 Figure 2

Figure 2. From left to right: opening of the energy gap for nanocrystals with d ∼ 1.6 nm (247 atoms), d ∼ 1.4 nm (163 atoms), and d ∼ 1.1 nm (71 atoms). Respective energy gap energies are 2.39, 2.90, and 3.93 eV. The eigenvalues were aligned by the lowest occupied levels.

exhibits the energy levels for different zinc blende nanocrystals, showing the opening of the energy gap when the structures become smaller. This effect can be understood by a simple quantum well model, where the energy difference between eigenvalues increases as the width of the well decreases. In Figure 2, the eigenvalues for different nanocrystals were aligned by the deepest O s levels, which are the lowest occupied states and less influenced by quantum confinement. Using this procedure, we observe that the energy shift of the LUMO is larger than the HOMO, as expected by effective mass models (smaller effective masses will produce a larger shift in energy).

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Figure 3. Size dependence of the energy gap for several saturated nanocrystals. The up triangles are the calculated gap energies shifted by 2.61 eV, the red circles are the experimental values extracted from ref 31, and the green dashed line is the Eg curve fitting.

The stability of the nanostructure also depends on its size. This can be estimated by calculating the nanocrystals’ formation energy. As a general trend, we observe that the formation energy increases as the size of the nanocrystals decreases, which is in agreement with previous calculations.30 This indicates that smaller nanoparticles are not as stable as larger ones, although they will be present during the growth process. The set of saturated nanocrystals allowed us to observe the effects related with quantum confinement. In Figure 3, the main quantum confinement effect is shown. As expected, the energy gap decreases when the nanocrystal diameter increases, for both AC and BC nanocrystals. The small dispersion observed on the values for the nanocrystal energy gap (up triangles) is related to the different forms and symmetry of the nanocrystals. The calculated energy gap values obtained with LDA were rigidly shifted in such a way that the bulk energy gap value coincides with the experimental one. In our case, the rigid shift was 2.61 eV, meaning that, for all of our nanocrystals, the energy gap was shifted by this value. Averaging all the obtained values with LDA and the experimental values from ref 31, and references therein, as shown in Figure 3, the best fit for the variation of the energy gap as a function of the diameter d of the nanocrystal is (in eV)

Eg ) 3.41 + 3.87 × d-1.83 These results indicate that our calculations are in good agreement with experimental values. Another observed effect is related to the structural properties of nanocrystals. For bulk ZnO, the bond length between the Zn and O atoms is 1.94 Å, but it can be larger/smaller at the center/ surface of some nanocrystals. The bond length of zinc/oxygen to the hypothetical hydrogen atoms at the surface is approximately 1.59 Å/1.07 Å, although this will change depending on the way the H potentials are generated. In the wurtzite nanocrystals, the c/a ratio changes from 1.63 (smaller NC) to 1.61 (largest NC), showing that this value trends to the bulk value (1.6018 Å) when the size is increased. Unsaturated Nanocrystals. The surface saturation used in the previous section is a theoretical artifact to remove the surface states from the energy gap. In principle, its surface cannot be compared directly to what is observed in real nanocrystals, although quantum confinement effects are correctly modeled. This kind of saturation resembles a perfect saturation, which will be hardly reached experimentally. Without these hydrogen atoms, surface effects are analyzed. To better understand these effects and their implications in some of the ZnO nanocrystals’

Figure 4. Surface reconstructions for a nonsaturated NC with (a) 87 atoms, presenting broken bonds; (b) 87 atoms, showing adislands; (c) 147 atoms, presenting planar faces and zinc dimers; (d) 39 atoms, presenting planar faces and changes in bond angles; and (e) 35 atoms, presenting changes in bond angles.

properties, we removed all hydrogen atoms from the surface of our nanocrystals and optimized these structures, allowing all atoms to go to their minimum energy positions. We observed that the surface reconstructs in a large variety of new arrangements. Because of these structural changes, the electronic structure of the nanocrystals is also modified. As we have analyzed the surface of more than 20 different nanocrystals, with different structures, symmetries, and sizes, we believe we were able to sample most of the possible structural configurations for these nanocrystals. A few of these structures are recursive for several different nanocrystals. The more commonly observed motifs are (i) planar faces, (ii) surface dimers, (iii) hearth-shaped rings (or broken bonds), and (iv) adislands. All these motifs can be observed in one or more of the nanocrystals shown in Figure 4. The planar faces observed in our nanocrystals are also reported in other studies.31,32 This structure occurs in both ZB and WZ phases. For large nanocrystals, the ZnO bond lengths vary from 1.784 to 2.012 Å, and for small ones, the bond lengths vary from 1.827 to 1.992 Å. The smallest and largest values for these bond lengths occur when the hexagonal rings of the faces are more deformed, which usually happens in the edges of the planar faces. We did not observe a trend that correlates a size dependence with how planar the nanocrystal surface will be. However, when the nanocrystal is smaller, almost all atoms are at the surface, and the structural effect of a planar face is more radical to the whole nanoparticle, changing even the structure of atoms at its center, as can be observed in Figure 4d. The surface dimers occur at the corners of some of our nanocrystals, as shown in Figure 4c. These dimers are composed of the same element, that is, oxygen dimers or zinc dimers. They appear in both WZ and ZB structures. For the zinc dimers, we observe for large nanocrystals an average bond length of 2.302 Å, whereas for medium nanocrystals, the average bond length is 2.352 Å. In the small nanocrystals, these dimers are not observed due their limited sizes.

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Figure 5. Projected density of states for ZnO nanocrystals with (a) 35 atoms (centered in Zn-Zn rich), (b) 35 atoms (centered in O-O rich), and (c) 87 atoms (centered in Zn-O rich). We set the Fermi energy to be the reference level.

We also observe the formation of 10-atom rings that appear due to the break of some internal Zn-O bonds. Depending on the view, this motif has the shape of a heart (heart-shaped), as can be seen in Figure 4a. This motif is present mostly in ZB nanocrystals. It is interesting to note that some of the atoms in this ring only have two nearest neighbors. We have tried to rearrange the position of these atoms in such a way that the O atom that belongs to this ring, and which has only two nearest Zn neighbors, is moved toward an internal Zn atom, returning to a tetrahedral environment, similar to standard ZnO. Interestingly, after a structural optimization, the atom prefers to stay at this undercoordinated position. For some nanocrystals, when larger surfaces exist, we also observe adislands composed of four or more atoms, like in Figure 4b. These structures are probably the seeds of new planes that will grow on the surface of a nanocrystal. Besides all effects on the structural rearrangements of the nanocrystals, deep changes also occur in the electronic structure of these nanocrystals. The existence of these surfaces leads to the formation of defect levels (or surface levels) in the energy gap of the nanocrystal. The density of these trap states depend on the size of the nanocrystal and on the structure of its surface. In Figure 5, we show the projected density of states of a few characteristic nanocrystals, showing the presence of trap states in the energy gap. These states are related to the surface reconstruction present in nonsaturated ZnO nanocrystals. We observe that, in some cases, the levels inserted in the energy gap are spin-polarized, leading to a macroscopic magnetization in these nanostructures even without the insertion of magnetic impurities. It is also interesting to compare the projected DOS of very similar AC nanocrystals, but where the types of atoms are switched, that is, one nanocrystal is centered in a Zn atom, whereas the other is centered in an O atom. This also changes the surface termination of these nanocrystals: Zn-rich surfaces become O-rich surfaces. The nanocrystal centered in an oxygen atom does not suffer so many changes/reconstructions in its structure compared with the nanocrystal centered in a zinc atom.

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Figure 6. Spin charge density for nondoped nanocrystals. The number of atoms is (a) 35, (b) 87, (c) 92, and (d) 147.

We also observe that the resulting electronic and magnetic behavior is very different. In Figure 5a,b, we can compare the DOS of these two nanocrystals. For the Zn-centered nanocrystal, which is also Zn-rich, we observe that the magnetization is mainly related to s levels, whereas for O-centered nanocrystals, which are O-rich, we observe that the magnetization is mostly related to p levels. In O-centered nanocrystals, the amount of surface levels near the Fermi level is larger than the Zn-centered ones. Also, the magnetic moment for the O-centered nanocrystal is 3 times larger than that for the Zn-centered. The different behavior between these nanocrystals, which are basically the same in structure, but different in atom concentration, might lead to very different results, indicating that each surface of a nanocrystal will have a different signature and lead to a different magnetic behavior. The most interesting thing about this intrinsic magnetization is that it occurs without magnetic impurities. Several studies try to explain this effect by proposing that intrinsic defects, such as oxygen vacancies33 or zinc vacancies,34 are the responsible for the observed magnetism. However, the population of these defects is usually not large enough to produce a macroscopic magnetic response. There is a consensus in the literature that this kind of magnetism is related to defects in oxide nanostructures. In previous studies,35,36 we proposed that the intrinsic magnetism is related to the surface reconstruction that ZnO nanoparticles can present, as shown in the isosurfaces of Figure 6. The origin of this kind of magnetization observed in nondoped ZnO nanostructures and another oxides is still a open topic. In our study, we could not isolate only one defect responsible for this phenomena, and we believe that extended defects (which means the surface) are responsible for the insertion of delocalized, spin-polarized states in the energy gap, resulting in a macroscopic magnetization of the samples. Discussion and Analysis Our study involves two models for ZnO nanocrystals, which can represent different limiting cases: in the first, all dangling bonds at the surface are saturated with hydrogen atoms,

Surface and Quantum Confinement Effects in ZnO NCs excluding the effects related to the surface of the nanoparticles. Consequently, this model is very useful to understanding the phenomena related to quantum confinement effects but is not very realistic because it does not consider surface effects. The second model considers that the nanocrystals do not have any saturation at the surface. This model allows us to observe a large set of reconstructions that nanoparticles can present and is a good approximation to understanding the properties of these surfaces. As mentioned before, now we have the two limiting models for nanocrystals surfaces: the perfect saturation, where all atoms at the surface resemble bulk atoms, and no saturation, which would be the model of a nanocrystal in vacuum. Experimentally, these nanocrystals are usually grown in colloidal solutions.37 Consequently, they are somehow saturated. Unfortunately, experimental measurements do not have the precision necessary to give the exact nature of the interaction between the organic molecules and the nanocrystals. We can infer, however, that the saturation due to these organic molecules will not be so perfect as our model with H atoms, nor so absent, as in our model without any saturation. We can consider that experimental results are in between these two models. In this case, not all dangling bonds are saturated and neither all are unsaturated. The second situation is experimentally improbable because, in growth conditions, the nanoparticles will have some molecules bonded to them. Our model without saturation would be a very good model for nanocrystals involved in an inert gas medium. As a consequence, we expect that novel phenomena in nanocrystals will emerge from a mixture of the effects proposed here: quantum confinement and surface effects. We expect that the density of surface states in colloidal nanocrystals will be smaller than those reported here, depending on the type of saturation. The results reported by us for an unsaturated nanocrystal are an upper bound for the effects of surfaces. Experimental studies focusing on the detailed structure of the interface between the solvent and the nanostructure would be very useful to elucidating these problems. Conclusion In conclusion, we have performed DFT calculations with LDA approximation on several ZnO nanocrystals in both wurtzite and zinc blende structures. In a first step, with saturated NCs to avoid surface states into the energy gap, we have shown that these nanoparticles are in a quantum confinement regimen. The most evident observation is the variation of the energy gap as the nanocrystal’s size is reduced. When the saturation is removed and the geometry of the nanocrystal is optimized, we observe several reconstructions that occur at the surfaces. The observed reconstructions include planar faces, broken bonds, dimers at the surface, and adislands. Besides these structural modifications, we could also observe that surface levels inserted in the energy gap can be spinpolarized, and nanocrystals can have a magnetization without the addition of magnetic impurities. We conclude that nanoparticles presenting similar structures, but different concentrations of each species, can have completely different properties, such as different surface reconstructions and respective total magnetization. This fact emphasizes the importance of surface effects in the properties of zinc oxide nanocrystals. Our results also indicate that further studies on the structure of surfaces of nanoparticles are necessary to obtaining a complete understanding of these issues.

J. Phys. Chem. C, Vol. 114, No. 43, 2010 18297 Acknowledgment. This work was supported, in part, by Brazilian agencies CAPES, FAPESP, and CNPq. We thank CENAPAD for the computational support. References and Notes (1) Schwartz, D. A.; Norberg, N. S.; Nguyen, Q. P.; Parker, J. M.; Gamelin, D. R. J. Am. Chem. Soc. 2003, 125, 13205. (2) Peng, X.; Manna, L.; Yang, W.; Wickham, J.; Scher, E.; Kadavanich, A.; Alivisatos, A. P. Nature 2001, 404, 59. (3) Shevchenko, E. V.; Talapin, D. V.; Murray, C. B.; O’Brien, S. J. Am. Chem. Soc. 2006, 128, 3620. (4) Yu, H.; Li, J.; Loomis, R. A.; Wang, L.-W.; Buhro, W. E. Nat. Mater. 2003, 2, 517. (5) Arantes, J. T.; Dalpian, G. M.; Fazzio, A. Phys. ReV. B 2008, 78, 045402. (6) Huang, X.; Makmal, A.; Chelikowsky, J. R.; Kronik, L. Phys. ReV. Lett. 2005, 94, 236801. (7) Dalpian, G. M.; Tiago, M. L.; Lopez del Puerto, M.; Chelikowsky, J. R. Nano Lett. 2006, 6, 501. (8) Janotti, A.; Van de Walle, C. G. Rep. Prog. Phys. 2009, 72, 126501. ¨ zgu¨r, U ¨ .; Alivov, Ya. I.; Liu, C.; Teke, A.; Reshchikov, M. A.; (9) O Dogan, S.; Avrutin, V.; Cho, S.-J.; Morkoc¸, H. J. Appl. Phys. 2005, 98, 041301. (10) Wang, Z. L. J. Phys.: Condens. Matter 2004, 16, R829. (11) Zhou, J.; Fei, P.; Gao, Y.; Gu, Y.; Liu, J.; Bao, G.; Wang, Z. L. Nano Lett. 2008, 8, 2725. (12) Kong, X. Y.; Wang, Z. L. Nano Lett. 2003, 3, 1625. (13) Zhou, J.; Xu, N. S.; Wang, Z. L. AdV. Mater. 2006, 18, 2432. (14) Park, W. I.; Jun, Y. H.; Jung, S. W.; Yi, G.-C. Appl. Phys. Lett. 2003, 82, 964. (15) Matatov-Meytal, Y. I.; Sheintuch, M. Ind. Eng. Chem. Res. 1998, 37, 309. (16) Ryu, Y.; Lee, T.-S.; Lubguban, J. A.; White, H. W.; Kim, B.-J.; Park, Y.-S.; Youn, C.-J. Appl. Phys. Lett. 2006, 88, 241108. (17) Heo, Y. W.; Kang, B. S.; Tien, L. C.; Norton, D. P.; Ren, F.; La Roche, J. R.; Pearton, S. J. Appl. Phys. A: Mater. Sci. Process. 2005, 80, 497. (18) Wan, Q.; Li, Q. H.; Chen, Y. J.; Wang, T. H.; He, X. L.; Li, J. P.; Lin, C. L. Appl. Phys. Lett. 2004, 84, 3654. (19) Pearton, S. J.; Abernathy, C. R.; Overberg, M. E.; Thaler, G. T.; Norton, D. P.; Theodoropoulou, N.; Hebard, A. F.; Park, Y. D.; Ren, F.; Kim, J.; Boatner, L. A. J. Appl. Phys. 2003, 93, 1. (20) Lee, J.; Kang, B. S.; Hicks, B.; Chancellor, T. F., Jr.; Chu, B. H.; Wang, H.-T.; Keselowsky, B. G.; Ren, F.; Lele, T. P. Biomaterials 2008, 29, 3743. (21) Hohenberg, P.; Kohn, W. Phys. ReV. 1964, 136, 864. (22) Capelle, K. Braz. J. Phys. 2006, 36, 1318. (23) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, 1133a. (24) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (25) Dalpian, G. M.; Yan, Y.; Wei, S.-H. Appl. Phys. Lett. 2006, 89, 011907. (26) Huang, X.; Lindgren, E.; Chelikowsky, J. R. Phys. ReV. B 2005, 71, 165328. (27) Lee, Z.; Jeon, K.-J.; Dato, A.; Erni, R.; Richardson, T. J.; Frenklach, M.; Radmilovic, V. Nano Lett. 2009, 9, 3365. (28) Ma¨dler, L.; Stark, W. J.; Pratsinis, S. E. J. Appl. Phys. 2002, 92, 6537. (29) Kwak, H.; Tiago, M. L.; Chelikowsky, J. R. Solid State Commun. 2008, 145, 227. (30) Zhao, M.; Xia, Y.; Tan, Z.; Liu, X.; Mei, L. Phys. Lett. A 2007, 372, 39. (31) Freeman, C. L.; Claeyssens, F.; Allan, N. L.; Harding, J. H. Phys. ReV. Lett. 2006, 96, 066102. (32) Tusche, C.; Meyerheim, H. L.; Kirschner, J. Phys. ReV. Lett. 2007, 99, 026102. (33) Sundaresan, A.; Bhargavi, R.; Rangarajan, N.; Siddesh, U.; Rao, C. N. R. Phys. ReV. B 2006, 74, 161306. (34) Wang, Q.; Sun, Q.; Chen, G.; Kawazoe, Y.; Jena, P. Phys. ReV. B 2008, 77, 205411. (35) Schoenhalz, A. L.; Arantes, J. T.; Fazzio, A.; Dalpian, G. M. Appl. Phys. Lett. 2009, 94, 162503. (36) Podila, R.; Queen, W.; Nath, A.; Arantes, J. T.; Schoenhalz, A. L.; Fazzio, A.; Dalpian, G. M.; He, J.; Hwu, S. J.; Skove, M. J.; Rao, A. M. Nano Lett. 2010, 10, 1383. (37) Garcia, M. A.; Merino, J. M.; Fernndez Pinel, E.; Quesada, A.; de la Venta, J.; Ruı´z Gonza´lez, M. L.; Castro, G. R.; Crespo, P.; Llopis, J.; Gonza´lez-Calbet, J. M.; Hernando, A. Nano Lett. 2007, 7, 1489.

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