First-Principles Investigations of InN Nonpolar Surface

Jun 4, 2009 - Antonio Aliano , Giancarlo Cicero , and Alessandra Catellani. ACS Applied Materials & Interfaces 2015 7 (9), 5415-5419. Abstract | Full ...
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J. Phys. Chem. C 2009, 113, 11323–11328

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First-Principles Investigations of InN Nonpolar Surface Functionalization A. Terentjevs,*,† G. Cicero,‡ and A. Catellani§ Physics and Materials Science and Chemical Engineering Departments, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy, and CNR-IMEM, Parco Area dell Scienze 37/A, 43100 Parma, Italy ReceiVed: December 17, 2008; ReVised Manuscript ReceiVed: April 21, 2009

In this paper we present a theoretical investigation of the InN nonpolar surface functionalization and propose a grafting mechanism for different functional groups. Ab initio calculations were first applied to explore the electronic properties of clean surfaces; afterward, they were employed to address InN nonpolar surface functionalization. InN surfaces were found to be highly reactive upon exposure to the most common functional groups: methanethiol (CH3-SH), acetic acid (CH3-COOH), methylamine (CH3-NH2), and methanol (CH3-OH). They all strongly bind to the surface with exothermic reaction. Introduction Indium nitride (InN) belongs to the group III nitrides, which have become an important class of semiconductor materials to be employed in many electronic systems. During the past decade this material has been investigated intensively both experimentally1-8 and theoretically.9-14 A complete overview of the structural and electronic properties of InN was given by Walukiewicz et al.15 InN has also been considered a promising material for photovoltaic applications16,17 because of its high electron affinity (∼5.4 eV15), high electron mobility, and saturation velocities. In particular, it has been proposed that InN can be employed as active material in thirdgeneration photovoltaic systems like those proposed by Gra¨tzel.18 In these solar cells, one can take advantage of the nanostructured form of the inorganic compound to increase the active surface area where light-absorbing molecules are being deposited. It was recently discovered that nanostructured InN films can be obtained in the form of nanowires that grow along the polar [0001] axis, exhibiting hexagonal cross section and nonpolar exposed lateral surfaces.19 Furthermore, increased attention has recently been paid to nonpolar nitride surfaces to produce epitaxial films, and substrates, to obtain optoelectronic material with superior quality: in this case, indeed, better control of the growth process, reduced defect concentration, minimization of charge localization, and dipolar fields can be achieved.20 Better comprehension of the clean nonpolar surfaces of InN, along with a theoretical investigation of their functionalization, is thus highly desirable for understanding the grafting mechanism and controlling electronic and structural properties. Very few experimental approaches have addressed the functionalization processes of nitrides surfaces and in particular of InN until now.21-26 Arafat et al.23 and Coffinier et al.26 investigated the reaction of hydrogen-terminated nitride surfaces exposed to molecules containing a terminal unsaturated C-C bond (olefin). Bermudez21,22 explored direct attachment of thiols * To whom correspondence should be addressed. E-mail: [email protected]. † Physics Department, Politecnico di Torino. ‡ Materials Science and Chemical Engineering Department, Politecnico di Torino. § CNR-IMEM.

on clean GaN surfaces in ultra-high-vacuum conditions in a highly controlled atmosphere. Finally, Chen et al.25 proved that a standard wet-chemistry technique that exploits the oxide reactivity toward organosilane can be employed to achieve nitride functionalization. As for the theoretical investigations, there are no simulations at the atomistic level of InN functionalization. The aim of this work is to shed some light on the theoretical “gap” and present a study of the intrinsic reactive properties of InN clean nonpolar surfaces with common functional groups found in organic molecules by atomistic simulations. In particular, in this paper we show the results of first-principle investigations of the electronic structure of InN clean and functionalized (11j00) nonpolar surfaces. By means of ab initio calculations, we have studied the energetics, stability, and geometry of the surfaces exposed to several organic groups (-OH, -COOH, -NH2, and -SH) to explore functionalization procedures as an alternative to silanization, which is commonly used for silicon surfaces and has been lately exported to nitride surfaces.25 In the second section we describe our computational approach; the third section presents results for InN nonpolar clean and functionalized surfaces. Finally, in the fourth section we summarize our results. Computational Method Our theoretical investigations are based on density functional theory (DFT) within the local density approximation (LDA). It is well-known that DFT strongly underestimates band gaps and different corrections have been proposed to consider the complex problem of nitrides’ electronic properties.11,12,14,27,28 In the case of InN, early theoretical DFT studies (in 1980s and 1990s) within the LDA gave zero or slightly negative band gap values.29-33 Only recent implementation of additional corrections to LDA such as self-interaction correction (SIC) and Green function-based approaches (e.g., GW) allowed values for the InN band gap close to the experimental one (∼0.7 eV34) to be obtained: 0.59 eV with GW,11 0.58 eV with SIC, and 0.82 with GW.12 LDA is however recognized as accurate in describing ground-state properties, such as those addressed in the present work. In our calculations, electronic wave functions are expanded in plane waves, and electron-ion interactions are treated by

10.1021/jp811148z CCC: $40.75  2009 American Chemical Society Published on Web 06/04/2009

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employing ultrasoft pseudopotentials. In the case of indium the 4d electrons are explicitly considered as valence electrons since it is well-known that they are required to describe the structural properties of bulk InN35 correctly. Surface calculations were performed in supercells containing symmetric InN slabs with a (1 × 1) surface periodicity, thus mimicking a perfectly cleaved stoichiometric surface. In the case of the (11j00) surface, slabs contained up to 16 InN layers, whereas in the case of the (112j0) surface we used up to 12 InN layers. A vacuum space of about 14 Å was included in the supercells to avoid spurious interaction between periodic images. All the calculations were done with a plane wave cutoff of 30 Ry, and the Brillouin zone (BZ) sampling was done by employing an 8 × 8 × 8 Monkhorst-Pack mesh for the bulk calculations and an 8 × 8 × 1 grid for the surface calculations. Structures were considered converged when forces acting on atoms were less than 0.001 au. Within the computational scheme presented above, we have obtained equilibrium lattice parameters for InN in the wurtzite (WZ) structure of a ) 3.524 Å, c/a ) 1.618, and u ) 0.378 (In-N bond length ) 2.157 Å). These values are in good agreement with the experimental lattice parameters (a ) 3.538 Å, c/a ) 1.612, and u ) 0.37736) and previous theoretical LDA values.11,12,14,27 Surface reactivity was addressed by first optimizing the InN surfaces and the organic molecules separately; subsequently, we exposed our (1 × 1) surface to a selected type of molecules and relaxed the whole system. This approach corresponds to simulation of surface coverage of one monolayer: each In-N surface bond is exposed to one molecule. For each of the cases that we analyzed, we observed spontaneous dissociation by minimizing the forces on the atoms starting from equilibrium geometries of the reactants, separated by 3.5 Å approximately. For this reason we did not have to employ more complex computational schemes such as the nudged elastic band method,37 which are generally needed to derive minimum energy reaction paths. To prove that our results on surface reactivity are not dependent on the specific choice of the exchange-correlation functional (LDA in our case), for a selected case (the methanethiol molecule) we have applied the Perdew-BurkeErnzerhof (PBE) functional. In this case we used the corresponding PBE theoretical WZ-InN equilibrium lattice parameters, a ) 3.595 Å, c/a ) 1.62, and u ) 0.378, in agreement with other theoretical works (see, for example, Stampfl and Van de Walle33). Finally, to investigate the role of different corrections to improve the LDA band gap, we have considered inclusions of ad hoc LDA+U38 and of an atom-centered repulsive potential of Gaussian shape14,39 during the In pseudopotential generation. We explicitly verified that, beyond a modification to the band gap, these corrections do not change the overall picture of InN bulk structural and electronic properties. Results InN Clean Nonpolar Surfaces. The relaxed structures for the (1×1)-InN(11j00) and (1×1)-InN(112j0) surfaces are shown in Figure 1. Upon relaxation the In-N bonds at the surface become shorter with respect to the bulk ones of about 0.10 Å for the (11j00) surface and 0.12 Å for the (112j0) surface; furthermore, the In-N bond axis tilts about 8-9°. The surface energies were estimated to be 1.502 and 1.595 J/m2 for the (11j00) face and (112j0), respectively (the approach proposed

Terentjevs et al.

Figure 1. Balls and sticks representation of relaxed structures for the (11j00) (above) and (112j0) (below) InN surfaces (side views). Large (small) spheres represent In (N) atoms.

Figure 2. InN (11j00) electronic band structure. Shaded area represents the projected bulk band structure, whereas the continuous lines are surface states. Zero energy is set at the bulk VBM. The point in the surface BZ indicated with P is the k-point where electronic charge density has been calculated and plotted in Figure 3.

by Fiorentini and Methfessel40 was used): both surface relaxation and surface energies are quite similar for these two nonpolar surfaces. In Figure 2 the electronic band structure of the (11j00) surface is presented; the shaded area is the projected bulk band structure whereas the continuous lines represent surface states. The zero of energy is set at the bulk valence band maximum (VBM).

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Figure 4. HOMO (left panel) and LUMO (right panel) charge density isosurface (shaded yellow-green area) of methanethiol (sketched globes represent different atomic species explicitly indicated by labels).

Figure 3. Electronic charge density isosurface (denoted by the shaded yellow-green area) calculated at P point of the surface BZ (see Figure 2) for HO (above) and LU (below) states of the InN (11j00) surface. Larger (smaller) sketched globes represent In (N) atoms.

Band energies for bulk and surface states are aligned with respect to the average electrostatic potential of the bulk and of j point the band gap is zero: the slab calculations.41,42 At the Γ as previously stated, it is well-known that LDA underestimates InN gap, which has been experimentally established to be 0.7 eV.34 Figure 2 shows that, in the band gap region immediately j , there are two surface states: one occupied (highest away from Γ occupied state, HO) and the other unoccupied (lowest unoccupied state, LU). As reported in Figure 3 the HO charge density is localized on the N surface atom whereas the LU charge density is localized mainly on the surface In atom. This analysis shows that at the surface a charge transfer occurs from the In to the N atom: The electron density in the In dangling bond is transferred to N, giving a doubly occupied state on the surface N atoms and an empty state on the surface In atoms. This observation has implications for surface reactivity with organic molecules: an electrophilic species would preferentially bind and react at the N site, whereas a nucleophilic one would attach to the In atom. Exposure of the InN (11j00) Nonpolar Surface to Water. Before presenting the results of InN surface functionalization, we first discuss the effect of humidity (water in the vapor phase) on the InN surface structure. Indeed, water is often present as traces both during crystal growth and during surface functionalization procedures. For this reason it is important to address how InN surfaces are modified by the presence of water molecules and, in particular, to examine whether surface passivation would occur involving a water-splitting reaction,

as observed for other semiconductor surfaces (see, for example, refs 43 and 44 and references therein). Our simulations show that water molecules dissociate spontaneously at the InN nonpolar surfaces, with the H2O molecule breaking into two fragments (-H and -OH). Upon dissociation, an H group binds to the surface N atom (H-N ) 1.05 Å) and an -OH group is bonded to the surface indium atom (In-O ) 2.04 Å). This water-splitting reaction is exothermic and the reaction energy is about ca. -2.37 eV/molecule. This result indicates that a clean InN surface is readily passivated when exposed to water molecules; thus, if one wants to functionalize this surface with organic molecules to exploit its intrinsic reactive properties, a highly controlled dry environment is required. Nonetheless, hydroxyl groups formed at the InN surface upon water reaction can be used to tailor the surface properties with organosilane molecules as already demonstrated in ref 25. We will focus on the intrinsic reactive properties of the InN nonpolar surfaces in the following paragraphs. InN (11j00) Nonpolar Surface Functionalization. For the investigation of the surface functionalization we studied the reaction of the InN (11j00) nonpolar surface with four types of molecules: methanethiol (CH3-SH), acetic acid (CH3-COOH), methylamine (CH3-NH2), and methanol (CH3-OH). All these molecules have a similar structure (CH3-XH) and differ in the -XH functional group, which we have chosen as representative of the most common groups found in organic molecules like dyes. These molecules also present a “similar” electronic structure, with the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) localized on the -XH part of the molecule (see, for example, methanethiol, in Figure 4). This means that -XH is the most reactive part, and for this reason, in our simulations, we considered initial structures where the -XH group is facing the surface InN atoms, that is, with an orientation expected to be favorable for reaction based on electronic arguments. In all the cases the reaction occurs as follows,

CH3-XH + InN f CH3-X-InN-H

(1)

and the reaction energy is defined as

1 ∆E ) (Eprod. - EInN - n · ECH3XH) n

(2)

where ∆E is the reaction energy, Eprod. is the total energy of the surface after the molecules have reacted, EInN and ECH3XH are the energies of the isolated systems (surface and organic molecule), and n is the number of organic molecules in the supercell calculation. In the following, we first analyze in detail the reaction of the InN surface with methanethiol and then summarize the results for the other molecules. The reaction of methanethiol with a

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Figure 6. Electronic band structure for the clean (top panel) and methanethiol functionalized (bottom panel) InN (11j00) nonpolar surface.

Figure 5. Top panel: ball-and-sticks representation of the InN (11j00) nonpolar surface functionalized with methanethiol (CH3-SH). Bottom panel: electronic charge density isosurface (shaded yellow-green area) of the highest occupied state (sketched globes represent different atomic species explicitly indicated by labels).

InN (11j00) nonpolar surface is spontaneous and barrierless. The reaction energy (defined by the formula (2)) is -2.82 eV/ molecule. CH3-SH dissociates into two parts: CH3-S- binds to an indium surface atom with an In-S bond length of about 2.46 Å whereas H- binds to the surface N atom with a bond length of about 1.04 Å. The structure of the InN (11j00) nonpolar surface functionalized with methanethiol is shown in Figure 5 (top panel). The highest occupied (HO) electronic charge density of the functionalized surface (bottom panel of Figure 5) corresponds to a surface state with large contribution of the sulfur atom of methanethiol. The dangling bond of the In surface atom is saturated by bonding with the S atom of methanethiol, resulting in an almost flat In-N surface bond (tilt ∼3°) to recover a bulklike configuration. The In-N bond length at the surface layer is modified accordingly. The other molecules that we considered react with the InN surface following a similar process: dissociation of the functional group is spontaneous with release of a hydrogen atom. The reaction energies are -2.74, -2.00, and -2.28 eV/molecule for CH3-COOH, CH3-NH2, and CH3-OH, respectively. The bond lengths formed at the surface are as follows: for acetic acid N-H ) 1.07 Å, In-O ) 2.08 Å; for methylamine N-H ) 1.05 Å, In-N ) 2.12 Å; for methanol N-H ) 1.05 Å, In-O ) 2.05 Å. The bond lengths In-O and In-N are very close (about 2.1 Å) whereas for the methanethiol the bond length In-S is larger by about 0.5 Å. The larger In-S distance can be simply

explained by the larger atomic radius of sulfur with respect to oxygen and nitrogen. From the discussion above, one may expect that surface states are removed since the functionalized system is closer in geometry to the unrelaxed configuration accompanied by saturation of the surface dangling bonds. Indeed, the analysis of the electronic band structure of the functionalized InN surface reveals that the unoccupied surface state of the clean surface is pushed at higher energy after molecular adsorption: see Figure 6 for a comparison of clean surface (top panel) and the case of a surface functionalized with methanethiol (bottom panel). The highest occupied (HO) state is instead a surface state, which is strongly localized on the attached molecules, and for example in the case of methanethiol has highest contribution from the p atomic orbital of the sulfur atom and less contribution from the N atoms of the InN surface bilayer and the H atoms of the CH3 part of the molecule. The lowest unoccupied (LU) state is instead a bulk state. Detailed information on charge density rearrangement occurring at the surface after functionalization takes place is obtained by the analysis of the projected density of states (PDOS) presented in Figure 7a-d for the surface N and In atoms before and after molecular grafting. Parts (e) and (f) of Figure 7 are instead the DOS projected on the S atom of the methanethiol in the case of the free molecule (Figure 7e) and in the case of the molecule attached to the InN surface (Figure 7f). The PDOS in Figure 7a,b show that the large contribution of charge localized on N atoms for the clean surface is completely redistributed when the reaction occurs and the dangling bond is saturated with an H atom. More importantly, it is remarkable that, upon CH3-S- attachment, the sulfur PDOS becomes spread over a wide range of energies (the electronic states are not single energy levels anymore) because of the rehybridization of its electronic states with the indium levels. From the comparison of pictures in parts (d) and (f) of Figure 7, one notices that there is an overlap of In and S states: the S-In bond appears to have contribution from the p orbital of indium and the p orbital of sulfur in an energy range of about 3 eV from the VBM, but a larger contribution comes from states at energy lower than 4 eV from the VBM. The fact that such low-energy electrons contribute to the In-S bond indicate that this is a strong bond, as is indeed reflected by the particularly large energy gain for this functionalization process.

InN Nonpolar Surface Functionalization

J. Phys. Chem. C, Vol. 113, No. 26, 2009 11327 energies (of about ∼0.8 eV/molecule in this case) with respect to GGA approaches, yet the qualitative results are unchanged. Finally, and again only for the case of methanethiol, we studied how this molecule would react with the InN (112j0) nonpolar surface. As in the case of the (11j00) surface, we found that the reaction is barrierless and it is characterized by a reaction energy of -2.73 eV/molecule. The S-H bond breaks when reaction occurs, forming an In-S bond of about 2.44 Å and an N-H bond of about 1.04 Å. These bond lengths are very close to those found for the InN (11j00) surface, confirming that these two nonpolar surfaces present very similar properties. We reasonably expect that all the other CH3-XH molecules considered in our study would behave at the (112j0) surface in a way similar to those found for the (11j00) surface. Conclusions

Figure 7. PDOS of the (11j00) clean and methanethiol functionalized surface. DOS for s (red curve) and p (green curve) orbitals projected on the outer N atom of the clean (a) and methanethiol functionalized (b) surface; on the In outer atom of the clean (c) and methanethiol functionalized (d) surface; on the sulfur atom of isolated methanethiol (e) and on the sulfur atom of the molecule attached to InN (f). The zero of energy corresponds to the VBM. The vertical scales of the functionalized surface (panels b, d, and f) have been increased ×7 with respect to the clean surface.

To verify the effect of the exchange-correletion potential, we performed the calculation for the functionalization with methanethiol, applying gradient corrections in the PBE formulation. Also in this case we found that methanethiol spontaneously dissociates at the InN surface: an In-S bond of about ∼2.5 Å is formed upon reaction at surface; this value is very close to the LDA result (∼2.46 Å). The PBE reaction energy is -2.07 eV/molecule. As expected, LDA tends to overestimate reaction

Ab initio DFT-LDA electronic structure calculations were first used for the investigation of electronic properties of bare InN (11j00) and (112j0) nonpolar surfaces. The two surfaces appear to be very similar in terms of surface relaxation and surface energy: this similarity is reflected in their reactive properties when exposed to organic molecules. Prior to surface functionalization, we analyzed the effect of water vapor on the clean InN surfaces. We observed that the clean surface readily reacts with water, leading to exothermic spontaneous dissociation. Upon water attachment the surface dangling bonds are completely saturated and surface reactivity is drastically reduced. This evidences that if one wants to exploit the reactivity of the clean InN surface with organic molecules, it is necessary to avoid contact with air humidity and to perform molecular grafting in a controlled environment. Subsequently, we studied the functionalization of InN surfaces with several small molecules in the form CH3-XH, where -XH represents the most common functional end groups: acetic acid (CH3-COOH), methylamine (CH3-NH2), methanol (CH3-OH), and methanethiol (CH3-SH). From our study we found that the InN nonpolar surfaces are highly reactive, and for all the above-mentioned molecules, we observed that grafting at the InN surface is achieved by simply exposing the clean surface to the molecular vapor. The attachment of the CH3-XH molecules at the surface occurs spontaneously and it is a highly exothermic process. In each of the cases that we considered the reaction involves the -XH functional group of the organic molecule and the InN bond at the surface: the -XH group dissociates into two parts with the -H atom binding to the N atom and the -X fragment binding to the In atom. We also show that functionalization of the surface removes all the surface dangling bonds, but while the LU state becomes a bulk empty state, the HO state remains a surface state mostly localized on the -X fragment of the reacted molecule. The strength and thus the stability of the In-X bond formed upon functionalization is demonstrated not only by the high value of the calculated reaction energy but also by the analysis of the PDOS, which shows contribution to the In-X bond from electronic states that are low in energy with respect to the top of the valence band of InN. Acknowledgment. This work is a part of the NANOLICHT project supported by the ERANET initiative “NanoSci-ERA: NanoScience in the European Research Area” (within the EU FP6). Computer time was provided by the Ju¨lich Supercomputing Centre and by CINECA through the CNR-INFM “Iniziativa Calcolo Parallelo”.

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References and Notes (1) Lu, H.; Schlaff, W. J.; Wu, H.; Yeo, W.; Pharkya, A.; Eastman, L. F. Appl. Phys. Lett. 2000, 77, 2548. (2) Davydov, V. Y. Phys. Status Solidi B 2002, 229, R1. (3) Sugita, K.; Takatsuka, H.; Hashimoto, A.; Yamomoto, A. Phys. Status Solidi B 2003, 240, 421. (4) Saito, Y.; Yamaguchi, T.; Kano, K.; Araki, T.; Nanishi, Y.; Teragushi, N.; Suzuki, A. J. Cryst. Growth 2002, 237, 1017. (5) Saito, Y.; Harima, H.; Kurimoto, E.; Yamaguchi, T.; Teragushi, N.; Suzuki, A.; Araki, T.; Nanishi, Y. Phys. Status Solidi B 2002, 234, 796. (6) Swartz, C. H.; Tomkins, R. P.; Myers, T. H.; Lu, H.; Schaff, W. J. Phys. Status Solidi B 2005, 2, 2250. (7) Wu, J.; Walukiewicz, W.; Yu, K. M.; Ager, J. W., III.; Haller, E. E.; Lu, H.; Shaff, W. J.; Saito, Y.; Nanishi, Y. Appl. Phys. Lett. 2002, 80, 3967. (8) Nanishi, Y.; Saito, Y.; Yamaguchi, T. Jpn. J. Appl. Phys. 2003, 42, 2549. (9) Bechstedt, F.; Furthmu¨ller, J.; Ferhat, M.; Teles, L. K.; Scolfaro, L. M. R.; Leite, J. R.; Davydov, V. Y.; Ambacher, O.; Goldhahn, R. Phys. Status Solidi A 2003, 195, 628. (10) Carrier, P.; Su-Huai, W. J. Appl. Phys. 2005, 97, 033707. (11) Usida, M.; Haamada, N.; Shiraishu, K.; Oshiyama, A. Jpn. J. Appl. Phys. 2004, 43, L407. (12) Furthmu¨ller, J.; Hahn, P. H.; Fuchs, F.; Bechstedt, F. Phys. ReV. B 2005, 72, 205106. (13) Janotti, A.; Segev, D.; Van de Walle, C. G. Phys. ReV. B 2006, 74, 045202. (14) Segev, D.; Janotti, A.; Van de Walle, C. G. Phys. ReV. B 2007, 75, 035201. (15) Walukiewicz, W.; Ager, J. W., III.; Yu, K. M.; Liliental-Weber, Z.; Wu, J.; Li, S. X.; Jones, R. E.; Denlinger, J. D. J. Phys. D: Appl. Phys. 2006, 39, R83. (16) Trybus, E.; Namkoong, G.; Henderson, W.; Burnham, S.; Doolittle, W. A.; Cheung, M.; Cartwright, A. J. Cryst. Growth 2006, 288, 218. (17) Vaddiraju, S.; Mohite, A.; Chin, A.; Meyyappan, M.; Sumanasekera, G.; Alphenaar, B. W.; Sunkara, M. K. Nano Lett. 2005, 5, 1625. (18) Gra¨tzel, M. Nature 2001, 414, 338. (19) Rizzi. A. University of Go¨ttingen, Go¨ttingen, Germany, private communication, 2007.

Terentjevs et al. (20) Waltereit, P.; Brandt, O.; Trampert, A.; Grahn, H. T.; Menniger, J.; Ramsteiner, M.; Reiche, M.; Ploog, K. H. Nature 2000, 406, 865. (21) Bermudez, V. Surf. Sci. 2002, 499, 109. (22) Bermudez, V. Langmuir 2003, 19, 6813. (23) Arafat, A.; Schroe¨n, K.; Louis de Smet, C. P. M.; Sudho¨lter, E. J. R.; Zuilhof, H. J. Am. Chem. Soc. 2004, 126, 8600. (24) Baur, B.; Steinhoff, G.; Hernando, J.; Purrucker, O.; Tanaka, M.; Nickel, B.; Stutzmann, M.; Eickhoff, M. Appl. Phys. Lett. 2005, 87, 263901. (25) Chen, C.-F.; Wu, C.-L.; Gwo, S. Appl. Phys. Lett. 2006, 89, 252109. (26) Coffinier, Y.; Boukherroub, R.; Wallart, X.; Nys, J.-P.; Durand, J.-O.; Stie´venard, D.; Grandidier, B. Surf. Sci. 2007, 601, 5492. (27) Van de Walle, C. G.; Segev, D. J. Appl. Phys. 2007, 101, 081704. (28) Filippetti, A.; Spaldin, N. A. Phys. ReV. B 2003, 67, 125109. (29) Tsai, M.-N.; Jenkins, D. W.; Dow, J. D.; Kasowski, R. W. Phys. ReV. B 1988, 38, 1541. (30) Xu, Y.-N.; Ching, W. Y. Phys. ReV. B 1993, 48, 4335. (31) Cristensen, N. E.; Gorczyca, I. Phys. ReV. B 1994, 50, 4397. (32) Sta¨dele, M.; Majewski, J. A.; Vogl, P.; Go¨rling, A. Phys. ReV. Lett. 1997, 79, 2089. (33) Stampfl, C.; Van de Walle, C. G. Phys. ReV. B 1999, 59, 5521. (34) Wu, J.; Walukiewicz, W.; Yu, K. M.; Shan, W.; Ager, J. W., III.; Haller, E. E.; Lu, H.; Shaff, W. J.; Metzger, W. K.; Kurtz, S. J. Appl. Phys. 2003, 94, 6477. (35) Wright, A. F.; Nelson, J. S. Phys. ReV. B 1995, 51, 7866. (36) Paczkowicz, W.; Cerny´, R.; Krukowski, S. Powder Diffr. 2003, 18, 114. (37) Hankelman, G.; Uberuaga, B. P.; Jo´nsson, H. J. Chem. Phys. 2000, 113, 9901. (38) The value for the Hubbard parameter U was taken from the work of Janotti et al.13 for the InN bulk: U ) 1.9 eV. (39) Christensen, N. E. Phys. ReV. 1984, 30, 5753. (40) Fiorentini, V.; Methfessel, M. J. Phys.: Condens. Matter 1996, 8, 6525. (41) Baldareschi, A.; Baroni, S.; Resta, R. Phys. ReV. Lett. 1988, 61, 734. (42) Sgiarovello, C.; Binggeli, N.; Baldereschi, A. Phys. ReV. B 2001, 64, 195305. (43) Cicero, G.; Catellani, A.; Galli, G. Phys. ReV. Lett. 2004, 93, 016102. (44) Catellani, A.; Cicero, G. J. Phys. D: Appl. Phys. 2007, 40, 6215.

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