J. Phys. Chem. C 2009, 113, 229–234
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Hydrogenated Monolayer Sheets of Group 13-15 Binary Compounds: Structural and Electronic Characteristics Jukka T. Tanskanen, Mikko Linnolahti,* Antti J. Karttunen, and Tapani A. Pakkanen* UniVersity of Joensuu, Department of Chemistry, P.O. Box 111, FI-80101 Joensuu, Finland ReceiVed: August 15, 2008; ReVised Manuscript ReceiVed: October 27, 2008
Perhydrogenated group 13-15 binary monolayers have been studied by quantum chemical calculations, with focus on group 13 nitrides, phosphides, and arsenides. The electronegativity differences between the group 13 and group 15 elements polarize the surface hydrogens of the monolayers, giving rise to electrostatic H-H interactions. The perhydrogenated group 13-15 monolayers with highly polarized surface hydrogens prefer monolayers that are structurally analogous to a (110) slab cut from the corresponding diamond structure. In the case of weakly polarized surface hydrogens, the monolayers structurally analogous to a (111) slab of the corresponding diamond structure are preferred over (110). At nanoscale, the electrostatic H-H interactions lead to preference of curved structures, such as nanotubes. Introduction A single layer of graphite, i.e., graphene sheet, is composed of carbon atoms with sp2 hybridization. Perhydrogenation of the graphene sheet produces a graphane monolayer,1 which is structurally analogous to a hydrogenated (111) sheet of diamond,2,3 each carbon atom of the sheet having sp3 hybridization with tetrahedral coordination. Similar structural characteristics apply for boron nitride, a monolayer of hexagonal boron nitride (hBN) being an isostructural and isoelectronic analogue of graphene. As a consequence, full hydrogenation of a monolayer of h-BN might be expected to produce a hydrogenated (111) sheet of cubic boron nitride (c-BN). Besides BN, a wealth of heavier group 13-15 binary compounds are experimentally known4 and are widely applied in semiconductor devices, such as solar cells.5,6 The use of hydrogen in the synthetic process of group 13-15 thin films is known to decrease the internal stress and increase the optical gaps of the films.7-9 Examples of hydrogen-containing group 13-15 binary compounds are BN,7,10 AlN,8,9,11-13 GaN,14-16 GaP,17,18 and GaAs18,19 thin films. While having somewhat uncharacterized atomic-level structures, IR spectroscopy has turned out useful in the characterization of the vibrations associated with hydrogen atoms, leading to suggestions of their atomic scale structures. For instance, the existence of both B-H and N-H bonds has been verified for the hydrogenated BN thin films,10 while for the hydrogenated AlN films, the hydrogens have been proposed to be mainly bound to nitrogens.9 The different Pauling electronegativities20 of the constituent atoms of group 13-15 binary compounds are of particular significance, as they alter the degree of ionicity of the bonds. Generally, the electronegativity differences are largest for the nitrides and about the same for phosphides and arsenides. In the hydrogenated group 13-15 binary compounds, the partial ionicity of the bonds between the group 13 and group 15 atoms polarizes the associated hydrogen atoms, as well, giving rise to electrostatic interactions between hydrogens.21 The electrostatic H-H interactions have been shown to have a strong impact on the structural characteristics of boron nitrides, the hydrogenated * To whom correspondence should be addressed. E-mail: Mikko.Linnolahti@ joensuu.fi;
[email protected]. Fax: (+358) 13-251-3344.
(111) sheet of c-BN preferring to bend due to repulsive electrostatic H-H interactions.21,22 However, the electrostatic H-H interactions are attractive for the hydrogenated (110) sheet of c-BN, thereby the resulting (110) monolayer becoming energetically favored over the (111) one.23 The monolayers of the hydrogenated group 13-15 binary compounds, other than BN, have been studied to less extent, and no periodic structural trends have been reported. Here, we report a theoretical study on perhydrogenated group 13-15 monolayers, focusing on the low-index (110) and (111) sheets of the diamond-like structure. The energetic, structural, and electronic characteristics of the monolayers of the group 13-15 binary compounds, covering the first three rows in the Periodic Table, are determined by quantum chemical calculations. In addition, calculated IR spectra are compared with the related experimentally known thin films. Computational Details Two-dimensional fully hydrogenated group 13-15 monolayers were fully optimized by periodic calculations using the CRYSTAL0624 quantum chemistry software. Furthermore, vibrational frequencies, together with IR spectra, were calculated for the monolayers to study the effect of thermodynamics and to verify them as true local minima. Periodic calculations were performed by the hybrid density functional B3LYP25 method, which has been shown to apply for group 13-15 binary compounds.6 Generally, use of optimized basis sets is necessary for the periodic calculations and, hence, the following basis sets were used: B/N: a modified 6-21G*;26 Al: a modified 86-21G*;27 P: a modified 85-21G*;28 Ga: 86-4111d41G*27b,29 basis with polarization functions adopted from the Karlsruhe split-valence basis set (def-SVP)30 and the exponent optimized for GaN (0.207 f 0.1736); As: def-SVP.30 The standard 6-31G** basis set was applied for hydrogen. Default optimization convergence thresholds and extra large integration grid, as implemented in the CRYSTAL code, were utilized in the calculations. In the SCF process, the threshold applied for total energy was 10-10 a.u. The electronic characteristics of the monolayers were analyzed on the basis of B3LYP-calculated band gaps and total density of states-plots (DOS). Six Legendre
10.1021/jp807300m CCC: $40.75 2009 American Chemical Society Published on Web 12/11/2008
230 J. Phys. Chem. C, Vol. 113, No. 1, 2009
Figure 1. Side and top views of the fully hydrogenated (110) and (111) slabs of group 13-15 diamond-like structures.
polynomials were used for the expansion of the DOS plots. Molecular B3LYP calculations and natural population analyses31 (NPA) were performed by TURBOMOLE v. 5.10.32,33 The optimizations were carried out for perhydrogenated group 13-15 sheets of molecular formula X33Y33H88, where X ) B, Al, or Ga and Y ) N, P, or As. A split valence (def-SVP)30 basis set was applied for all molecular systems. Results and Discussion Infinite fully hydrogenated (110) and (111) monolayer sheets of the diamond-like structures were studied for BN, AlN, GaN, BP, AlP, GaP, BAs, AlAs, and GaAs. The corresponding fully hydrogenated (111) monolayers are experimentally known for group 14 elemental hydrides, SiH and GeH, with covalent Si-Si and Ge-Ge bonds.34,35 The structures of the hydrogenated group 13-15 (110) and (111) monolayers are schematically illustrated in Figure 1. The monolayers are composed of XYH2 units, where X ) B, Al, or Ga and Y ) N, P, or As (see Figure 1). Accordingly, the relative energies for the infinite monolayers can be determined by dividing the total energies by the number of XYH2 units in the respective unit cells. The relative energies and band gaps for the infinite hydrogenated group 13-15 monolayers are given in Table 1 and in Figure 2. Besides the relative energies, we determined the free energies of reaction XY + H2 f XYH2, where XY is a pristine group 13-15 monolayer and XYH2 is the corresponding perhydrogenated monolayer sheet (Table 1). In the cases of BN, AlAs, and GaAs, the pristine monolayers are thermodynamically favored, while for AlN, GaN, BP, AlP, GaP, and BAs, the perhydrogenated monolayers are thermodynamically favored. The features of the calculated infrared spectra for the perhydrogenated monolayers are summarized in Table 3. For comparison, IR features of related experimentally prepared group 13-15 thin films are given in Table 3. It should be noted that the experimentally prepared thin films are typically amorphous materials with somewhat uncharacterized atomiclevel structures, while the studied monolayers represent novel nanostructures for which there is no experimental evidence, yet. Thereby, the reported monolayers do not necessarily represent the thin films. Possible agreement between the calculated and the experimental IR data could indicate the presence of similar structural fragments in the experimentally prepared thin films as in the described monolayer structures. In addition to the periodic calculations, finite perhydrogenated (110) and (111) sheets with a stoichiometry of X33Y33H88 were fully optimized at the B3LYP level of theory (Table 2).
Tanskanen et al. Furthermore, natural population analyses (NPA) were performed for the finite sheets to illustrate the electronic charge distribution within each sheet (Table 2). In the following sections, we present the results obtained for perhydrogenated group 13 nitrides, phosphides, and arsenides, making comparisons to experiments where available. Perhydrogenated Group 13 Nitride Monolayers. The perhydrogenated (110) monolayers are clearly favored over the (111) for the studied group 13 nitrides (Table 1 and Figure 2), the (110) monolayers being stabilized by attractive electrostatic H-H interactions. The attractive interactions originate from the partially ionic nature of the B-N, Al-N, or Ga-N bond, giving rise to hydrogens with positive and negative partial charges. The electronegativity differences decrease in the order AlN > GaN > BN (Table 1). Consequently, the electrostatic H-H interactions are strongest for the AlNH2 monolayers, which have the largest difference in relative energy between (110) and (111). The closest H-H distances for the group 13 nitride (110) and (111) monolayers are 2.24 and 2.60 Å for BN, 2.59 and 3.13 Å for AlN, and 2.67 and 3.23 Å for GaN, respectively. The closest H-H distances are thus shorter for the (110) than for the (111) monolayers. The characteristics of the hydrogenated (110) and (111) monolayers of c-BN will be discussed in detail below. The following considerations are analogous for the AlNH2 and GaNH2 monolayers. Polarization of the B-N bonds gives rise to BH and NH hydrogens with negative and positive partial charges, respectively. The BH hydrogens have increased spatial requirements due to gain of electron density, while the NH hydrogens have decreased spatial requirements due to loss of electron density. The perhydrogenated (111) monolayer, with BH hydrogens on one side of the monolayer and NH hydrogens on the other, prefers to bend because in planar orientation the electrostatic repulsion between BH hydrogens is stronger than the repulsion between NH hydrogens.21,23 For the (110) monolayer, the H-H interactions take place between hydrogens having partial charges of different sign (see Figure 1), giving rise to electrostatic attraction between hydrogens. Multilayering of the monolayers introduces attractive electrostatic H-H interactions between adjacent layers, resulting in preference for multilayered structures.23 Alongside with the periodic calculations on infinite monolayers, we perfomed molecular calculations on the (110) and (111) isomers of X33Y33H88 (Table 2). Only the hydrogenated BN (110) sheet remains planar, the other molecules undergoing structural transformations (Figure 4). The hydrogenated AlN (110) sheet becomes strongly twisted, the GaN (110) showing small distortion from planarity. All molecular (111) sheets prefer to bend, the effect being the strongest for AlN. The distortions of the molecular sheets from planarity suggest the corresponding infinite monolayers to be metastable. The structural distortions are due to electrostatic H-H interactions. Because of the largest electronegativity difference between Al and N, the structural distortions are the strongest for the hydrogenated AlN sheets. The spontaneous bending of the (111) sheets due to repulsive H-H interactions results in elongation of the closest H-H distances on one side of the sheet, while on the other side the closest H-H distances are shortened with respect to the corresponding infinite monolayers. In the molecular (110) BN and GaN sheets, the closest H-H distances are about the same as in the corresponding infinite monolayers. Due to the strongest attraction between surface hydrogens, the closest H-H distances are the shortest for AlN (110) sheet, around 2.1 Å, resulting in the twisted structure. Overall, the electrostatic H-H interactions
Hydrogenated Group 13-15 Monolayers
J. Phys. Chem. C, Vol. 113, No. 1, 2009 231
TABLE 1: Pauling Electronegativity Differences between Heteroatoms (∆χ), Relative Energies (∆E), Gibbs Corrected Relative Energies (∆G, T ) 298.15 K, P ) 0.1 MPa), and Band Gaps (Eg) of the Perhydrogenated Infinite (110) and (111) Sheets of Group 13-15 Diamond-Like Structures, Together with Free Energies for Perhydrogenation of Pristine Monolayer Sheets (∆Gr, T ) 298.15 K, P ) 0.1 MPa) periodic calculations of infinite (110) monolayers ∆χa
∆Eb
∆Gb
Pauling units
(kJ/mol/XYH2-unit)
(kJ/mol/XYH2-unit)
BN AlN GaN
1.0 1.4 1.2
-22.2 -30.4 -21.1
BP AlP GaP
0.2 0.6 0.4
2.0 -6.4 -5.1
BAs AlAs GaAs
0.1 0.6 0.4
4.3 -3.7 -2.2
hydrogenation reaction energies ∆Gr (kJ/mol/XYH2)
Eg (eV) (110)
(111)
(110)
(111)
8.6 7.9 6.4
6.7 5.7 5.4
73.7 -42.6 -46.1
90.1 -14.9 -26.8
5.5 5.4 4.7
5.7 5.1 4.3
-35.1 -32.1 -24.9
-37.5 -25.0 -18.0
4.9 4.6 3.8
5.0 4.0 3.1
-28.9 0.2 9.7
-30.4 5.8 14.9
nitrides -16.4 -27.8 -19.3 phosphides 2.4 -7.1 -6.9 arsenides 1.5 -5.6 -5.2
a Data from reference.36 b The energies in kJ/mol/XYH2-unit, where X ) B, Al, or Ga and Y ) N, P, or As, are given with respect to the (111) monolayers.
TABLE 2: Relative Energies (∆E) and Averaged NPA Charges for Isomeric Perhydrogenated (110) and (111) Sheets of Molecular Formula X33Y33H88 (where X ) B, Al, or Ga and Y ) N, P, or As) NPA charges nitrides
X(XH) N(NH) H(XH) H(NH)
phosphides
X(XH) P(PH) H(XH) H(PH) a
arsenides ∆E (kJ/mol/X33Y33H88) X(XH) As(AsH) H(XH) H(AsH) (110) (111)
-471 0
(110) (111)
-388 0
(110) (111)
-249 0
(110) (111)
168 0
(110) (111)
4 0
(110) (111)
60 0
(110) (111)
204 0
(110) (111)
66 0
(110) (111)
117 0
BN 0.830 0.846
-1.184 -1.154
-0.099 -0.044
0.452 0.351
1.724 1.697
-1.739 -1.709
-0.431 -0.279
0.446 0.403
1.487 1.462
-1.571 -1.552
-0.344 -0.203
0.433 0.391
-0.518 -0.513 AlP 1.000 1.005 GaP 0.714 0.719 BAs -0.608 -0.600 AlAs 0.922 0.928 GaAs 0.639 0.643
0.410 0.429
0.018 0.005
0.067 0.046
-0.773 -0.758
-0.358 -0.283
0.113 0.073
-0.565 -0.552
-0.260 -0.201
0.096 0.059
0.538 0.556
0.002 -0.017
0.041 0.025
-0.673 -0.654
-0.354 -0.289
0.082 0.045
-0.466 -0.447
-0.354 -0.289
0.064 0.030
AlN
GaN
BP
Figure 2. Top: Relative energies (∆E) and Gibbs corrected relative energies (∆G) of the infinite perhydrogenated (110) monolayers with respect to the infinite perhydrogenated (111) monolayers of group 13-15 diamond-like structures. Bottom: Band gaps (Eg) of the perhydrogenated group 13-15 (110) and (111) monolayers.
have a strong impact on the structural characteristics of hydrogenated group 13 nitrides, at nanoscale possibly leading to a preference of curved structures, such as nanotubes and -cages. The calculated stretching vibrations associated with H atoms for the group 13 nitride (110) and (111) monolayers, together
a The energies in kJ/mol are given with respect to the (111) isomer.
with the corresponding IR features obtained experimentally for the related thin films, are summarized in Table 3. The N-H stretching vibrations appear in all spectra at around 3200-3400 cm-1, B-H at 2500-2700 cm-1, Al-H and Ga-H at 1900-2100 cm-1. The stretching vibrations of the energetically favored BNH2 (110) monolayer are close to the experimental values, suggesting possible presence of (110) monolayer structural fragments in the experimentally prepared thin films. There is no similar agreement for AlN and GaN. In this context,
232 J. Phys. Chem. C, Vol. 113, No. 1, 2009
Tanskanen et al.
TABLE 3: B3LYP-Calculated Stretching Vibrations Associated with H Atoms for the Infinite Perhydrogenated Group 13-15 Monolayers, Together with the Corresponding IR Features for the Related Experimentally Known Thin Films nitrides wavenumber (cm-1)
phosphides assignment
wavenumber (cm-1)
(111) exp. (110) (111) exp. (110) (111) exp.
2490-2500 3410-3420 2720-2730 3260-3270 2525,10 2520-26007 3450,10 34347 AlNH2 1940-1950 3350-3360 2100-2110 3350-3360 not observed9 32509 GaNH2 1940-1950 3400-3410 2070-2080 3400-3410 210015 3350-350016
wavenumber (cm-1)
BPH2
BNH2 (110)
arsenides assignment
BH NH BH NH BH NH
2550-1560 2420-2430 2590-2600 2390-2400
AlH NH AlH NH AlH NH
1970-1980 2420-2430 2030-2040 2420-2430
GaH NH GaH NH GaH NH
1960-1970 2420-2430 2020-2030 2410-2420 180018 222018
BAsH2 BH PH BH PH
2560-2580 2230-2250 2600-2610 2220-2230
AlH PH AlH PH
1980-1990 2230-2240 2020-2030 2240-2250
AlH AsH AlH AsH
GaH PH GaH PH GaH PH
GaAsH2 1960-1970 2220-2230 2000-2010 2230-2240 1760,18 1200-190019 2040,18 212019
GaH AsH GaH AsH GaH AsH
AlPH2
BH AsH BH AsH AlAsH2
GaPH2
it should be noted that hydrogens have been suggested to be mainly bound to nitrogens in the AlN:H thin films.9 The band gaps of the hydrogenated group 13 nitride monolayers decrease upon moving from boron to gallium, the gaps of the energetically favored (110) monolayers being higher than the gaps of (111) monolayers (Table 1 and Figure 2). The gap for the (110) BNH2 monolayer is around 8.6 eV, and drops down to 6.4 eV for (110) GaNH2. The total DOS plots calculated for the group 13 nitride monolayers are somewhat different for the (110) and (111) monolayers (Figure 3). Perhydrogenated Group 13 Phosphide Monolayers. Phosphorus is less electronegative than nitrogen. As a consequence, the hydrogens in the perhydrogenated group 13 phosphides are less polarized than in the corresponding nitrides, and hence, the electrostatic attractions between the surface hydrogens are
assignment
less siginificant for the phosphides. This is clearly seen in the relative energies of the (110) and (111) monolayers, the differences being about an order of magnitude smaller than in the case of the nitrides (Figure 2 and Table 1). For the perhydrogenated group 13 phosphide monolayers, (110) is favored over (111) for AlP and GaP. In the case of BP, the (111) monolayer is favored over (110) due to the very small electronegativity difference between B and P atoms. The closest H-H distances for the group 13 phosphide (110) and (111) monolayers are 2.88 and 3.26 Å for BP, 3.32 and 3.93 Å for AlP, and 3.22 and 3.94 Å for GaP, respectively. Molecular calculations on the group 13 phosphide (110) and (111) isomers of X33Y33H88 show that all (110) sheets and the (111) sheet of BP remain planar, while the perhydrogenated AlP and GaP (111) sheets undergo structural transformations
Figure 3. Total DOS plots for the infinite perhydrogenated group 13 nitride (left), phosphide (middle), and arsenide (right) monolayers. The DOS plots for the (110) and (111) monolayers are given in red and blue, respectively. The plots have been shifted to give the Fermi energy as zero.
Hydrogenated Group 13-15 Monolayers
Figure 4. Finite B3LYP-optimized perhydrogenated (110) and (111) sheets of group 13 nitride diamond-like structures.
into structures, which resembling those of carbon nanotubes of zigzag orientation. The molecular sheets remaining planar have the closest H-H distances about the same as in the corresponding infinite monolayers. Bending of the molecular X33Y33H88 (111) sheets of AlP and GaP results in a slight preference for the (111) sheets over the (110) ones (Table 2), suggesting molecular group 13 phosphides to prefer curved structures at the nanoscale. The calculated stretching vibrations associated with H atoms for the hydrogenated group 13 phosphide (110) and (111) monolayers, together with the experimentally detected IR features for GaP:H thin films, are summarized in Table 3. Infrared data for hydrogenated boron and aluminum phosphide thin films was not available. Both the P-H and Ga-H stretching vibrations appear at wavenumbers about 200 cm-1 higher than the experimental values obtained for the thin films.17,18 The band gaps of the studied hydrogenated group 13 phosphide monolayers follow the same trends as the previously described group 13 nitride monolayers. The band gaps decrease upon moving from boron to gallium, the energetically favored monolayers having larger gaps (Figure 2). Generally, the gaps of the studied phosphides are smaller than those of the nitrides, the gap of the energetically favored GaPH2 (110) monolayer dropping down to 4.7 eV. The total DOS plots are qualitatively similar for the (110) and (111) monolayers, suggesting them to have similar electronic properties (Figure 3). Perhydrogenated Group 13 Arsenide Monolayers. The electronegativity of As is practically equal to that of P, and hence, one could expect the structural characteristics of the group 13 arsenides to be similar to the corresponding phosphides. This is demonstrated in Table 1 and Figure 2, showing that the perhydrogenated (110) monolayers are favored for AlAs and GaAs, while (111) is preferred for BAs. The closest H-H distances for the arsenide (110) and (111) monolayers are 3.11 and 3.46 Å for BAs, 3.48 and 4.11 Å for AlAs, and 3.50 and 4.13 Å for GaAs, respectively. All finite group 13 arsenide (110) sheets with a stoichiometry of X33Y33H88 prefer planar orientation. The molecular AlAsH2 and GaAsH2 (111) sheets are clearly bent into zigzag orientation, the (111) sheet of BAs remaining planar. The perhydrogenated AlAs (111) sheet is more curved than the corresponding GaAs sheet, which is due to the stronger electrostatic repulsion between the surface hydrogens in AlAs. The closest H-H distances of the molecular sheets remaining planar are about the same as in the corresponding infinite monolayers, in analogy with the group 13 phosphide sheets. Bending of the molecular X33Y33H88 (111) sheets of AlAs and GaAs results in a preference for the (111) sheets over the (110) ones (Table 2), suggesting molecular group 13 arsenides to prefer curved structures at the nanoscale, in analogy with the group 13 phosphides.
J. Phys. Chem. C, Vol. 113, No. 1, 2009 233 The calculated IR stretching features for the group 13 arsenide (110) and (111) monolayers, together with the experimentally detected IR features for hydrogenated GaAs thin films, are summarized in Table 3. Infrared data for hydrogenated BAs and AlAs thin films was not available. In the case of GaAs, the calculated As-H stretching vibrations appear at wavenumbers about 100-200 cm-1 higher than in the experimentally prepared thin films. The range of experimental values for Ga-H vibrations is broad,19 thus not allowing direct comparison. The band gaps of the perhydrogenated group 13 arsenide monolayers follow the same trends as the group 13 phosphides, the gaps of the arsenides being somewhat smaller (Figure 2). Notably, the band gaps of the GaAs monolayers are around 3-4 eV, lying close to the semiconducting regime. The DOS plots for perhydrogenated (110) and (111) monolayers of AlAs and GaAs show differences at the valence region, suggesting them to have dissimilar electronic characteristics (Figure 3). Conclusions The structural and electronic characteristics of fully hydrogenated monolayers of group 13-15 binary compounds, BN, BP, BAs, AlN, AlP, AlAs, GaN, GaP, GaAs, were studied by quantum chemical B3LYP calculations. The monolayers were structurally analogous to (110) and (111) slabs cut from the respective group 13-15 diamond-like structures. Infinite monolayers were studied by periodic calculations and molecular calculations of finite sheets were included for comparison. The calculated IR spectra for the infinite monolayers were analyzed and compared with the experimentally determined IR features of the related hydrogenated group 13-15 binary thin films. Characteristic for the hydrogenated group 13-15 monolayers, the different electronegativities of the constituent heteroatoms give rise to polarized surface hydrogens. The electrostatic interactions between the polarized hydrogens, which are attractive for (110) and repulsive for (111) slabs, have a strong impact on the structural and electronic characteristics of the perhydrogenated group 13-15 monolayers. The monolayers with a large electronegativity difference between the constituent heteroatoms, such as the group 13-nitrides, prefer (110) slabs. When the electronegativity differences are small, namely in the cases of BP and BAs, the (111) slabs are energetically favored. The band gaps of the hydrogenated group 13-15 monolayers decrease in the order nitrides > phosphides > arsenides. The large band gaps of the perhydrogenated group 13-nitride monolayers suggest them to be insulating, while the gaps of the studied group 13-arsenides drop down to the semiconducting regime. Overall, we have shown that fully hydrogenated group 13-15 monolayers are strongly influenced by the electrostatic H-H interactions. The molecular perhydrogenated group 13-15 sheets have a tendency for spontaneous bending, thereby potentially giving rise to new families of fully hydrogenated group 13-15 nanostructures, such as nanotubes and nanocages. References and Notes (1) Sofo, J. O.; Chaudhari, A. S.; Barber, G. D. Phys. ReV. B 2007, 75, 153401. (2) Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. ChemPhysChem 2006, 7, 1661. (3) Tanskanen, J. T.; Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. Chem. Phys. 2007, 340, 120. (4) Wells, R. L.; Gladfelter, W. L. J. Cluster Sci. 1997, 8, 217. (5) Dimroth, F. Phys. Status Solidi C 2006, 3, 373. (6) Timoshkin, A. Y.; Schaefer, H. F. J. Phys. Chem. C 2008, 112, 13816. (7) Anutgan, T. A.; Anutgan, M.; Ozdemir, O.; Atilgan, I.; Katircioglu, B. Surf. Coat. Technol. 2008, 202, 3058.
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