Passivation of CuI Quantum Dots - The Journal of Physical Chemistry

Article pubs.acs.org/JPCC

Passivation of CuI Quantum Dots Jing Wang,†,‡ Shu-Shen Li,‡ Ying Liu,*,† and Jingbo Li*,‡ †

Department of Physics, Hebei Normal University, and Hebei Advanced Thin Film Laboratory, Shijiazhuang 050024, Hebei, China State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

‡

ABSTRACT: Using the first-principles band structure method, the electronic properties and optical properties of cupric iodide (CuI) quantum dots (QDs) are studied for the first time. A model is proposed to passivate the surface atoms of CuI QDs. In this model, pseudohydrogen atoms are used to passivate the dangling surface bonds, which remove the localized in-gap surface states. The size dependence of the QD gaps is obtained and is found to evolve as ΔEg = 1.60/d0.84 as the effective diameter d decreases. The energy of the calculated absorption peak is shifted higher with the decreasing d and the full width at half-maximum of the peak becomes larger as d increases, which are in good agreement with previous experiments. It is confirmed, although the local density approximation (LDA) calculations underestimate the band gap, that they give the trend of band gap shift as much as that obtained by the hybrid PBE0 for CuI QDs. These results provide understanding of the effects of the dimensionality of CuI nanocrystals, and it is expected that the method used in this work will be a practical approach to the study of other I−VII semiconductor nanocrystals. quantum dots.19−21 Quantum size effects in CuI nanocrystals embedded in glass have been studied experimentally, and unusual luminescence behavior has been observed, including luminescence elongation followed by the increase in the light exposure.19 Using the hybrid electrochemical/chemical (E/C) method, β-CuI nanocrystallites with mean diameters ranging from 10 to 180 Å have also been synthesized on an atomically smooth graphite substrate.20,21 However, to date, theoretical studies of the electronic properties of CuI QDs, or even of any of the I−VII semiconductor QDs, have not been reported. There is a particular problem with calculating the properties of QDs in that the electronic properties of QDs depend not only on their size, geometry, and relaxation but also on adequately passivating the surface atomsʼ dangling bonds to remove the ingap states. For instance, large organic molecules are often used to passivate nanostructure surfaces in experiments. Because of the complexity of simulating large molecules on a surface, however, it is difficult to simulate a realistic experimental situation in calculations. We have, therefore, employed pseudohydrogen atoms as discussed below to passivate the surfaces. This approach has been successfully applied to investigations of Si nanostructures,22,23 III−V and II−VI QDs,24−27 and some core/shell QDs.28 These studies provide us with a good way to understand the effects of dimensions in quantum confinement systems. For I−VII semiconductors, they are slightly different from other IV, III−V, and II−VI semiconductors in that CuI

1. INTRODUCTION Various semiconductor nanocrystals or quantum dots (QDs) have been synthesized, and it has been found that their optical and electrical properties are dramatically different from their bulk counterparts.1−4 As the size decreases, quantum confinement effects and surface states become very important as does the shape of the particle. The particle size also impacts the phase stability,5 which is a critical parameter determining the suitability of a particular QD for a particular application. The electronic structures of the QDs can also be tailored through their size and shape leading to many novel physical and chemical properties.6 A typical semiconductor nanocrystal with 1−10 nm diameter consists of about 100−104 atoms. These small colloidal nanocrystals appear promising as advanced functional materials and can already be found in various nanoscale electronic and optoelectronic devices, such as lasers,7−10 solar cells,11 and single-electron transistors.12,13 In the past two decays, much effort has been directed toward the electronic and optical properties of IV, III−V, II−VI, and some wide-band gap oxide semiconductor nanocrystals, and great progress has been made. Cupric iodide (CuI), as a p-type semiconductor with a large and direct band gap (more than 3 eV) in the zinc-blend ground-state phase, is a promising material for constructing short wavelength emitters and for making transparent optoelectronic devices. Recently, considerable research effort, both experimentally and theoretically, has been devoted to the study of the band structure and transport properties of CuI.14−21 Since Tennakone et al. reported the usage of CuI as a hole-collecting agent in a dye-sensitized solidstate cell,15 much attention has been focused on studying the properties of CuI, including thin CuI films17,18 and CuI © 2012 American Chemical Society

Received: May 20, 2012 Revised: September 4, 2012 Published: September 5, 2012 21039

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Cu−7/4H and I−1/4H bond lengths. We model tetrahedral Cu(7/4H)4 or I(1/4H)4 cluster with Cu or I atom at the body center. Through relaxation, the Cu−7/4H and I−1/4H bond lengths calculated with the LDA are 1.61 and 1.92 Å, respectively. Subsequently, pseudohydrogen atoms are used to passivate the surface atoms of the QD along the Cu−7/4H and I−1/4H bond lengths. The procedure was therefore the following. First, a large bulk γ-CuI structure with a Cu atom fixed in the center was built. Next, the bare (unpassivated) QDs were built by choosing a sphere of radius r (depending on the size of the QD) and by removing all the atoms outside of this sphere. In the next step, some of the surface Cu ions and I ions with more than two dangling bonds were removed to ensure electroneutrality.36,37 Subsequently, we used the 7/4H and 1/4H pseudohydrogen atoms to passivate the dangling bonds of surface Cu and I atoms, respectively. Finally, geometry optimizations were performed by putting the built CuI QD into a supercell, where the QDs are surrounded by a vacuum layer of 10 Å which allowed us to ignore unphysical interactions.

has both valence and ionic character. The goal of the present paper is to begin a comprehensive study and guide for future experimental studies regarding the effects of the geometric shape and size-dependent electronic structures in CuI QDs. Herein, an extensive first-principles study of these QDs on the basis of density functional theory (DFT) was performed with focus on the size dependence of the electronic structures and optical properties in CuI QDs. The rest of this paper is arranged as follows. Section 2 describes the calculation details and the passivation method. Results are discussed in section 3, including the evolution of the band gap of the CuI QDs, the comparison of the electronic structure of the QDs to the bulk CuI, the effects of the passivation, the optical properties, and the comparison of band gap difference between local density approximation (LDA) and PBE0 calculations. Finally, a brief summary is given in section 4.

2. THEORETICAL METHODS In the present work, the electronic properties are studied and total-energy calculations are performed using the projectedaugmented wave (PAW) method29 and a plane wave basis set as implemented in the Vienna ab initio simulation package (VASP)30 on the basis of DFT. In all the calculations, the convergence with respect to the plane-wave cutoff energy and k-sampling has been checked, and all the atoms are allowed to relax until the Hellman-Feynman forces acting on them are less than 0.05 eV/Å. The Monkhorst-Pack method31 is used to sample k-point mesh in the Brillouin zone. An 8 × 8 × 8 k-grid is used for the bulk CuI, and only the Γ-point is used for the QD calculations. Low-temperature γ-CuI has a zinc-blend-type structure belonging to space group F4̅3m. The lattice constant calculated within DFT with generalized gradient approximation (GGA) is 6.060 Å, which is in good agreement with the recent experimental value of 6.058 Å.16,17 All calculations of QDs discussed below have been constructed using this parameter value. For QDs, how to deal with the dangling bonds on the surface is an important and crucial aspect of any study. By passivation, one can get rid of extra states in the band gap. Within the context of a theoretical calculation, the dangling surface bonds can be passivated by using pseudohydrogen atom, ZH, which has a fractional nuclear charge Z and a corresponding fractional electronic charge. In several of our earlier works,32−35 a simple and feasible method to passivate the III−V and II−VI QDs and quantum wires (QWs) was proposed, and very good results were obtained. In the present study, pseudohydrogen atoms have been used to passivate the I−VII QDs, CuI QDs with both valence and ionic character, for the first time. As one of the binary ANB8−N crystals,36 the zinc-blend γ-CuI crystal is predominantly covalent as a result of fourfold coordination. Thus, it is good enough to determine the nuclear charges Z of the pseudohydrogen atoms by a simple chemical consideration of the covalent bond. Here, a Cu atom has one valence electron and is coordinated by four I atoms. Thus, each Cu atom contributes one-quarter (1/4) of an electron to each bond. Because each bond has two electrons, we choose to use a Z = 2 − 1/4 = 7/4 pseudohydrogen (7/4H) to passivate the Cu dangling bonds. For the case of the I atom, each atom is surrounded by four Cu atoms and has seven valence electrons. The stable electron configuration of an I atom has eight electrons forming the closed-shell configuration, and so it needs Z = (8−7)/4 = 1/4 pseudohydrogen (1/4H) atoms to passivate the I dangling bonds. The next question is how to fix the

3. RESULTS AND DISCUSSION A. Bulk. Before studying the QDs, it is necessary to understand the electronic properties of bulk γ-CuI. Here, we briefly summarize the electronic properties of bulk CuI. γ-CuI has a direct band gap at the Γ-point. The energy band gap calculated within the local density approximation (LDA) is 1.30 eV, much smaller than the experimental value of 3.2 eV18 because of the well-known LDA error whereby LDA (or GGA) calculations underestimate the band gap of a semiconductor. As we are only concerned with the band-edge characteristics and the changes in the band gap in CuI QDs, the LDA band gap error will be largely canceled when the results are expressed as differences between the properties of the QDs and the corresponding properties of the bulk material as shown in several previous works.33−35 Figure 1 shows the calculated total and projected density of states (DOS) and the wave function square contours of the valence band maximum (VBM) and the conduction band minimum (CBM). From the DOS pattern, it may be seen that the valence band edge of CuI has a majority of Cu 3d and a minority of I 5p characters, whereas the conduction band edge is derived largely from the mixing of the s states (both of Cu 4s and I 5s) and the effect of strong p− d repulsion.38 As shown in Figure 1b and c, the wave function square contours of VBM are mostly localized on the Cu sites with a bit on the I sites, while the CBM state localizes at both Cu and I sites. This further indicates the characteristics of the p−d hybridization of the VBM state and the mixing of the s states and the effect of the p−d repulsion of the CBM state as mentioned above. B. Quantum Dots. We have performed calculations for four different-sized QDs: Cu13I16(7/4H)12(1/4H)24, Cu 43 I 44 ( 7/4 H) 36 ( 1/4 H) 40 , Cu 79 I 68 ( 7/4 H) 72 ( 1/4 H) 28 , and Cu135I140(7/4H)76(1/4H)96. Excluding the pseudohydrogen atoms, the total numbers of Cu and I atoms (Ndot) are 29, 87, 147, and 275, respectively, as shown in Table 1. All four of these QDs have a nearly spherical shape and are only approximately stoichiometric. Here, the effective diameters are estimated by the expression d = (a/2)(Ndot)1/3, where a is the optimized lattice constant of the bulk CuI which we take to have the value of 6.06 Å. This gives effective diameters d = 0.93, 1.34, 1.60, and 1.97 nm for the QDs with 65, 163, 247, and 447 atoms as listed in Table 1. Comparing the structures before and 21040

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Figure 2. The calculated band gap energy differences with respect to bulk CuI for different-sized CuI QDs. The line is the fitted curve ΔEg = 1.60/d0.84.

of 13.6 ± 3.1, 17.8 ± 5.9, and 41.2 ± 37.3 Å were also in good agreement with the variational calculation of Kayanuma39 for spherical semiconductor particles. The small differences in the fit parameters may arise from the different particle sizes investigated in this simulation and used in the experiments. It is well-known that the wave function characteristics of VBM and CBM states of QDs have profound effects on their potential device applications. The wave function square contours of the VBM and CBM for fully passivated CuI QDs have therefore been investigated to make clearer the natures of these bands. Figure 3 shows the wave function square contours of a selected QD, Cu43I44(7/4H)36(1/4H)40, from three different perspectives. It is found that (1) the wave functions of VBM and CBM are mostly distributed in the interior of the dot and there is almost no distribution on the surface-passivating pseudohydrogen atoms. This indicates that the surfacepassivating method is very effective and works well with CuI QDs. (2) The VBM state of the QDs has a predominantly p−d hybridization characteristic, and the wave function square contours are mostly localized on Cu sites. For the CBM state, the wave function square contours are mainly localized on the I sites and have a mostly s-like envelope function symmetry. Comparing with the wave functions of bulk CuI, as shown in Figure 1b and c, we found that the VBM and CBM states in the QDs, such as in Figure 3, inherit well the atomic characteristic of the corresponding states in the bulk CuI. C. Effects of the Passivation on the CuI QDs. CuI has both valence and ionic character, and so the pseudohydrogen method described in section 2 was checked in greater detail to give a clear illustration of the effects of passivation for the small 65 atom QD, Cu13I16(7/4H)12(1/4H)24. Figure 4a shows results for the fully passivated cluster; Figure 4b shows results for the bare CuI case (no passivation); Figure 4c shows results with only the Cu atoms passivated; Figure 4d shows results for the case with only the I atoms passivated. In each case, the density of states and the corresponding wave function square contours viewed from the (001) and (110) directions are shown. In each case, the LDA relaxation was treated independently so that the geometry is optimized separately. For the fully passivated QD, as shown in Figure 4a, the LDA energy band gap is 2.97 eV and there are no surface states in the gap. In Figure 4b−d, the surface states arising from incomplete passivation are marked

Figure 1. (a) The total and projected densities of states (DOS) for bulk CuI. The Fermi energy is taken to be the zero of energy. (b, c) Views of the wave function square contours of the VBM and CBM from the (110) direction. The blue and purple balls represent Cu and I atoms, respectively.

Table 1. Summary of the QD Details and Results, Including the Numbers of Each Type of Atom Used To Construct the QDs, the Effective Diameter (d), the Band Gaps (Eg), and the Differences between the Calculated Band Gaps for the QDs and the Bulk (ΔEg = EQD − Ebulk g g ) number of atoms QDs

total

Cu

I

1 2 3 4

65 163 247 447

13 43 79 135

16 44 68 140

7/4

H

12 36 72 76

1/4

H

24 40 28 96

d (nm)

Eg (eV)

ΔEg (eV)

0.93 1.34 1.60 1.97

2.97 2.60 2.38 2.15

1.68 1.30 1.09 0.78

after the LDA relaxation, the QDs are found to contract a little. On the surface, most of the Cu atoms move inward by about 0.08 Å, and most of the I atoms move inward by about 0.02 Å. For these four different-sized QDs, the energy band gaps were calculated and are listed in Table 1. As the size decreases, the band gap of the CuI QD becomes larger and larger as a result of the quantum confinement effect. Figure 2 shows the LDA band gaps of the four QDs as a function of the effective diameter. Similarly, the difference of the band gaps between the bulk QDs and the bulk, ΔEg = EQD g − Eg , was fitted by using the α expression ΔEg = β/d , where α and β are fit parameters, and d is the effective diameter of the QD. The best fit parameters were found to be α = 0.84 and β = 1.60. Here, small differences exist between the simulation values of this work and the results of previous experiments.19,20 Nevertheless, our simulation results provide a good understanding of the size effects in CuI QDs. In ref 19, the blueshift of CuI nanocrystals with average radii ranging from 2.3 to 5.1 nm showed good agreement with a strong confinement model. For ref 20, the blueshifts of CuI nanocrystals with the average particle heights 21041

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Figure 3. Wave function square contour plots for the VBM and CBM states for the 163 atom CuI QD Cu43I44(7/4H)36(1/4H)40. The views are from the (001), (110), and (111) directions. The blue, purple, and green balls represent Cu, I, and pseudohydrogen atoms, respectively. The color scheme is the same for all figures in this paper.

by arrows in the DOS patterns. For the bare CuI QD, the surface is reconstructed during the LDA structural relaxation. In the band gap, there are two peaks of localized surface states. Most of these surface states are distributed on the surface Cu dangling bonds, and a small proportion of surface states are distributed on the top and bottom I dangling bonds according to the wave function square contours of Figure 4b. When the I dangling bonds are passivated, the Cu dangling bonds act as donor defects, which induce a great many surface states near the CBM as shown in the DOS of Figure 4c. From the corresponding wave function square contour, it can be seen that the surface states are mainly located at the near surface Cu sites and that there is a little distribution on the I sites. For the case of CuI QD with only the Cu dangling bonds passivated, near the VBM there appear surface states which arise mainly from the I dangling bonds as shown in the wave function square contour in Figure 4d. Here, the I dangling bonds act as acceptor defects. This analysis indicates that passivation removes surface states from the energy gap or near the gap edge while leaving the VBM and CBM states unchanged. Therefore, the passivation scheme used in this study works well for the CuI QDs. We believe that this passivation method described in section 2 will also be useful for investigating the properties of other I−VII semiconductor nanostructures. D. Optical Properties of the Passivated CuI QDs. As for the optical properties, the passivated QDs, Cu13I16(7/4H)12(1/4H)24 and Cu43I44(7/4H)36(1/4H)40, were considered. Here, the frequency-dependent dynamic dielectric function was calculated by using a summation over conduction band states. The frequency-dependent imaginary part of the dielectric function is determined by a summation over empty states using the following equation:40

(2) (ω) = εαβ

4π 2e 2 1 lim 2 Ω q→0 q

∑ 2ωkδ(εc k − εvk − ω) c ,v ,k

× ⟨uc k + eαq |uv k ⟩⟨uc k + eβ q |uv k ⟩*

(1)

where the indices c and v refer to conduction and valence band states, respectively, and uck is the cell periodic part of the wave functions at the k-point k. The real part of the dielectric tensor is obtained by the usual Kramers−Kronig transformation, (1) εαβ (ω) = 1 +

2 P π

∫0

∞

(2) εαβ (ω′)ω′

ω′2 − ω 2 + iη

dω′

(2)

where P denotes the principal value. Then, the optical adsorption coefficient I(ω) can be obtained from the dynamical dielectric response functions ε(ω), and the explicit expression is given by the following equation: I(ω) =

2 ω[ ε1(ω)2 + ε2(ω)2 − ε1(ω)]1/2 7/4

1/4

7/4

(3) 1/4

For Cu13I16( H)12( H)24 and Cu43I44( H)36( H)40, 500 and 800 bands were used to get the dynamical dielectric functions, respectively, and good convergence can be achieved. The photon energy covers from 0 to 25 eV. Figure 5 a and b has plotted the calculated dynamical dielectric functions, including imaginary part ε1 and real part ε2. Using eq 3, the optical adsorption coefficient spectra are shown in Figure 5c and d. According to our calculated ε2, two main peaks lie at about 4.53 and 7.29 eV for Cu13I16(7/4H)12(1/4H)24 (see Figure 5a) and at 4.92 and 7.37 eV for Cu43I44(7/4H)36(1/4H)40 (see Figure 5 b). For absorption spectra, as shown in Figure 5c and d, there are peaks located at about 7.61 and 7.50 eV for Cu13I16(7/4H)12(1/4H)24 and Cu43I44(7/4H)36(1/4H)40, respectively. The energy of the peak is shifted higher from 7.50 to 7.61 eV as the effective diameter of the QDs decreases. Second, 21042

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Figure 4. The density of states (DOS) and the corresponding wave function square contours viewed from the (001) and (110) directions for 65 atom CuI QD Cu13I16(7/4H)12(1/4H)24. (a) The fully passivated QD, (b) the bare QD, (c) the QD with unpassivated Cu dangling bonds, and (d) the QD with unpassivated I dangling bonds. The Fermi energy is set to zero. Surface states are marked by arrows.

the full width at half-maximum of the peak is obviously larger for Cu43I44(7/4H)36(1/4H)40 with the effective diameter of 1.34 nm than for Cu13I16(7/4H)12(1/4H)24 with the effective diameter of 0.93 nm. The two effects are in good accordance with the fluorescence emission characteristics reported by Hsiao et al.20 E. Comparison of Band Gap Difference between LDA and PBE0 Calculations. To overcome the well-known LDA error and to further verify the correctness of band gap differences, ΔEg, between QDs and the bulk, the accurate band gap of a small CuI QD with the hybrid PBE0 functional has been calculated on the basis of VASP codes with version 5.2. Here, the PBE0 functional contains 25% of the Fock exchange and 75% of the conventional PBE exchange functional. The calculated results are listed in Table 2. For bulk CuI, the hybrid PBE0 gives the band gap of 3.203 eV, which is in a good agreement with the experimental value of 3.2 eV.18 For the small QD, Cu13I16(7/4H)12(1/4H)24, the band gap difference from the bulk is 1.72 eV on the basis of the PBE0 method with only 0.04 eV difference from the result on the basis of the LDA

method. The relative deviation of band gap difference of the LDA from the PBE0 can be measured by the following formula: σ(d) = (ΔELDA − ΔEPBE0 )/ΔEPBE0 . For the small sample, we g g g get the value of 2.33%. As expected, although the LDA calculations underestimate the band gap, they can give the trend of band gap shift as much as the PBE0 calculations for CuI QDs. Because the PBE0 calculations expend too much computing cost, here, simply the small QD was selected to perform the PBE0 calculations. It is necessary to point out that, generally, as the effective diameter d of QDs increases, the relative deviation will reduce because the energy difference ΔEg(d → ∞) = Eg(d → ∞) − Ebulk = 0 whether on the basis of g PBE0 or LDA calculations.

4. CONCLUSIONS In summary, the electronic structures and optical properties of different-sized, approximately spherical CuI QDs have been studied using DFT within LDA. Pseudohydrogen atoms are used, for the first time, to passivate the surface dangling bonds 21043

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Figure 5. (a, b) The dynamical dielectric function ε(ω) = ε1(ω) + iε2(ω) as a function of the photon energy ω for Cu13I16(7/4H)12(1/4H)24 and Cu43I44(7/4H)36(1/4H)40. The solid and short dash lines represent the calculated real and imaginary parts of dielectric function, respectively. (c, d) Calculated optical adsorption spectra for the same two QDs.

Table 2. Comparison of the Band Gap Shift Obtained at PBE0 and LDA Methods for Cu13I16(7/4H)12(1/4H)24a

a

method

Ebulk g

EQD g

ΔEg

PBE0 LDA

3.20 1.30

4.92 2.97

1.72 1.68

ACKNOWLEDGMENTS

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REFERENCES

J. Wang is supported by the National Natural Science Foundation of China (Grant No. 11147172), the Natural Science Foundation of Hebei Province (Grant No. A2012205069), and the PhD Funding Support Program of Education Ministry of China (Grant Nos. 20090460500 and 201003149). J. Li gratefully acknowledges financial support from the “One-Hundred Talent Plan” of the Chinese Academy of Sciences and National Science Fund for Distinguished Young Scholar (Grant No. 60925016). This work is also supported by the National Basic Research Program of China (973 Program) under Grant No. 2009CB929300, the National High Technology Research and Development Program of China under Contract No. 2009AA034101 and NSFC No. 11274089.

All data are in units of eV.

of I−VII semiconductor nanocrystals, and the passivation successfully removes the surface states in or near the energy gap. As the size d decreases, the difference, ΔEg, between the band gaps for the QDs and for bulk CuI increases as ΔEg = 1.60/d0.84. The VBM and CBM states of the passivated QDs are distributed mostly in the interior of the dots, and they have characteristics similar to those of bulk CuI. The energy of the calculated absorption peak is shifted higher with the decreasing effective diameter of the QDs and the full width at halfmaximum of the peak becomes larger as the effective diameter increases, which are in good agreement with previous experiments. In addition, we confirm that the LDA calculations give the trend of the band gap shift as much as the PBE0. All these results provide, for the first time, a good theoretical understanding of the size effect in CuI QDs.

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(1) Alivisatos, A. P. Science 1996, 271, 933−937. (2) Woggon, U. Optical Properties of Semiconductor Quantum Dots: Springer-Verlag: Berlin, 1996. (3) Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, 8706−8715. (4) Yoffe, A. D. Adv. Phys. 2001, 50, 1−208. (5) Zhang, H.; Banfield, J. F. J. Phys. Chem. B 2000, 104, 3481−3487. (6) Li, J.; Wang, L. W. Nano Lett. 2003, 3, 1357−1363. (7) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H. J.; Bawendi, M. G. Science 2000, 290, 314−317. (8) Kazes, M.; Lewis, D. Y.; Ebenstein, Y.; Mokari, T.; Banin, U. Adv. Mater. 2002, 14, 317−321.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.L.); [email protected] (J.L.). Notes

The authors declare no competing financial interest. 21044

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The Journal of Physical Chemistry C

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(9) Duan, X.; Huang, Y.; Agarwal, R.; Lieber, C. M. Nature (London) 2003, 421, 241−245. (10) Achermann, M.; Petruska, M. A.; Kos, S.; Smith, D. L.; Koleske, D. D.; Klimov, V. I. Nature (London) 2004, 429, 642−646. (11) Huynh, W. U.; Dittmer, J. J.; Alivisatos, A. P. Science 2002, 295, 2425−2427. (12) Klein, D. L.; Roth, R.; Lim, A. K. L.; Alivisatos, A. P.; McEuen, P. L. Nature (London) 1997, 389, 699−701. (13) Akiyama, T.; Wada, O.; Kuwatsuka, H.; Simoyama, T.; Nakata, Y.; Mukai, K.; Sugawara, M.; Ishikawa, H. Appl. Phys. Lett. 2000, 77, 1753−1755. (14) Cardona, M. Phys. Rev. 1963, 129, 69−78. (15) Tennakone, K.; Kumara, G. R. R. A.; Kumarasinghe, A. R.; Wijayantha, K. U. G.; Sirimanne, P. M. Semicond. Sci. Technol. 1995, 10, 1689−1693. (16) Yashima, M.; Xu, Q.; Yoshiasa, A.; Wada, S. J. Mater. Chem. 2006, 16, 4393−4396. (17) Hull, S.; Keen, D. A. Phys. Rev. B 1994, 50, 5868−5885. (18) Sirimanne, P. M.; Soga, T.; Kunst, M. J. Solid State Chem. 2005, 178, 3010−3013. (19) Masumoto, Y.; Kawabata, K.; Kawazoe, T. Phys. Rev. B 1995, 52, 7834−7837. (20) Hsiao, G. S.; Anderson, M. G.; Gorer, S.; Harris, D.; Penner, R. M. J. Am. Chem. Soc. 1997, 119, 1439−1448. (21) Penner, R. M. Acc. Chem. Res. 2000, 33, 78−86. (22) Wang, L. W.; Li, J. J. Phys. Chem. 1994, 98, 2158−2165. (23) Han, J.; Chan, T. L.; Chelikowsky, J. R. Phys. Rev. B 2010, 82, 153413-1−153413-4. (24) Wang, L. W.; Li, J. Phys. Rev. B 2004, 69, 153302-1−153302-4. (25) Huang, X.; Lindgren, E.; Chelikowsky, J. R. Phy. Rev. B 2005, 71, 165328-1−165328-6. (26) Besteiro, L. V.; Tortajada, L.; Tiago, M. L.; Gallego, L. J.; Chelikowsky, J. R.; Alemany, M. M. G. Phy. Rev. B 2010, 81, 121307(R)-1−121307(R)-4. (27) Kwak, H.; Tiago, M. L.; Chan, T. L.; Chelikowsky, J. R. Phys. Rev. B 2008, 78, 195324-1−195324-9. (28) Wang, L. W.; Li, J. Appl. Phys. Lett. 2004, 84, 3648−3650. (29) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953−17979. (30) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169−11186. (31) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 5188−5192. (32) Peng, H.; Li, J.; Li, S. S.; Xia, J. B. J. Phys. Chem. C 2008, 112, 13964−13969. (33) Peng, H.; Li, J. J. Phys. Chem. C 2008, 112, 20241−20245. (34) Gai, Y.; Peng, H.; Li, J. J. Phys. Chem. C 2009, 113, 21506− 21511. (35) Deng, H. X.; Li, S. S.; Li, J. J. Phys. Chem. C 2010, 114, 4841− 4845. (36) Naicker, P. K.; Cummings, P. T.; Zhang, H.; Banfield, J. F. J. Phys. Chem. C 2009, 113, 1863−1871. (37) Naicker, P. K.; Cummings, P. T.; Zhang, H.; Banfield, J. F. J. Phys. Chem. B 2005, 109, 15243−15249. (38) Wang, J.; Li, J.; Li, S. S. J. Appl. Phys. 2010, 108, 043713-1− 043713-5. (39) Kayanuma, Y. Phys. Rev. B 1988, 38, 9797−9805. (40) Gajdoš, M.; Hummer, K.; Kresse, G.; Furthmüller, J.; Bechstedt, F. Phys. Rev. B 2006, 73, 045112-1−045112-9.

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dx.doi.org/10.1021/jp3048778 | J. Phys. Chem. C 2012, 116, 21039−21045