Optical Absorption Spectra and Polarizabilities of Silicon Carbide

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Optical Absorption Spectra and Polarizabilities of Silicon Carbide Nanotubes: A First Principles Study Lu Wang,† Jing Lu,*,† Guangfu Luo,† Wei Song,† Lin Lai,† Mingwei Jing,† Rui Qin,† Jing Zhou,† Zhengxiang Gao,*,† and Wai Ning Mei‡ Mesoscopic Physics Laboratory, Department of Physics, Peking UniVersity, Beijing 100871, P. R. China, and Department of Physics, UniVersity of Nebraska at Omaha, Omaha, Nebraska 68182-0266 ReceiVed: June 10, 2007; In Final Form: August 21, 2007

We have calculated the optical absorption spectra and polarizabilities of silicon carbide nanotubes by using the density functional theory within the local density approximation. Most of the examined single-walled silicon carbide nanotubes (SWSiCNTs) exhibit the first strong absorption peak around 3 eV, while the ultrathin (5, 0) SWSiCNT exhibits the first three strong peaks in the 1.5-4.0 eV region. The screened polarizabilities of SWSiCNTs are contributed by the localized valence electrons and can be described by a classical dielectric cylindrical shell model, compared with the delocalized π-electrons and the semimetallic shell model of carbon nanotubes. The longitudinal screened polarizabilities of SWSiCNTs are apparently larger than the transverse ones by a factor of 3.5-8.1, suggesting the possibility of their aligned synthesis in electric fields. In multiwalled silicon carbide nanotubes, the inner tube is partially shielded by the outer tube for light polarized perpendicular to the tube axis, compared with the nearly complete shielding effects in multiwalled carbon nanotubes.

Introduction 1991,1

Since their discovery in carbon nanotubes (CNTs) have attracted many research efforts because of their special mechanical and electronic properties as well as their potential applications. Single-walled carbon nanotubes (SWCNTs) can be either metallic or semiconducting depending on their helicity and diameter.2 Postsynthesis separation of metallic and semiconducting SWCNTs3-5 or controlled synthesis of SWCNTs is needed to obtain SWCNTs with similar electronic properties. This causes extra work for manufacturing electronic devices of SWCNTs, and many researchers try to synthesize tubular forms of other semiconductors at the nanoscale. Silicon carbide (SiC) is a semiconducting material of great technological interest for devices designed to operate at high temperatures, high power, high frequency, and in harsh environments.6 The one-dimensional nanoscale tubular forms of SiC, silicon carbide nanotubes (SiCNTs), were first synthesized in 2001.7,8 Many experimental9-14 and theoretical15-23 studies have been reported for SiCNTs in recent years. SiCNTs were predicted to be semiconducting, independent of the helicity and diameter from density functional theory (DFT) calculations.18 They have potential applications as hydrogen storage devices21 and tips for atomic force microscopy and scanning tunneling microscopy.22 The optical absorption is a fundamental optical property of material and can be easily measured experimentally. The optical absorption spectra have been widely used to investigate the electronic properties of nanotubes experimentally.24-27 For example, the chemical and electrochemical doping of CNTs has been successfully probed by optical absorption spectra in previous studies.28-33 Many theoretical studies34-40 have been * Corresponding author. E-mail: [email protected] (J.L.); zxgao@ pku.edu.cn (Z.G.). † Peking University. ‡ University of Nebraska at Omaha.

applied to nanotubes to gain a better understanding of the optical properties and to interpret experiments. Barone et al.36,37 calculated optical transitions in semiconducting and metallic SWCNTs by using the DFT and the novel TPSSh metageneralized gradient approximation hybrid functional41 and obtained results in excellent agreement with experiments. Polarizability is also an important basic parameter of nanotubes relating the dielectric response to the external electric field. Aligned SWCNTs have been synthesized in electric fields,42,43 which can be interpreted by their anisotropic polarizabilities calculated from previous theoretical studies.44-47 Optical absorption spectra may also be used to study the electronic properties of SiCNTs, and aligned synthesis of SiCNTs in electric fields is possible if the their polarizabilities are strongly anisotropic. To our knowledge, the optical and dielectric responses of SiCNTs have not been calculated. The main objective of the present work is to investigate the optical absorption and polarizabilities of SiCNTs and their possible dependence on diameter, chirality, and band gap. The second objective is to identify characteristic differences in these properties among SiCNTs, boron nitride nanotubes (BNNTs), and CNTs. In this article, we calculate the optical absorption spectra and the unscreened optical polarizabilities of singlewalled silicon carbide nanotubes (SWSiCNTs) by using the DFT within the local density approximation (LDA). The static and optical screened polarizabilities of SWSiCNTs and multiwalled silicon carbide nanotubes (MWSiCNTs) are obtained by using the density functional perturbation theory (DFPT)48-50 within the LDA. Computational Details We construct the structures of SiCNTs with only Si-C bonds, which was predicted to be the most stable structures from the previous work.17 The tube is placed in a hexagonal supercell with its axis along the z-direction, and periodic boundary conditions are applied along the x-, y-, and z-directions. We

10.1021/jp074484y CCC: $37.00 © 2007 American Chemical Society Published on Web 12/04/2007

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use norm-conserving pseudopotentials51 and plane-wave basis sets in all the calculations, implemented in CASTEP code.52 The energy cutoff of the plane wave is 470 eV. Electronic exchange and correlation are treated in the LDA based on the Ceperley and Alder53 data as parametrized by Perdew and Zunger.54 In geometry optimizations, a Monkhorst-Pack55 k-point grid of 1 × 1 × 7 is used, and the intertube separation is greater than 7 Å. Both the atomic coordinates and the lattice parameter along the tube axis are fully optimized by a conjugate gradient technique56 until the maximum force on each atom is less than 0.03 eV/Å and the maximum stress is less than 0.05 GPa. Band structure and optical property calculations are performed for the optimized geometries with a uniform 1 × 1 × 99 k-point, and the intertube separation is kept greater than 9 Å. The interaction of a photon with the electrons in the system is described in terms of time-dependent perturbations of the ground-state electronic states. The optical response is obtained from calculating the transitions between the occupied and unoccupied electronic states as implemented in CASTEP.52 We define the complex dielectric function as (ω) ) 1(ω) + i2(ω), and the imaginary part of the dielectric function 2(ω) is given by the equation

2(ω) ) 2e2π Ω0

|〈c, k|uˆ ‚r|V, k〉|2 δ[Ec(k) - Ev(k) - pω] ∑ k,V,c

(1)

where u is the vector defining the polarization of the incident electric field, and c and V represent the conduction and valence bands, respectively. Hence only the interband transitions are considered in the calculations. Then we calculate the real part 1 from the imaginary part 2 with the help of the KramersKronig transformation:57-59

1(ω) ) 1 +

2 P π

ω′ (ω′)

∫0∞dω′ ω′2 2- ω2

(2)

where P implies that the principal value of the integral is to be taken at the point ω′ ) ω.57-59 The optical absorption coefficients can be easily calculated from the complex dielectric function. Since the calculations are based on DFT-LDA and independent-particle approximation, the local field effects (LFEs) and excitonic effects are neglected. Phonons and their optical effects are also neglected. The frequency-dependent unscreened longitudinal and transverse electronic polarizabilities per unit length, denoted by Run,ele (ω) and Run,ele (ω), respectively, can be calculated from || ⊥ the real part 1 with the relations

(ω)/Ω 1,||(ω) ) 1 + 4πlR un,ele ||

(3)

1,⊥(ω) ) 1 + 4πlRun,ele (ω)/Ω ⊥

(4)

where l is the lattice parameter along the tube axis, and Ω is the volume of the supercell. The unscreened polarizability only takes into account the polarization of the individual single-particle wave functions, while the screened one includes their mutual interaction as well.44 We calculate the screened polarizabilities of SiCNTs by using the DFPT scheme. In the DFPT scheme, a weak perturbation electric field is applied to the system with all the ions clamped, and the first-order change in wave function is computed by minimizing the second-order perturbation in the

total energy.49 The electronic polarizability is obtained from the second derivative of the total energy with respect to the perturbation electric field:46,48

Rb,ele ) ⊥

∂E2 ∂2x

(5)

) Rb,ele ||

∂E2 ∂2z

(6)

where E is the total energy, and x and z are the perturbation electric fields in the x- and z-directions, respectively. Rb,ele and ⊥ are the transverse and longitudinal electronic polarizRb,ele || abilities of a periodically repeated array of SiCNTs, respectively. Since the response of the whole electronic system is achieved self-consistently, the LFEs have been taken into account, and what we obtain are the screened electronic polarizabilities. These electronic polarizabilities are actually the static limit of the electronic contributions (Rb,ele(0)). We perform Γ-point phonon calculations in the DFPT scheme to obtain the ionic polarizabilities, Rb,ion.48 The static polarizability consists of the electronic and ionic polarizabilities, namely, Rb(0) ) Rb,ele + Rb,ion. However, the ionic contributions are negligible at high frequencies because of the inertia of the ions,60 and the dielectric response at optical frequencies arises almost entirely from the electronic polarizability. Generally speaking, the electronic polarizability is nearly independent of the frequency if the electronic excitation is absent. Therefore, we have screened and unscreened optical polarizabilities: Rb(∞) ≈ Rb,ele(∞) ≈ Rb,ele(0) and Run(∞) ≈ Run,ele(∞) ≈ Run,ele(0), respectively, in the region without electronic excitation (in the case of SWSiCNTs, the region is ω < 1 eV). The polarizabilities we obtained in the above calculations are the values per supercell, and we convert them to values per unit length along the tube axis for comparison. Our polarizability calculations provide the transverse response of a periodically repeated array of SiCNTs rather than an isolated SiCNT because of the supercell and periodic boundary conditions. It is necessary to remove the depolarization fields originating from the periodic images. Similar to our previous polarizability calculations on BNNTs,61 we adopt the twodimensional Clausius-Mossotti correction47,61 to obtain the transverse polarizabilities of isolated SiCNTs. The conversion relation is

Ω ⊥ - 1 ) R⊥ ) 2πl ⊥ + 1

Rb⊥ 2πl b R 1+ Ω ⊥

(7)

where Ω is the volume of the supercell, l is the lattice parameter along the tube axis, Rb⊥ is the transverse polarizability of an SiCNT in a periodic array, and R⊥ is the transverse polarizability of an isolated tube. The longitudinal screened polarizability of an isolated SiCNT can be obtained directly from the value of the periodically arranged SiCNTs, namely, R|| ) Rb||, because the response of nanotubes to longitudinal electric fields is additive.47,61 On the basis of a series of convergence tests, we set the intertube separation to 9 Å and the k-point grid to 1 × 1 × 19 in all the polarizability calculations. Results and Discussion A. Band Structures and Optical Absorption Spectra. As a result of the structure optimizations within DFT-LDA, the

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TABLE 1: Radii, Band Gaps, and Optical and Static Transverse and Longitudinal Screened Polarizabilities (per unit length) of SiCNTs as a Function of the Chiral Vector (n, m)a (n, m)

R (Å)

(5, 0) 2.5 (6, 0) 3.0 (7, 0) 3.5 (8, 0) 3.9 (9, 0) 4.4 (12, 0) 5.9 (15, 0) 7.3 (4, 4) 3.4 (5, 5) 4.2 (6, 6) 5.1 (7, 7) 5.9 (8, 8) 6.8 (9, 9) 7.6 (12, 12) 10.1 (15, 15) 12.7 (18, 18) 15.2 (4, 4)@(9, 9) 7.6b (7, 0)@(15, 0) 7.3b

un Eg R⊥(∞) Run ⊥ (∞) R⊥(0) R||(∞) R|| (∞) R||(0) (Å2) (Å2) (Å2) (Å2) (Å2) (eV) (Å2)

0.2 0.7 1.2 1.4 1.5 1.9 1.9 2.2 2.2 2.3 2.3 2.4 2.4

6.1 7.6 9.1 10.8 12.6 18.4 25.0 9.0 12.0 15.3 18.8 22.6 26.2 39.0 52.8 68.1 29.7 29.0

19.7 33.7 48.5 36.3 58.1 87.1

6.7 8.2 9.9 11.8 13.7 20.2 9.8 13.1 16.7 20.7 25.0 29.2 44.1

38.6 41.0 43.1 48.6 54.6 56.9 60.6 79.4 81.4 98.7 44.6 56.1 57.3 67.5 78.9 89.8 91.2 101.1 135.2 137.1 168.7 204.3 147.4 148.5

54.1 59.9 67.3 75.1 83.3 108.3 60.5 76.1 91.6 107.2 122.0 137.3 183.2

Figure 2. Band structure and density of states (DOS) of the (5, 0) SWSiCNT. The arrows indicate optically allowed transitions at the Γ-point that are possibly responsible for the first three strong absorption peaks of the (5, 0) SWSiCNT.

a The transverse and longitudinal unscreened optical polarizabilities un (per unit length) are denoted with Run ⊥ (∞) and R|| (∞), respectively. b For the outer tube.

Figure 3. Complex dielectric functions and optical absorption spectra for polarization parallel to the axis for the (5, 0) SWSiCNTs. Figure 1. Calculated band gap versus the radius of SWSiCNTs. The calculated band gap of an isolated hexagonal SiC sheet (2.6 eV) is shown as a dashed horizontal line.

average Si-C bond length is about 1.77 Å in SWSiCNTs, which is in good agreement with other DFT calculations15,18 and slightly shorter than the experimental value of 1.89 Å in 2HSiC.62 After optimization, Si atoms move toward the tube axis, and C atoms move in the opposite direction, resulting in a buckling structure. The calculated SWSiCNTs are all semiconductors with band gaps ranging from 0.2 to 2.4 eV. Moreover, all the zigzag SWSiCNTs have a direct band gap at the Γ-point, whereas all the armchair SWSiCNTs have an indirect band gap. The calculated band gaps of SWSiCNTs are listed in Table 1 and are also shown in Figure 1 as a function of the radius. In general, the calculated band gaps of the SWSiCNTs increase with their radii and approach the calculated band gap (2.6 eV) of an isolated hexagonal SiC sheet. The above results agree well with previous DFT calculations.15,16,18 Figure 2 shows the band structure and density of states of the (5, 0) SWSiCNT, which has an ultrasmall diameter (5 Å). The calculated band gap is direct with a value of 0.2 eV at the Γ-point. Because the LFEs perpendicular to the axis of SWSiCNTs are significant, any calculated optical absorption spectra for polarization perpendicular to the tube axis without inclusion of the LFEs are not reliable. On the other hand, we find that the dielectric responses of SiCNTs to electric fields

along the axis are much larger than those perpendicular to the axis, as shown in the next section. Hence strong optical responses are expected to occur only for light polarized along the axis, and we only present the optical absorption spectra for polarization parallel to the tube axis. The calculated complex dielectric functions and optical absorption spectrum for polarization parallel to the axis for the (5, 0) SWSiCNTs are displayed in Figure 3. The real part 1, imaginary 2, and absorption spectrum consist of three strong peaks in the 1.5-4 eV region. These initial three strong peaks in the absorption spectrum are ascribed to optically allowed transitions with energies of 1.8, 2.5, and 3.4 eV, respectively. Figure 4a,b shows the band structure and density of states of the (12, 0) and (12, 12) SWSiCNTs, respectively. The calculated band gap of the (12, 0) SWSiCNT is direct and 1.9 eV at the Γ-point, whereas the (12, 12) SWSiCNT has an indirect band gap of 2.4 eV. The calculated complex dielectric functions and optical absorption spectra for polarization parallel to the axis are displayed in Figure 5 for the (8, 0), (12, 0), (5, 5), (8, 8), and (12, 12) SWSiCNTs, which have diameters larger than 8 Å. Although the band gaps of the five SWSiCNTs vary from 1.4 to 2.4 eV, the positions of the first strong peaks of the five SWSiCNTs are all at around 3 eV with similar widths. We compare the band structure and optical absorption spectra for SWSiCNTs with single-walled boron nitride nanotubes (SWBNNTs), which were studied in previous DFT calcula-

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Figure 4. Band structures and density of states (DOS) of the (a) (12, 0) (b) (12, 12) SWSiCNTs. The arrow D indicates the optically allowed transition at the Γ-point that is possibly responsible for the first strong peak of the (12, 0) SWSiCNT, and the arrow E indicates the optically allowed transition at about 1/12 of the line Γ-Z that is possibly responsible for the first strong peak of the (12, 0) SWSiCNT. Figure 6. (a) Transverse screened polarizability per angstrom versus the radius of SWSiCNTs. The solid curves are fits from a classical dielectric cylindrical shell model. (b) Longitudinal screened polarizability per angstrom versus the radius of SWSiCNTs. The solid lines are linear least-squares fits.

Figure 5. Complex dielectric functions and optical absorption spectra for polarization parallel to the axis for the (8, 0), (12, 0), (5, 5), (8, 8), and (12, 12) SWSiCNTs.

tions.38,61 The band structures of SWSiCNTs and SWBNNTs have similar dependences on the chirality and diameter. Both zigzag SWSiCNTs and SWBNNTs are predicted to have a direct band gap, whereas the armchair SWSiCNTs and SWBNNTs have an indirect one. The band gaps of SWSiCNTs and SWBNNTs generally increase with the radius and approach the band gaps of isolated SiC and BN sheets, respectively. The first strong peak was found at 5.5 eV in the absorptive part 2 of the dielectric function for the electric field parallel to the tube axis of all the examined SWBNNTs except the ultrathin SWBNNTs,38 compared to the corresponding value of 3 eV for similar-sized SWSiCNTs. On the other hand, semiconducting SWCNTs have a calculated optical band gap (E11) of 0.6-1.8 eV, and metallic SWCNTs have an optical band gap of 1.9-2.5 eV from previous TPSSh/3-21G studies.36,37 B. Polarizabilities. The optical and static transverse and longitudinal screened polarizabilities per unit length of the

isolated SiCNTs are listed in Table 1. We notice that the longitudinal screened polarizabilities are larger than the transverse ones by a factor of 3.5-8.1, exhibiting strong anisotropy. The screened polarizabilities per pair of Si and C atoms are R⊥(∞)/Npair ) 3.2-5.4 Å3, R⊥(0)/Npair ) 3.4-5.6 Å3, R||(∞)/ Npair ) 17.0-20.2 Å3, and R||(0)/Npair ) 23.1-28.3 Å3. We note that R||(∞)/Npair and R||(0)/Npair approach the calculated in-plane optical and static screened polarizabilities per pair of Si and C atoms (23.6 and 17.4 Å3) of an isolated hexagonal SiC sheet, respectively, with increasing tube radius. The ratio between the static and optical screened polarizabilities of SWSiCNTs also exhibits anisotropy: R⊥(0)/R⊥(∞) ranges from 1.08 to 1.13, while R||(0)/R||(∞) ranges from 1.36 to 1.40. The ratio R||(0)/R||(∞) is close to the calculated ratio (1.36) of the in-plane static and optical screened polarizabilities of an isolated hexagonal SiC sheet. It has been pointed out44 that the LFEs along the axis can be ignored because an external electric field along the axis will not induce any bound charge for infinitely long SWCNTs, whereas the LFEs perpendicular to the axis of SWCNTs are remarkable because of the buildup of bound surface charge if an electric field is applied perpendicular to the axis. In our previous work, we found similar behavior in SWBNNTs.61 There is a good agreement between the unscreened and screened longitudinal optical polarizabilities of SWSiCNTs, suggesting that LFEs along the tube axis are also negligible in SWSiCNTs. The unscreened transverse optical polarizabilities of SWSiCNTs are approximately 2.2-3.2 times that of the screened ones, slightly larger than a factor of 1.7-2.4 for SWBNNTs but smaller than a factor of 4-5 for SWCNTs.44 In other words, the LFEs perpendicular to the tube axis in SWSiCNTs are stronger than those in SWBNNTs but weaker than those in SWCNTs. Figure 6a,b shows the transverse and longitudinal screened polarizabilities per unit length versus the radius of an SWSiCNT, respectively. For comparison, we construct a classical model

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Figure 7. (a) Comparison of the screened optical transverse polarizabilities per angstrom versus the radius among SWCNTs (blue triangles), SWSiCNTs (green stars), and SWBNNTs (red circles). (b) Comparison of the screened optical longitudinal polarizabilities per angstrom versus the radius among semiconducting SWCNTs (blue squares), SWSiCNTs (green triangles), and SWBNNTs (red stars).

of an infinitely long dielectric cylindrical shell with an outer radius RM, a thickness of the wall dM, and a dielectric constant M. From electrostatics, the longitudinal polarizability per unit length has a linear relation with RM if dM is a constant. We find that all the calculated screened longitudinal polarizabilities of SWSiCNTs can be fitted with the following linear relations: R||(0) ) 18.3R, and R||(∞) ) 13.4R, with R in Å2 and R in Å, a result in agreement with the dielectric cylindrical shell model. The transverse polarizability per unit length of the dielectric cylindrical shell model is

RM,⊥ )

RM2(2RM - dM)dM(M2 - 1) 2[2RM + (M - 1)dM][2RMM - (M - 1)dM]

(8)

By fitting the calculated transverse screened polarizabilities to this relation, we obtain the effective values of SWSiCNTs: RM ) R + 1.42 Å, dM ) 3.5 Å, and M ) 8.6 for the optical transverse screened polarizabilities, and RM ) R + 1.48 Å, dM ) 3.7 Å, and M ) 10.9 for the static transverse screened polarizabilities. We expect that for large-radius SWSiCNTs where RM . dM and dM is a constant, the transverse polarizability has linear relations with the radius. A comparison of the optical screened transverse polarizabilities per unit length among SWSiCNTs, SWBNNTs,61 and SWCNTs47 is presented in Figure 7a. The transverse polarizabilities of SWCNTs are fitted to the curve R⊥(0) ) 0.4 (R + 1.3 Å)2 according to the previous DFPT-LDA study,47 and the transverse polarizabilities of SWSiCNTs and SWBNNTs61 are fitted to the classical dielectric cylindrical shell model. For nanotubes with radii smaller than 4 Å, the optical screened transverse polarizabilities for similar-sized SWCNTs and SWSiCNTs have close values, and they are larger than those of similar-sized SWBNNTs. For the nanotubes with radii larger than 4 Å, the optical transverse screened polarizabilities for

similar-sized nanotubes have the relation R⊥[SWCNT] > R⊥[SWSiCNT] > R⊥[SWBNNT], and the differences enlarge with the radius. Considering that the π-electrons of both metallic and semiconducting SWCNTs are delocalized, the behavior of the transverse polarizability of SWCNTs can be understood in terms of an empty lattice model of electrons moving freely on a cylinder of infinitesimal thickness,44 and the transverse polarizabilities can be fitted to a semimetallic shell model (R⊥ ∼ R2).47 On the other hand, the C-Si and B-N bonds are partially ionic,16 and the valence electrons of SiCNTs and BNNTs are localized. Thus we can describe the behavior of the transverse polarizabilities of SiCNTs and BNNTs by the classical dielectric cylindrical shell model, where R⊥ ∼ R for large-radius nanotubes. A comparison of the optical screened longitudinal polarizabilities per unit length among SWSiCNTs, SWBNNTs,61 and semiconducting SWCNTs47 is presented in Figure 7b. The longitudinal polarizabilities for similar-sized nanotubes have the relation R||[SWCNT] > R||[SWSiCNT] > R||[SWBNNT]. Moreover, the difference in the longitudinal screened polarizability between similar-sized nanotubes is significantly larger than that in the transverse screened polarizability. The longitudinal polarizability of SWCNTs have the relation R|| ∼ 1/Eg2 with the band gap and can be derived from linear-response theory63 in combination with the fact that SWCNTs have a small band gap from previous studies.44,47 We note that the band gaps of similar-sized nanotubes have the relation Eg[SWCNT] < Eg[SWSiCNT] < Eg[SWBNNT] from previous DFT calculations.47,61 Therefore, the smaller the band gap of the nanotube, the larger the optical screened longitudinal polarizability, which might also be interpreted by the linear-response theory.63 The electric interactions along the tube axis between constituent tubes of MWSiCNTs are quite weak, and the optical longitudinal screened polarizabilities of all the MWSiCNTs are approximately the sum of the optical longitudinal screened polarizabilities of the constituent tubes, as shown in Table 1. The additive property of the longitudinal response was also reported in multiwalled carbon nanotubes (MWCNTs)47 and multiwalled boron nitride nanotubes (MWBNNTs).61 The optical transverse screened polarizabilities of the two investigated MWSiCNTs are smaller than the sums of the values of their components but larger than the values of the outer tubes; thus the inner tube is partially shielded by the outer tube in MWSiCNTs for light polarized perpendicular to the axis. Following the previous work,45,61 we define optical shielding S as

S(∞) )

outer total Rinner ⊥ (∞) + R⊥ (∞) - R⊥ (∞)

Rinner ⊥ (∞)

× 100%

(9)

outer where Rinner ⊥ (∞) and R⊥ (∞) are the optical transverse polarizabilities of the isolated inner and outer tubes, respectively, and Rtotal ⊥ (∞) is the total optical transverse polarizability of MWSiCNTs. We obtain optical shieldings S of 61 and 56% for the (4, 4)@(9, 9) and (7, 0)@(15, 0) MWSiCNTs, respectively, a little larger than the optical shielding S (39-46%) of similarsized MWBNNTs.61 On the other hand, similar-sized MWCNTs have a much larger shielding S of 90-95%.45 The optical transverse polarizabilities of the outer tubes of similar-sized MWCNTs, MWSiCNTs, and MWBNNTs decrease in the outer following order: Router ⊥ (∞)[MWCNT] > R⊥ (∞)[MWSiCNT] outer > R⊥ (∞)[MWBNNT]. Therefore, the larger the optical transverse polarizability of the outer tube, the stronger the optical shielding effects. It can be understood in a simple way: A

Optical Absorption Spectra of SiCNTs smaller inner field is applied to the inner tube instead of the outer field because of the shielding of the outer tube. For similarsized outer tubes, the larger the transverse polarizability of the outer tube, the smaller the ratio of the inner field to the outer field and the weaker the polarization of the inner tube, hence the larger the shielding S. The nearly complete shielding effects in MWCNTs attribute to their delocalized π-electrons,47 whereas the optical shielding effects of MWSiCNTs attribute to their localized valence electrons. The inner tube is also partially shielded by the outer tube in MWSiCNTs if a transverse static electric field is applied. The static shielding effects of MWSiCNTs were not obtained since the calculations of the static polarizabilities of MWSiCNTs are very time-consuming. Conclusions In summary, we have calculated the optical properties of isolated SWSiCNTs within the framework of DFT-LDA. The first strong absorption peak was found around 3 eV for all the calculated SWSiCNTs except the ultrathin (5, 0) SWSiCNT, which exhibits the first three strong peaks in the 1.5-4.0 eV region. These absorption spectra reflect the semiconducting nature of all the examined SWSiCNTs. The linear response of isolated infinite SWSiCNTs and MWSiCNTs to electric field perturbation has been calculated within DFPT-LDA. The calculated screened polarizabilities of SWSiCNTs can be described by a classical dielectric cylindrical shell model, suggesting that the polarizabilities of SiCNTs are mainly contributed by localized valence electrons. The LFEs perpendicular to the axis in SWSiCNTs are as significant as those in SWBNNTs, but are smaller than those in SWCNTs. The calculated optical transverse polarizabilities of the SWSiCNTs are close to those of the similar-sized SWCNTs as the radius is smaller than 4 Å, while they are smaller than those of the similar-sized SWCNTs as the radius is larger than 4 Å. By contrast, the calculated optical longitudinal polarizabilities of the SWSiCNTs are always smaller than those of the similarsized SWCNTs. Additionally, all the optical polarizabilities of the examined SWSiCNTs are larger than those of similar-sized SWBNNTs. The optical shielding efficiency in MWSiCNTs is slightly larger than that in MWBNNTs,61 but is significantly smaller than that in MWCNTs.45,47 Acknowledgment. This work was supported by the NSFC (Grant Nos. 10474123, 10434010, 1074003, 90606023, and 20731160012), National 973 Projects (Nos. 2002CB613505 and 2007CB936200, MOST of China), 211, 985, and Creative Team Projects of MOE of China, and Nebraska Research Initiative (No. 4132050400) of USA. Our calculations were partially carried out in the HP Cluster of the Calculation Center of Science and Engineering and the Cluster of the Institute of Condensed Matter and Material Physics, Peking University. References and Notes (1) Iijima, S. Nature 1991, 354, 56. (2) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (3) Krupke, R.; Hennrich, F.; von Lohneysen, H.; Kappes, M. M. Science 2003, 301, 344. (4) Maeda, Y.; Kimura, S.; Kanda, M.; Hirashima, Y.; Hasegawa, T.; Wakahara, T.; Lian, Y.; Nakahodo, T.; Tsuchiya, T.; Akasaka, T.; Lu, J.; Zhang, X.; Gao, Z.; Yu, Y.; Nagase, S.; Kazaoui, S.; Minami, N.; Shimizu, T.; Tokumoto, H.; Saito, R. J. Am. Chem. Soc. 2005, 127, 10287. (5) Maeda, Y.; Kanda, M.; Hashimoto, M.; Hasegawa, T.; Kimura, S.; Lian, Y. F.; Wakahara, T.; Akasaka, T.; Kazaoui, S.; Minami, N.; Okazaki, T.; Hayamizu, Y.; Hata, K.; Lu, J.; Nagase, S. J. Am. Chem. Soc. 2006, 128, 12239.

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