Excited State Properties of Allylamine-Capped Silicon Quantum Dots

Jan 24, 2007 - Small SiQDs have the advantage that a significant amount of experimental and theoretical data exists with which we can compare our resu...
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J. Phys. Chem. C 2007, 111, 2394-2400

Excited State Properties of Allylamine-Capped Silicon Quantum Dots X. Wang,† R.Q. Zhang,*,† T.A. Niehaus,‡,§ and Th. Frauenheim‡ Centre of Super-Diamond and AdVanced Films (COSDAF) and Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, China, Bremen Center for Computational Material Science, UniVersity of Bremen, 28334 Bremen, Germany, and German Cancer Research Center, Department of Molecular Biophysics, D-69120 Heidelberg, Germany ReceiVed: September 2, 2006; In Final Form: NoVember 23, 2006

Excited-state properties of allylamine-capped silicon quantum dots (SiQDs) from Si10 to Si59 are studied using a density-functional tight-binding method and compared with available experimental data. Signatures in vibrational and optical absorption spectra are revealed, which show the detailed effect of modification of the SiQDs with allylamine. It is verified that the modification could be expected to not only reduce the surface oxidation rate but also maintain an efficient electronic transition feature that facilitates blue emission. The optical properties show significant size dependence due to the quantum confinement effect. The increase in the number of allylamine molecules could only result in a slight red shift of emission spectra.

I. Introduction Semiconductor materials, especially silicon, comprise one of the most active frontiers in physics, chemistry, and biophysics.1 The interest in studying their electronic properties and light emission has significantly increased over the past decade.2-5 However, bulk silicon was found to be inefficient as a lightemitting material due to indirect transition characteristics. In contrast, various low-dimensional systems, such as porous silicon, silicon nanocrystals, and silicon quantum dots (SiQDs), possibly emit light at room temperature.6-8 Among these various low-dimensional materials, SiQDs as light emitters have been actively studied in recent years because of their good potential in biomedical applications and as candidates for new-generation optoelectronics. Park and coworkers9 found that various colors including red, green, blue, and white photoluminescence (PL) could be observed from the amorphous SiQDs by controlling the dot size; crystalline SiQDs embedded in a silicon nitride film also showed different PL emission energy by varying the flow rates of SiH4 and NH3 gases, and the hydrogen passivation of dangling bonds enhanced the PL intensity. These experiments revealed the strong advantages of silicon-based light-emitting diodes. Furthermore, they help us design the new biological chromophores in further investigations, since the SiQDs have been found to be an ideal candidate for biological fluorescence imaging without potential toxicology problems.10 Although previous reports have found that hydrogenated SiQDs show obvious PL emission in the blue region of the visible spectrum, their surfaces oxidize easily at room temperature,11 and this oxide surface passivation leads to a dipole-forbidden yellow-red emission.12 Functionalization of small-diameter SiQDs with foreign molecules to terminate their surfaces is an effective way of avoiding the oxidation.13,14 Thus far, a lot of work has been done that deals with the excitedstate properties of such nanoclusters. For example, Warner et * To whom correspondence should be addressed. E-mail: aprqz@ cityu.edu.hk. † City University of Hong Kong. ‡ University of Bremen. § German Cancer Research Center.

al.15 reported a simple synthesis processed at room temperature and atmospheric pressure to produce water-soluble silicon quantum dots that exhibit strong blue PL with a rapid rate of recombination. In their experiment, the Si-H surface bonds were terminated by allylamine with Si-C bond formation. This carbon-terminated surface not only maintains the direct band gap transition but also provides good reactivity due to the end amidogen. Thus, the allylamine-capped SiQDs become an excellent candidate for biomedical applications due to the ease of synthesis and optical properties. Although some properties of these allylamine-capped SiQDs, such as their Fourier transform infrared (FTIR) spectra and PL spectra, have been obtained in experiments, the physical mechanisms and chemical nature of the optically activated nanodots still need further investigation. In this work, a detailed theoretical study of various SiQDs is presented to understand the surface structure, and electronic and optical properties, as functions of size and symmetry. Following many previous works on the size-dependent optical properties of silicon nanoparticles measured and characterized using experimental11,16 and theoretical2,17-20 methods, we varied the SiQD size in our calculations from 10 to 59 silicon atoms to ensure a systematic and comprehensive comparison. Small SiQDs have the advantage that a significant amount of experimental and theoretical data exists with which we can compare our results. We pay more attention to Si35 and Si59, as their sizes are close to the experimental value 1.4 ( 0.3 nm.15 Our theoretical simulation and modeling are expected to provide insight and guidance in the interpretation of experiments and to reveal the main changes in optical properties induced by the modification of the SiQD surface. II. Computational Details In this study, we used a computationally efficient densityfunctional-based tight-binding approach (DFTB)21,22 and its time-dependent linear response extension TD-DFTB23 to study the energetic and optical properties of the various molecules adsorbed on the surfaces of SiQDs. The DFTB is derived from DFT as a second-order expansion of the DFT total energy

10.1021/jp065704v CCC: $37.00 © 2007 American Chemical Society Published on Web 01/24/2007

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functional with respect to the charge-density fluctuations around a given reference density. Several approximations including a γ-approximation Hamiltonian matrix element Hµν0 with a twocenter approximation are used to derive the total energy23 occ

EGS )

1

cµiHµν0cνi + ∑ ∆qRγRβ∆qβ + Erep ∑i ∑ 2 Rβ µν

In the equation, ∆qR and ∆qβ represent the Mulliken net charge on atoms R and β, respectively. The Erep, depending on the diatomic distances, is approximated as a sum of short-range repulsive potentials. The TD-DFTB method developed by Frauenheim and coworkers23 following the TD-DFT route of Casida24,25 is capable of efficiently handling the excited-state calculations of large systems. In the excited-state energy calculations, a self-consistent field (SCF) calculation is conducted first to obtain the singleparticle Kohn-Sham (KS) orbitals and the corresponding KS energies i. Then, a coupling matrix which gives the response of the SCF potential with respect to a change in the electronic density is obtained following

Kijσ,klτ )

qRijqβkl [γRβ + (2δστ - 1)mRβ] ∑ Rβ

where δ and m, respectively, represent the charge-density fluctuations and the magnetization, σ and τ are spin indices, i and k are indices of the occupied KS orbitals, whereas j and l are unoccupied ones. The exchange-correlation energy has been included in the γ and m. Their detailed expressions can be found in ref 23. The excitation energies (ωI) is obtained by solving the following eigenvalue problem

(ωij2δikδjlδστ + 2xωijKijσ,klτxωkl)FijσI ) ωI2FklτI ∑ ijσ (ωij ) j-i) The total energy of the excited-state is given as a sum of the ground-state energy EGS and the excitation energy ωI

EIΣ ) EGS + ωI In this study, only low-lying excited states were considered, as photon emission occurs often from the lowest-energy excited electronic state. Hence, iterative diagonalization methods could be applied to reduce the necessary operation. Moreover, we used a basis of numerically described s, p, and d atomic orbitals for Si atoms, s and p atomic orbitals for C, N, and O atoms, and s atomic orbitals for H atoms. Under the above approximations, coupling matrix K could be constructed easily with economical computational cost. Thus, it is possible for us to perform the excited-state calculations of large systems using TD-DFTB methods. To validate the reliability of the present approach, calculations were performed first for several small clusters including Si5H12, Si29H36, and Si35H36. Although these clusters in ground states possess Td symmetry, such a high symmetry is broken down under the excitation. Similar symmetry changes have also been reported in a previous theoretical work.20 Our calculated optical gap of Si5H12 (6.40 eV) is close to the experimental value (6.5 eV26) as well as other high-level ab initio results.27 For Si29H36, our calculated optical gap 4.42 eV is in excellent agreement with the previous results using multireference second-order perturbation MR-MP2 (4.45 eV28) and TD-DFT/B3LYP (4.53 eV28) methods. For Si35H36, our optical gap (4.37 eV) compares

well with MR-MP2 (4.33 eV27) and TD-DFT (4.42 eV28) results. The above tests indicate that the accuracy of TD-DFTB is comparable with the high-level ab inito calculations for the study of silicon nanostructures. III. Results and Discussion Geometrical Structures. The optimized geometries for both the hydrogenated SiQDs and the allylamine-capped SiQDs are displayed in Figure 1. The structure was constructed to be spherical to reduce the anisotropic effects. Our models are dangling-bond saturated by hydrogen atoms, however without resulting in any -SiH3 group. Analytical frequency calculations were performed for all stationary points located on the potentialenergy surface to assess the nature of an optimized structure. Our calculations show that the most stable hydrogenated SiQDs are those with Td symmetry. The Si-Si bond lengths are about ∼2.33-2.37 Å, and the inner bonds are a little longer than the surface bonds. The Si-H bond lengths are around 1.5 Å. These bond lengths are in good agreement with the experimental values. Moreover, allylamine-capped SiQDs also favor adopting high symmetries, including D2d and S4, and several imaginary frequencies were found in calculations of lower symmetry structures. Both the bond lengths of Si-Si and Si-H are slightly longer than that of hydrogenated Si clusters, which indicates that the allylamine adsorptions cause only small changes in the bonds and geometrical structures of silicon clusters. In excited states, the silicon cores favor being distorted due to the structure relaxation, deviating from high symmetries in ground states. The distortion causes several Si-Si bond length increases, while the surface Si-H bond lengths remain practically unchanged under excitation. With the cluster size increase, the distortion tends decreasing. For instance, in the first excited state of Si10H16, one of Si-Si bonds extends from 2.34 to 2.86 Å. Homologically, for Si29H36 and Si35H36, an obvious increase (about 0.4 Å) is found in one of the Si-Si bonds. However, the difference of the Si-Si bond is only 0.05 Å, between ground-state and excited-state Si59H60. Therefore, it is extrapolated that the structure distortion tends disappearing as the size further increases. Similar to the ground states of SiQDs, the general tendencies of structure distortion of excited states are not affected by the allylamine adsorption. The excited-state structure relaxation still results in distortion in the silicon core rather than in Si-H or Si-allylamine. Therefore, the geometrical structure changes of SiQD cores due to alylamine adsorption are minor. We further analyzed the vibrational spectra of allylaminecapped SiQDs (see Figure 2). For hydrogenated SiQDs, the peaks that appeared, ranging from 2097 to 2153 cm-1, are attributed to the strong Si-H stretching vibration. The Si-H bending mode leads to a very obvious peak at 644 cm-1. In experiments, these two vibrational modes were found at 2085 and 631 cm-1, respectively.29 The peak at 827 cm-1 was attributed to the scissor vibration of the H-Si-H group. The absorption positions of Si-Si bonds were at the side lower than 500 cm-1, with very weak peak intensity. The bonding of allylamine to the surface of the SiQDs was reflected by the peak at 1250 cm-1 for the Si-CH2 stretching vibration. The symmetric and asymmetric vibrations of C-CH2 and C-NH2 molecular fragments led to the absorbance between 2700 and 3600 cm-1. In this work, the IR spectrum of the 24 allylamine molecules adsorbed SiQDs is shown in Figure 2c which is similar to the experimental spectrum,15 except for the Si-H characteristic absorption peaks around 2100 and 650 cm-1. In consideration of the space steric effects, it is impossible for the

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Wang et al. TABLE 1: Binding Energies, HOMO-LUMO Energy Gaps, and Absorption Energies of Single-Allylamine-Capped Si35H36 and Si59H60 on Various Adsorption Positions (Net Mulliken Charges of the Allylamine Are Also Included) adsorption position Si35H36 Si59H60

Figure 1. Optimized structures for the hydrogenated and allylaminecapped SiQDs, where yellow and red balls represent C and O atoms, respectively.

Figure 2. Calculated IR spectra of allylamine and various SiQDs.

allylamine to substitute all surface H atoms on SiQDs, so the absence of vibrational absorption of Si-H bonds in experiments possibly due to the oxidation of a small amount of H atoms that are not allylamine-capped. We also explored the vibrational spectra of allylamine and oxide-passivated SiQDs (in Figure

1 2 3 1 2 3

Ebinding EHOMO-LUMO Eabsorption (eV) (eV) (eV) 2.44 2.43 2.44 2.36 2.44 2.43

4.14 4.15 4.18 3.64 3.64 3.64

4.36 4.36 4.35 3.70 3.72 3.71

net Mulliken charge (au) -0.058 -0.046 -0.047 -0.050 -0.044 -0.045

2d), which are in reasonable agreement with experimental results.15 This supports the notion that the allylamine adsorption decreases the oxidation rate of the SiQD surface. In general, our geometrical and frequency results are found to be in gratifying agreement with recently reported experimental and calculational data. Thus, our computational method (DFTB) is proven to be a sufficiently reasonable and accurate tool to complement experiments. Adsorption Sites. In the experiment, the Si-H surface bond is treated with both a compound containing a CdC bond and a platinum catalyst to produce a variety of surface types through the formation of a Si-C surface bond.15 To understand the allylamine adsorption on the surface of SiQDs, we first study the interaction between allylamine and silicone in different adsorption positions. For example, there are three different adsorptions for the allylamine molecule to locate on the surface of Si35H36 and Si59H60 (denoted by Nos. 1, 2, and 3 in parts c and d of Figure 1) according to topological analyses. The binding energies, the highest-occupied molecular orbital (HOMO)-lowest-unoccupied molecular orbital (LUMO) energy gaps, the absorption energies of the SiQDs, and the net Mulliken charges of the allylamine molecules are tabulated in Table 1. We found that the allylamine carries a negative charge due to its receiving electrons from hydrogen-terminated SiQDs. This can be ascribed to the higher electronegativity of carbon atoms compared to silicon atoms.30 Moreover, the allylamine molecule adsorbed at the No. 1 position receives more electrons than those at the other two positions because there are two hydrogen atoms bonding with the No. 1 Si atom. However, their HOMOLUMO energy gaps and absorption energies show little difference. This indicates that the adsorption positions, especially the single hydrogen adsorption positions, affect the optical properties of hydrogenated SiQDs to a small degree such that they could be ignored in the following study. Optical Properties. While there is only slight site dependence on the allylamine adsorption, the number of allylamine molecules adsorbed on the SiQD surface has a clear effect on the optical characters. Figure 3 shows the absorption energies of SiQDs vs the number of adsorbed allylamine molecules. Clearly, the absorption energies decrease with an increasing number of allylamine molecules. However, this change becomes weak when the cluster size exceeds that of Si35H36. For Si10H16, the adsorption of four allylamine molecules yields nearly a 0.6-eV decrease in absorption energy, while for Si29H36 the adsorption of 12 allylamine molecules causes only a 0.3-eV decrease of absorption energy. For larger SiQDs, such as Si35H36 and Si59H60, the adsorption of allylamine molecules causes only a negligible absorption energy shift. When the number of allylamine molecules increases from 4 to 20 on the Si35H36, the absorption energy changes tend to level off. The decrease nearly stops after adsorbing 20 allylamine molecules. For the Si59, the changes in absorption energy are already saturated at 3.55 eV

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Figure 3. The absorption energies as a function of the number of allylamine molecules on the surface of different size SiQDs.

TABLE 2: HOMO-LUMO Energy Gaps ∆E, the Maximal Absorption and Emission Peak Positions of Hydrogenated and Allylamine-Capped Silicon Nanoclusters (Numbers in Parentheses Denote the Number of Electronic Transition Orbitals) Si 10 29 35 35 35 59 exp15

no. allylamine molecules ∆E (eV) 0 0 0 4 8 0

5.98 4.33 4.31 4.13 4.18 3.66

absorption (nm)

emission (nm)

205.3 (26,27,28f29) 280.8 (74,75,76f77) 283.8 (86,87,88f89) 284.3 (132f137) 296.6 (184f185) 333.5 (146,147,148f149) 320

421.2 (29f23) 404.9 (77f74) 428.6 (89f86) 424.6 (137f128) 461.9 (185f178) 390.3 (149f146) 480

after adsorbing eight or even less allylamine molecules. The results indicate that, in small silicon clusters, the characters of adsorbed allylamine molecule will be more preponderant than those of silicon cores, but in large silicon clusters, the reverse effect could be seen, with the silicon core dominating the general optical properties. In addition, Figure 3 shows that the absorption energies decrease remarkably with the increase in the size of SiQDs due to the quantum confinement effect. From Si10H16 to Si59H60, the absorption energies shift from 6.1 to 3.7 eV. Among them, Si29H36 and Si35H36 show similar optical natures due to their having a similar diameter. The corresponding excited-state calculations were then performed, the detailed results of which are summarized in Table 2. The red shifts of the maximal absorption peaks are caused by the increase in the size of SiQDs, while the shift of emission spectra is inconspicuous. The tendencies of absorption energy changes can also be found in their energy gaps. For instance, the HOMO-LUMO energy gap of Si10H16 is 5.98 eV, while the value decreases to 3.66 eV in Si59H60. Since the electron of hydrogenated SiQDs transfers from HOMO to LUMO in their absorption spectra, the small energy gap leads to a small optical gap, as well as a small amount of electronic transition energy. Thus the absorption peak shows a remarkable red shift as the size of SiQDs increases. We also studied the excited states of allylamine-capped Si35. For the Si35 capped with eight allylamine molecules, its absorption and emission peaks appear at 296.6 and 461.9 nm, respectively, which are close to the experimental values (320 and 480 nm). Furthermore, we can extrapolate from the above discussion that more allylamine adsorption will lead to a smaller red shift of the peaks, showing better agreement with the experiment. Figure 4 shows the calculated absorption and emission spectra of Si35H28(C3H6NH2)8. The peaks were broadened by a Gaussian function with a 3-nm half-width. Since the absorption and emission spectra were all obtained with the same broadening,

Figure 4. Calculated absorption (solid curve) and emission (dash curve) spectra of Si35H28(C3H6NH2)8 (the arrows denote the first excited single state).

their peak height and position are comparable. The absorption and emission spectra include several excited-states, but the former ranges from 250 to 300 nm, while the latter has a wider range from 300 nm to 480 nm. Several strong response peaks in the range of shorter wavelengths correspond to the higher excited states. According to Kasha’s rule, optical emissions will always occur from the lowest state. Thus, more attention was paid to the absorption and emission peaks of the first excited single state (denoted by arrows in Figure 4). It is found that the emission strength is weaker than that of absorption, and the emission peak exhibits a strong red-shift because of the relaxation under excitation. Since absorption and emission spectra show a substantial PL quantum yield in the visible region, it is possible to use allylamine-capped SiQDs as a candidate of biological chromophores. Our analysis indicates that the most crucial factor for tuning the optical properties is the size of allylamine-capped SiQDs, essentially the size of silicon cores. In contrast, the adsorption of different numbers of allylamine molecules takes only a little effect on the optical properties of SiQDs, especially for the large SiQDs. Electronic Properties. Additionally, we studied the electronic properties to further understand the interesting optical behaviors of SiQDs. For hydrogenated SiQDs, the HOMO of ground state is triply degenerated due to the Td symmetry of the structure. The LUMO is a holosymmetry delocalized orbital belonging to an A1 symmetry. The electron transfer from HOMO to LUMO mainly determines the absorption spectra. On the other hand, in excited state, the Td symmetry of the clusters is broken down under excitation due to the significant structure relaxation. The orbital energy level split takes place for the degenerate orbitals resulting in many orbitals with similar energies. For instance, the triply degenerated HOMO of the ground state splits up and form three orbitals denoted by HOMO-n (n ) 0, 1, or 2). The PL comes from the released energy of the electron transition between the LUMO and one of the HOMO-n. Figure 5a shows the general luminescent process of the Si35H36. Compared to the LUMO in the ground state, the orbital energy of LUMO in excited-state is reduced by 1.58 eV, and at the same time, the delocalized orbital becomes relatively localized. This change can also be found in hydrogenated SiQDs of other sizes but becomes reduced in large SiQDs for a relatively weak geometrical relaxation effect. Hence, in general, the absorption energy is larger than the emission energy, and this difference will be reduced in large SiQDs (see Table 2) due to the increased structural rigidity. The electronic properties of allylamine-capped SiQDs are more interesting than those of uncapped SiQDs. Figure 5b shows

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Figure 5. MO diagram of ground-state and excited-state Si35H36 and Si35H32(C3H6NH2)4.

the orbital energy level and the PL process of Si35H32(C3H6NH2)4. The adsorbed allylamine results in some orbitals with energies around Fermi energy and narrows the energy gap, leading to increased complex features in electronic transition of allylamine-capped SiQDs. The electronic excitation takes place at inner electron (absorption, orbital No. 132 f No. 137; emission, orbital No. 137 f No. 128) but not between HOMO (No. 136) and LUMO (No. 137). Comparing the orbital properties, No. 132 orbital of Si35H32(C3H6NH2)4 is analogical to the HOMO of Si35H36 in ground state; No. 137 orbital in Si35H32(C3H6NH2)4 corresponds to the LUMO in Si35H36. In excited state, the energy of orbital LUMO (No. 137) is reduced as a result of geometrical relaxation. This indicates that most of the tendencies of allylamine-capped and uncapped SiQDs are similar. The allylamine adsorption does not affect the general natures of the optical properties of hydrogenated SiQDs. To further understand the analogy of the PL process, we compare the orbital schematic diagram of a SiQD (Si35H36) with those after allylamine adsorption (Si35H16(C3H6NH2)20 and Si35H12(C3H6NH2)24) (see Figure 6). For absorption spectra, the electrons transit from the orbitals in the middle column to the orbitals in the right column. It is found that the electron transition orbitals of Si35H36 and Si35H16(C3H6NH2)20, especially the part of silicon core (Si35), are similar, showing that the contributions of allylamine molecules in these orbitals are quite small. The observation is further confirmed using other allylamine-capped SiQDs such as Si35H12(C3H6NH2)24 for which their electron transition orbitals are generally similar to that of uncapped SiQDs, though the signs (() of electron clouds (e.g., denoted by red and blue in the Figure 6) are reversed. Thus, we conclude

that the allylamine adsorption does not affect the electron transition. This can also explain why the allylamine molecule only affects a little on the optical features of SiQDs. In addition, our results show that the charge transfer between the SiQD core and the allylamine is not sensitive to the size of SiQDs. For example, similar net Mulliken charges in each allylamine molecule were found in different SiQDs with four adsorbed allylamine molecules (-0.047 (Si10H16), -0.047 (Si35H36), and -0.047 (Si59H60)). For an increased number of allylamine molecules adsorbed on the SiQD, only a little increase of charge transfer was observed. In the case of Si35H36, when the number of allylamine molecules increases from 4 to 24, the net Mulliken charge of each allylamine molecule increases slightly from -0.047 to -0.061, and tend to saturate at around -0.06. Similar tendencies have also been found in the excited states of SiQDs, further supporting the observation that the allylamine adsorption could only affect slightly the optical transition of SiQDs. Additional supports to our conclusion were sought from the analysis of the electronegativity of the elements involved. As is well-known, the electronegativity of C (2.55) is smaller than those of N (3.04) and O (3.44) and is closer to that of the Si (1.90).30 Therefore, the charge transfer in Si-CR bond must be smaller than that in Si-NR bond or Si-OR bond. For example, in Si35H35(NH2) and Si35H35(OH), the adsorption groups carry negative charge -0.130 (-NH2) and -0.175 (-OH), respectively. Both of them obtain more negative charge than that of the allylamine molecule. Therefore, the formation of Si-C surface bond could result in a slight change in the electronic and optical characters of the SiQDs. As a result, the

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Figure 6. Schematic diagram for the orbitals of silicon quantum dots with different passivations. (For absorption spectra, the electrons transit from the orbitals in the middle column to the orbitals in the right column.)

allylamine molecule can offer excellent protection to the SiQDs. Reboredo et al.31 reported that alkyl passivation weakly affects optical gaps of SiQDs, whereas Puzder et al.3 found that the double bond oxygen at the surface of SiQDs substantially decreases the optical gaps of SiQDs. These reports are also supportive to our findings here that the electronegativity is an important factor to be considered in choosing the appropriate group to modify the surface of SiQDs. IV. Conclusion The excited-state properties of hydrogenated and allylaminecapped SiQDs, ranging from Si10 to Si59, have been studied systematically using the DFTB method. The obtained relative geometrical, energetic, electronic, and optical properties support the following several conclusions: (i) The allylamine molecule prefers to be adsorbed with symmetrical distribution on the surfaces of SiQDs such that the allylamine-capped SiQDs adopt high-symmetry structures, similar to those of the hydrogenated SiQDs. (ii) The dot size dominates the PL properties of SiQDs because of the crucial quantum confinement effect. (iii) The allylamine molecule adsorption only causes a small red shift of the emission spectra. Moreover, in large SiQDs, the allylamine effect is negligible. Finally, our study verifies that the allylamine is a good protecting molecule of SiQDs, as it reduces the surface oxidation rate and maintains optical properties in the visible region. Acknowledgment. The work described in this paper is supported by grants from the Research Grants Council of Hong Kong SAR [Project Nos. CityU 103305 and CityU 3/04C] and the Major State Research Development Program of China (Grant No. 2004CB719903).

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